River Cha ne1 Pattern 

nderin 

and Str 

By LUNA €3. LEOPOLD and M. GORDON WOLMAN 

PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS 

GEOLOGICAL SURVEY PROFESSIONAL PAPER 252--14 

UNITED STATES GOVI'RNM15N'T PRINTING OFFICE, WASHINGTON : 1957 
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEWART L. UDALL, Secretary 

GEOLOGICAL SURVEY 

Thomas B. Nolan, Director 

REPRINTED 1963 

For sale by the Superintendent of Documents, U.S. Government Printing Office 

Washington 25, D.C. - Price 50 cents (paper cover) 
CONTENTS 

Symbols 

Abstract _____.-_____----.~~-~~--.-----....------~-- 

Introduction and acknowledgmeiits- -. -.. . . . . ._. - - - - - -. 

The braided river__ -. -. __ .. __ -~ - - - - -. . . -. __ .__ - ___. 

Introduct,ion .._.__ __ ._ - ~ ~. . - - - __ -. -. ___ - - - __ - 

Horse Creek: t,ype locality of the braided stream-.-_ 

Stages in the development of a braid __.___._______ 

Changes associated with channel divisiou.. . . . - - - - 

Flume experiments .___ - ______ ___ ___ ~- - - __ -. . 

Divided and undivided reaches in the flume and 

in natural rivers ._.._._____._____._________ 

Summary: the braided river-.- ~ - -. - -. .. . _. __ -. __ 

Straight channels ....... -~ ._ __ - - __. . - - -. . - ~. . . - - ~- -. 

The wandering thalweg-_ ~. -. .- - -. . ~. -. . -~ - ~ - -. -. 

Pools and riffles.. . ._ ~ ~ ~ ~ ~ -. -. -. . ~ ~ - - - ~ 

Summary: straight chanuels .... . -~ ~ ~ __. . -. . -. 

The continuum of channels of differerit patterns.. . . -~ - 

Summary: cont,inuum of channel patterns. ._ - - - - - - - 

The nature of channel adjustment to independent controls. 

Development3 of river width_._ - -. - - __.__ ___ - 

Channel roughness and resistance-_ - -. -. . - - - - -. 

Resistance coritrollcd by size of bed material -... 

Resistancc rclated to bed configuration. _. __. 

Sediment transport, shear, and resistance.. ..___ 

Response of slope to changes of load in the flumePage 

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IV The nature of channel adjustment to independcii t, conObservations of adjustments in natural channels.. . . 

Summary and interpretatioii--- ___ - __ - - - - - - - - -. -. . 

Application of observatioiis on channel adjustment to thc 

problem of channel pattern _.... - ____ __ __ -. - -. . __ -. 

References cited _...___ __.___ ~ __________ .__. .___ ~__. 

Appendix___________.____________________-----..--. 

A. Analyses of sand sizes used in flume experiments 

and fed into flume-river .____._______

B. Data on size characteristics of sand on channel 

bed and on bars in flume-river.__ __ ___~ - ~ -. -. - 

C. Summary of data on flume experiments at California Institute of Technology .__._ -- - - ~ ~. . -. - 

D. Comparison of hydraulic characteristics of uiidivided and divided reaches of braided streams. 

E. Data on wavelength of meanders, bankfull discharge, and bankfull width ..___________

. 

F. Data on estimated bankfull discharge at various 

stream cross sections.. - - - - - - - - - - - - - - - - - - - - - - 

G. Distribution of bed-particle size in various stream 

cross sections ..._____._______ ~ _____..._._._ 

H. Values of hydraulic factors at various stream cross 

sections.. . . ~ ~ ~ -. - -. - - ~. . ~ -. - - - - -. . . . . -. . . - 

Index..__.-..- __._____..________

trols-Con tinued 

ILLUSTRATIONS 

FIGURE 28. Maps of Horse Creek and the Green River 

near Daniel, Wyo., showing dividing and 

rejoining of channels in 1877 and 1942 ...- 

29. Plan and profile of Horse Creek near Daniel, 

30. Central gravel bar in Horse Creek ....-_._ 

31. View of downst,ream end of central gravel 

bar in Horse Creek___-._- ___._.__.___ ~ 

32. Cross sections of braided reach, Horse Creek. 

33. View of initial channel in flume ._______._ 

34. Sketches and cross sections showing developmerit of braid in flume-river ..._..__._.. 

35. Braided channel in flume (runs 6-8) - - - - - 

36. Island formed in braided channcl in flume 

(run 30)_.._.__.~~_______~~___________ 

37. Progressive development of baa in flumeriver 

38. Measured and diagrammatic. profiles of 

flume-river. -. - - - - - - - - -. - - - - - - - - - - - - - - - 

39. Map of braided reach in the Green River 

near Daniel, Wyo- - ___ ___ ________ - ___ - 

40. Plan and profile of the New Fork River 

near Pinedale, Wyo- _____ -. .___. - - -. __ 

41. Plan and profile of Valley Creek near Downington, Pa _______________._...________ 

42. Plan and profile of bhe Middle River near 

Staunton, Va--_-_-._________________, 

WYO.__~_______.____________________ 

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FIGURE 43. Plan and profile of the Pop0 Agie River near 

Hudson, Wyo._---____________________ 

44. Profiles of three rivers of different channel 

paterns____-_________________________ 

45. Wavelength of meanders and of riffles in relation to bankfull discharge and channel 

width_________________________-______ 

46. Relation of channel slope to bankfull discharge in distinguishing braided, meandering, and straight channels ____ ___ -. - ___ - 

47. Plan and profile of Cottonwood Creek near 

Daniel, Wyo._ _____ ____ __ __ ______. . . - - 

45. View of braided reach of Cottonwood Creek49. Relation of relative smoothness to resistance, 

Brandywine Creek, Pa _________._

~___ 

50. Relation of relative smoothness to resistance, 

all data_______-------__---------.^^.- 

51. View of dunes in flume-river _________

52. Vertical profiles of velocity in flume-river. - 

53. View of initial channel in flume (run 29) - -. - 

54. View of bed of flume-river with no load after 

l)/s hours.______._______-_------------- 

55. View of bed of flume-river with no load after 

21 hours- ._________ __________ _____--__ 

56. View of bed of flume-river with load being 

introduced at r6te of 24 grams per minute57. View of bed of flume-river with load being 

introduced at rate of 55 grams per minute111 

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IV CONTENTS 

TABLES 

Page 

TABLE I. Comparison of divided and undivided reaches of Page I TABLE 5.Effect of change in load on stream slope, other 

braided streams, in natural rivers and flume- I conditions being constant ______-___ - __ ____ 70 

river .___________________________________ 50 

2. Comparison of channel factors in two runs of 

flume for which discharge was equal_------- 64 

3. Comparison of reaches of channel before and 

afler passage of sediment front .___-________ 67 

4. Relation of width of moving band of sediment 

to rate of load introduced _________ _______ 68 

6. Examples from river data of adjustments in 

depth, velocity, and slope to changes in 

suspended load at constant discharge and 

width-..- ._____.. ..__. ~ ________.___7Q 

I 

SYMBOLS 

area of cross section of flowing water 

drainage area 

exponent in relation of width to discharge when 

sediment concentralion, in pounds of sediment 

mean depth, defined as ratio of cross-sectional 

size of sediment particle 

median size of sediment particle; subscripts 25, 

75, or 84 refer to percent of sample finer than 

specified size 

exponent in relation of depth to discharge when 

dcx:QJ 

Darcy-W eisbach resis tance factor 

acceleration due to gravity 

numerical coefficient having a specific but unWKQb 

per pound of clear water 

area to width 

determined value 

E 

M 

P 

R 

Q 

S 

80 

T 

V* 

2) 

W 

Y 

P 

i-0 

sediment load, in units of weight per unit of tho 

exponent in relation of velocity to discharge when 

wetted perimeter, in feet 

water discharge, in cubic feet per second (cfs) 

hydraulic radius, in feet 

slope of water surface 

sorting coefficient of a granular mixture 

temperature, in degrees Fahrenheit 

shear velocity 

mean velocity defined as quotient of discharge 

width 

specific weight of water, or 62.4 pounds per cubic 

foot 

mass density of water 

intensity of boundary shear 

2) cx &" 

divided by cross-sectional area 
PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS 

RIVER CHANNEL PATTERNS: B AIDED, MEANDERING, AND S’I’fPAIGHT 

By LUNA B. LEOPQLD and M. GORDON W-OLMAN 

ABSTRACT 

Channel pattern is used to describe the plan view of a reach of 

river as seen from an airplane, and includes meandering, braiding, 

or relatively straight channels. 

Natural channels characteristically exhibit alternating pools or 

deep reaches and riffles or shallow reaches, regardless of the type 

of pattern. The length of the pool or distance between riffles in 

a straight channel equals the straight line distance between 

successive points of inflection in the wave pattern of a meandering river of the same width. The points of inflection are also 

shallow points and correspond to riffles in the straight channel. 

This distance, which is half the wavelength of the meander, 

varies approximately as a linear function of channel width. In 

the data we analysed the meander wavelength, or twice the 

distance between successive riffles, is from 7 to 12 times the 

channel width. It is concluded that the mechanics which may 

lead to meandering operate in straight channels. 

River braiding is characterized by channel division around 

alluvial islands. The growth of an island begins as the deposition 

of a central bar which results from sorting and deposition of the 

coarser fractions of the load which locally cannot be transported. 

The bar grows downstream and in height by continued deposition 

on its surface, forcing the water into the flanking channels, which, 

to carry the flow, deepen and cut laterally into the original banks. 

Such deepening locally lowers the water surface and the central 

bar emerges as an island which becomes stabilized by vegetation. 

Braiding was observed in a small river in a laboratory. 

Measurements of the adjustments of velocity, depth, width, and 

slope associated with island development lead to the conclusion 

that braiding is one of the many patterns which can maintain 

quasi-equilibrium among discharge, load, and transporting 

ability. Braiding does not necessarily indicate an excess of total 

load. 

Channel cross section and pattern are ultimately controlled 

by the discharge and load provided by the drainage basin. It is 

important, therefore, to develop a picture of how the several 

variables involved in channel shape interact to result in observed 

channel characteristics. Such a rationale is summarized as 

Channel width appears to be primarily a function of nearbankfull discharge, in conjunction with the inherent resistance of 

bed and bank to scour. Excessive width increases the shear on 

the bed at the expense of that on the bank and the reverse is true 

for very narrow widths. Because at high stages width adjustment can take place rapidly and with the evacuation or deposition of relatively small volumes of debris, achievement of a 

,relatively stable width at high flow is a primary adjustment to 

which the further interadjustments between depth, velocity, 

slope, and roughness tend to accommodate. 

’ follows: 

, 

Channel roughness, to the extent that it is determined by 

particle size, is an independent factor related to the drainage 

basin rather than to the channel. Roughness in streams carrying 

fine material, however, is also a function of the dunes or ot,her 

characteristics of bed configuration. Where roughness is 

independently determined as well as discharge and load, these 

studies indicate that a particular slope is associated with the 

roughness. At the width determined by the discharge, velocity 

and depth must be adjusted to satisfy quasi-equilibrium in 

accord with the particular slope. But if roughness also is variable, 

depending on the transitory configuration of the bed, then a 

number of combinations of velocity, depth, and slope will satisfy 

equilibrium. 

An increase in load at constant discharge, width, and caliber 

of load tends to be associated with an increasing slope if the 

roughness (dune or bed configuration) changes with the load. 

In the laboratory river an increase of load at constant discharge, 

width, and caliber resulted in progressive aggradation of long 

reaches of channel at constant slope. 

The adjustments of several variables tending toward the 

establishment of quasi-equilibrium in river channels lead to the 

different channel patternp observed in nature. For example, 

the data indicate that at a gi‘ven discharge, meanders occur at 

smaller values of slope than do’ braids. Further, at the same 

slope braided channels are associated with higher bankfull discharges than are meanders. An additional evample is provided 

by the division of discharge ar?pnd islands in braided rivers 

which produces numerous small channels. The changes in slope, 

roughness, and channel shape which accompany this division 

are in accord with quasi-equilibrium adjustments observed in 

the comparison of large and small rivers. 

INTRODUCTION AND ACKNOWLEDGMENTS 

From the consistency with which rivers of all sizes 

increase in size downstream, it can be inferred that the 

physical laws governing ‘the‘ formation of the channel 

of a great river are the same as those operating in a 

small one. One step toward understanding the mechanisms by which these laws operate in a river is to 

describe many rivers of various kinds. 

This study is primarily concerned with channel 

pattern; that is, with the plan view of a channel as 

seen from an airplane. In such a discussion some 

consideration must also be given to channel shape. 

Shape, as we shall use it, refers to the shape of the river 

39 
PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS 

cross section and the changes in shape which are 

observed as one proceeds along the stream, both 

headward to the ultimate rills and downstream to the 

master rivers. Because the shape of the cross section 

of flowing water varies, depending upon whether the 

river is in flood or flowing at low flow, shape must take 

into consideration the characteristics of river action 

at various stages of flow. 

The channel pattern refers to limited reaches of the 

river that can be defined as straight, sinuous, meandering, or braided. Channel patterns do not fall easily 

into well-defined categories for, as will be discussed, 

there is a gradual merging of one pattern into another. 

The difference between a sinuous course and a meandering one is a matter of degree and a question of how 

symmetrical are the successive bends. Similarly, 

there is a gradation between the occurrence of scattered 

islands and a truly braided pattern. 

The interrelationship between channels of different 

patterns is the subject of this study. Because neither 

braided channels nor straight channels have received 

the attention in the literature that meanders have, our 

observations of these patterns precede the discussion 

of the interrelations between channels of different 

patterns. 

The flume experiments described were conducted in 

the Sedimentation Laboratory of the California Institute of Technology during the time when the senior 

author was a visiting professor in the Division of Geological Sciences. For this opportunity, as well as for 

advice and encouragement, thanks are extended to Dr. 

Robert P. Sharp. The Division of Geological Sciences 

also financed the laboratory phase. 

Dr. Vito A. Vanoni of the institute not only allowed 

the use of his laboratory for the work but generously 

offered his counsel. Assembly of the laboratory equipment would not have been possible without the expert 

craftsmanship of Elton F. Daly of the Hydrodynamics 

Laboratory of the institute. 

An early draft of the manuscript was rend by a number of friends in and out of the Geological Survey. For 

help at various stages of the work particular thanks are 

extended to Norman H. Brooks, Ronald Shreve, and 

John P. Miller. 

For her careful work in compiling and computing 

data for this, as well as previous studies, we gratefully 

acknowledge the assistance of Ethel W. Coffay of the 

Geological Survey. 

THE BRAIDED RIVER 

INTRODUCTION 

In 1877 when field parties of the Hayden Survey were 

making the geologic reconnaissance of west-central 

Wyoming, Peale (1879) was impressed by the manner in 

which tributaries joined the upper Green River. In 

streams which do not exhibit a braided pattern, a 

tributary usually discharges all of its flow through a 

single channel into the channel of the master stream. 

Peale observed that, in contrast, Horse Creek “flows 

out into a broad valley in which it is side by side with 

the Green, and finally, to use an anatomical term which 

exactly describes it, joins the latter by anastomosis. 

There are at least five islands formed by the two streams 

in the lower end of the broad valley” (p. 528). 

The term “anastomosis” was apparently first applied 

to streams by Jackson (1834). Because it has occasionally been misapplied in the geomorphic literature, it is 

desirable here to recall its definition-the union of one 

vessel with another-or the rejoining of different 

branches which have arisen from a common trunk, so as 

to form a network. Successive division and rejoining 

with accompanying islands is the important charrtcteristic denoted by the synonymous terms, braided or 

anastomosing stream. 

A braided pattern probably brings to the minds of 

many the concept of an aggrading stream. Not until 

the work of Rubey (1952) was the problem of channel 

division and island formation discussed as one of the 

possible equilibrium conditions of a channel. The 

examples which are discussed here allow some elaboration of Rubey’s idea and perhaps a somewhat more 

complete picture of the manner in which the channel 

division around islands proceeds. 

HORSE CREEK: TYPE LOCfUJTY OF THE BRAIDED 

STREAM 

It is appropriate to use as the first example of a typical 

braided river the same stream to which the term 

“anastomosing’, was early applied. There has been 

but little change in the stream pattern between 1877 

and 1942 when the modern topographic map was 

published. Figure 28 shows the area near Daniel, 

Wyo., as depicted by Peale and as shown on a modern 

map. The islands shown by Peale still exist with but 

minor changes in form. 

Within a few miles of the point where Peale viewed 

the anastomosing reach of Horse Creek, 5 miles northwest of Daniel, Wyo., we mapped a reach of the river 

which includes a gaging station of the Geological Survey 

(fig. 29). At this place Horse Creek has a drainage 

area of 124 square miles and a mean discharge of about 

65 cfs derived primarily from the headwater mountain 

area in the Wyoming Range. Though not so well 

developed here as downstream, the braided pattern is 

apparent. The reach near the gaging station was 

chosen for study because the channel pattern is typical 

and because the discharge data obtained at the station 
RIVER CHANNEL PATTERNS 41 

sum of these widths is 20 to 30 percent greater than 

the 50-foot width of the undivided reach. In the 

downstream part of the left channel where the central 

bar of gravel has been deposited, the width is only 

slightly greater than in the rest of the left channel 

where there is no central bar. 

Opposite the gravel island, and on the right side of 

the little there is a slough which is alined with 

a grassed depression. During flood flow this slough 

and the depression water* The configuration of the slough and depression and their position in relation to the active right-hand channel indicate 

that they Once joined as a cont~uous active 

which has subsequently been blocked by deposition. 

In its active stage this old channel was separated from 

the present right-hand channel by an island, similar in 

can be used to analyse the flow characteristics of the 

braided channel. 

In figure 29 it can be seen that the reach at the gaging 

station has only a single channel, but withih a few 

hundred feet downstream the flow divides and then again 

joins into a single channel. The division begins as a low 

gravel bar (marked C) near the left bank which grades 

downstream into a central ridge meeting the tip of a 

gravel island (marked D) supporting a willow thicket. 

In the left channel about 200 feet downstream from the 

upper tip of the island, a linear gravel bar (marked 

E in fig. 29 and pictured in fig. 30) extends for nearly 

250 feet down the center of the channel. The bar ends 

near the junction of the main channels. 

The two channels divided by the willow-covered 

island are about equal in width, 30 to 40 feet. The 

vegetation had sprouted on the formerly bare gravel 

surface as can be seen in figure 31. On 425 square feet 

of area there were 80 individual plants, or one on every 

5 square feet approximately. 

Number 

Species of plants 

20 

17 

12 

lo 

7 

3 

2 

The plants were: 

Red top (Agrostis sp.) ------------ -- ------- --- ---- - 

Sweet Clover (Melilotus Sp.) _______________c__-_____ 

Bluestem (Agropyron Smithii) ______-_ ._____-_------ 

Foxtail (Hordeum sp.) - - - - - - - ___ - - - - __ - __ - __ - - __ Dandelion (Taraxacum sp.) - _ - - - - - - - - - - - - - 

Shepherd purse (Cruciferae) ________________________ 4 

Carrot weed (Umbelliferae) - - - - - - - - - - - - - - - - - - - - - - - - 

Mint (Labiatae) __________________________________ 2 

Two cross sections of the braided reach on Horse 

The valley bottom is 

Timothy (Phleum sP.)-- - - - - - - - - - - - - - - - - - - - - - - - - - - - 

Creek are shown on figure 32. 

character to the gravel island now smarating the two 

active channels. 

The linear bar in the left channel is nearly bare of 

vegetation except at its most headwater tip where 

young willows have become established. This can be 

seen in figure 30, which looks downstream along the 

central gravel bar. The man stands by the young 

willow at the headwater tip of the linear bar. Two 

other bits of now growth on the bar can be seen 20 feet 

and 70 feet farther downstream. 

The upstream end of the bar is gently rounded in 

cross section and lobate in form like a beaver tail. 

Downstream the bar becomes pointed, flat on tog, and 

trapezoidal in cross section (figure 31). 

When we first studied this linear bar there was no 

vegetation on the lower end. One year later some 

11 

BIG PINEY OUAORANGLE 

30.MINUTE SERIES 

I 

11O"lY 1942 1 

30' 

FIGURE 28. Maps of lower Horse Creek and the Green River near Daniel, Wyo.. comparing a sketch made by Peale (1879, pl. L) in 1877 and a Geological Survey 

map of 1942. The islands (marked A) shown by Peale existed in 1942 with but minor changes in form. Note the successive dividing and rejoining of river channels. 
I/ , 

JI 

I 

i 

I 

1 

I 

I 

WnlWa AMWMllBMV :1334 NI ‘NOllVA313 
.... ",",",it "'" ----......... .. _-__ 

--....... _ 'b ........ "_"_" -,,-

bounded by IW., low lo:tT'1«S, una 5 1..,\ ."d anothe. 

7 r .... t .1>0". low .. ·.lCl' Aurfaco:o. Wilhin the <'(mlln;", 1>&",,- of lhe 5-1001 t.c.....,. the gnI"el ",I."d ."d the 

adj..,~nt gn.,·~1 fin conteining the ebandon...! chnn~l 

lio e~ Ih ~ ... me ~le"uion. 'rhe new gruel b ... gcne..,ll,,· 

;" IIOrno"'''e, lower th ... , the le,·c1 of tho adj&eent iol .. "d, 

thougl, a~ a poi,,~ ebou~ hAl! , .... y dow" the l~ngth of 

the bar the Hat UI'P'" auri...,.. of Lbe bat it a~ the...."., 

elevatIOn ... the auriace 01 the island 

.TAoa [If TIIIt DKVELOPKIlI'T OP A .~ 

Th_ o~ntioruo auggeot " eequence of e~enU in 

the development of a bn.,dN. .-.,b. In an originally 

43 

......... -00. ___ .. __ ........... _ ................ 

.ingle Or undi~idNl ~hann~l, a .h"rt, lubmerged ...,nl...:l 

bar iA d~poAiled during = high Oow_ The head of lh~ 

!Ie"" 1P""'~1 bar iA romp<:HlC(i of the eo ........ fraction of the 

hed load ,,·hich iA mo,-,nll down the ~enter of Ihe d •• nne] 

bed. n"".U5C of lOme local condition no~ all the COarse 

particles Me traMpOlled IhrouKh thj~ particular re&<:h 

."d lOme &«umulale in llta ctn!eT of the .1I ... nnel. 

),1011 of the "",.Jle' parlidOi mo .... O,tt. and pMt lhe 

,,,,,ip;tnl hv, but part of the lintr frac,ion iI t .... pped 

by the COOU'Wr mattri,l OUld 10 dt~tedt Though 

th" dtptb is gradually I'fdo.>efd, vtiocily o,'er I~ 

P'O"';"( bar 1t",b 10 ... main un<hminisb...i or ,,"en '" 

'''<nUl' 10 thaI .ome particl. mo~i"l! along the 

......... ,_ero._ .. __ .. H .... ~ .... __ w ... , ...... __ ............ 1 
44 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS 

bar near the center of the channel roll along the length 

of the new bar and are deposited beyond the !ower end 

where a marked increase in depth is associated with a 

decrease in velocity. Thus the bar grows by successive 

addition at its downstream end, and presumably by 

some addition along the margins. The downstream 

growth is suggested by the fact that willows became 

established at the upstream tip while the downstream 

portions were still bare. A similar gradation in age of 

vegetation exists in many other islands studied. 

The growth of the gravel bar at first does not affect 

the width of the stream, but when the bar gets large 

enough, the channels along its sides are insufficient 

in width to remain stable. Widening then occurs 

by trimming the edges of the central bar and by cutting 

laterally against the original sides of the channel 

until a stable width has been attained. At the same 

time, some deepening of the flanking channels may 

occnr and the bar emerges as an island. The bar 

gradually becomes stabilized by vegetation. At some 

stage lateral cutting against the bar to provide increased channel width becomes just as difficult as 

against the banks of the original channel, and so the 

bar is not eliminated. The hydraulic properties of the 

channel during this process of island formation will be 

discussed in a later section. 

After the island has been formed, the new channels 

in the divided reach may become subdivided in the 

same manner. As successive division occurs, the 

amount of water carried by an individual channel 

tends to diminish so that in some of these, vegetation 

prevents further erosion and, by screening action, 

promotes deposition. 

The Horse Creek example demonstrates all of these 

features. The new gravel bar deposited in the left 

channel occupies the center of a channel not yet 

widened by stream action. The sequence of age of 

vegetation shows that the bar was extended downstream with time, and presumably was built in 2 or 

3 years, for at the time the lower part of the bar was 

bare, the willows at the upstream tip were not more than 

2 years old. 

The gravel island separating the two main channels 

is considerably wider than the new gravel bar. The 

right channel is separated from the abandoned channel 

by a former island which also was wider than the new 

bar. When a central linear gravel bar is deposited, 

the bar may continue to increase in width, forcing the 

channels farther apart. One reason for this lateral 

cutting into the original banks can be seen by the 

direction of the flow at the tip of the gravel island. 

The low bar (marked C in fig. 29) just below the 

cable has built downstream until it actually joins the 

upstream tip of the much older gravel island (marked 

D). At low flow the water which gets into the left 

channel pours over the downstream tip of the low bar 

in a direction nearly perpendicular to the general 

stream course as indicated by the riffle symbols between 

the letters C and D in figure 29. 

At high discharge the flow impinges against the 

left bank and subsequently produces a sharp bend in 

tha streamlines to the right as they become alined 

again with the left channel. Thus the low bar and 

the upper tip of the gravel island force the flow into a 

reverse curve or S-shaped path. As a consequence 

the left bank would tend to erode where the flow 

impinged against it, while the inside of this curve 

would be a zone of deposition which would blunt or 

widen the upstream tip of the gravel island. It is 

reasoned that the widening of an initial linear bar is 

probably due mostly to the deposition on the inside 

of bends that results from obstruction by the bar. 

The gravel island is interpreted as a stabilized and 

enlarged bar which had its origin in a manner typified 

by the new bar. The gravel in the bar and island are 

similar. The island has a thin layer of silt covering the 

surface of the underlying gravel; it is believed that 

during overbank flow, vegetation stopped the fine 

material and caused it to be deposited. Coarse material 

would ordinarily not be carried over the surface of the 

vegetated island for such material moves primarily in 

the swifter water of the established channels. 

The initial vegetation which sprouts on a new gravel 

bar begins the screening process and the consequent 

deposition of thin patches of silt or fine sand promotes 

the stand of vegetation. Screening of fine material and 

the improvement of the stand of vegetation by altering 

the texture of the surface layer are reciprocal and 

perpetuating. 

CHANGES ASSOCIATED WITH CHANNEL DIVISION 

FLUME EXPERIMENTS 

Experimental work in a flume at California Institute 

of Technology allowed us to test the hypothesis of bar 

deposition just outlined. The observations made in the 

laboratory provide some insight into not only the 

sequence of events leading to braiding but also into the 

hydraulic relations between the divided and undivided 

reaches of channel. First, the progressive development 

of braid? in the flume will be discussed and compared 

with field examples. Second, the interrelations of 

hydraulic facLors in both the laboratory and natural 

rivers will be analyzed. 

The 60-foot flume had a width of about 3 feet and 

was filled to a dcpth of about 5 inches with a poorly 

sorted medium sand (identical to run 1, app. A). 

Initial channels of various shapes and sizes were 

molded by means of a template mounted on a moving 
IU\"ER CHASS"!. PATT'ERSS 

, ..... -, __ .. _ ..... _ ... " ... _.~r ... _ 

r.rr'Aj(C', 0,," of lire 

"'-

II,il,.! ,·Ira",,"I~ ig pi,·lu ....... r in 

hKUr(' la, The l ... v~lil\jl r.m.1{<' .111<1 ... rriffi • f'Oim 

jl:ll«' for mtlUurU'jI: ~Ie",'ion 10 .11 ..... u ...... of 0.001 

1001 ,· .... ,ic.n.,· .• nd O.OO~ foot horizon,.U.", Th~ 1Ikr~ 

of II .. AuIII<' " ... adjl16l ... 1 by .... ' of j..-ks .. hi~h .upportf'(\ il •• nd $loP<" 01 0.01 ... ~,.., poAibl.· Tl,~ 

110"''''10: .. ·.,~r ilS<'lf .I.~ .... I .h~ inilial ~h.nnel ..... ,ion 

.nd 1I0P/'. 

The waler .uppl~· ws' ,,«i",ulaled from a "IO"I!:" 

• "'''p from whid, il "'"" l'''nll .... 1 10 "" overhMd Iftnk 

('(1"il'~1 ,,'i,h a ",eir ,h., pennilt\'d alll' d~t('(! ,hI--

.ha'lle '0 J:w, d ... "" a, ro".'ara he.d, Thp ~.~"""" w.'~. 

not dl'll"'" .hrough Ib~ .. i,...ulahllg .~.,.tcm AO"'rd o,·t. 

• hf w~i •• nd •• :u ,..,tun, ... 1 10 Ihp lump. Tb~ dis-I.al'l(f' 

imo Ih~ Hump ~ .. tem ..... m .... ul'l'd b~·. "emuri ~I ... , 

From Ih~ m.t~ .b. ,,'otft 80,,·....r i",o a 6-in.-l, pipe 

"'hirh 1 ... 1 10 a .,ill;"1!" """in II Ih. UI>P<'t ...,d or th. 

lI"OIt, .,,01 Ih~nee Ihrough a hOIl,·.,·romb fot "'IIOO.h;,,(t' 

out Ihe lurbulen.,... A l.foo. l~nll"lh of lIo"".o,dal 

elra",,"1 ro"glrurlw 01 wood 10,,,,,,,1 • he tr."$,tiu" fro", 

Ih~ .. iIling pool.o • Ire all""ial ~ha,,,,"1 ro"strueted ",it h 

Ihp templ.tp illlhe .. ",I bl'<.I. Diil<"ho~ ,,,,,,,I "'e,,, ill 

th~ I'llnKe or O.OI-o.tO d. 

At IhP d_MI"",m .n.1 of II .... nd d,annpl ..... a 

'l'llpuoid.1 ... tir. the ~Ie ... ,ion of .. hich " ... k~pt 

approximat~ly l~,·" "'illo llo~ .. "d b..d of th~ It~.m. 

1~1o ... Ih~ Il'llpt'ZOidal "'~ir .. 'II • __ ill;",; pool ... heno II .. 

.. nd ..,ulw out, and from ,,·hid, llo~ "'.,,,, " ... oItim'ned 

oft' and ""un'M to lhe .""'p furnishing tI,. "'al~r 

lupply. 

s...li",~nl ... 11 f..r illlo ,h. "l",'~m i" Ih~ {o"n 01 dry 

.. nd. From an ov.rhud hopP/'r.1 .he UPp<'l" enrl of 

Ih~ tlume, Ihe M"d wu rarri"!l OUI on • l!Jl}all en<ll_ 

bIolt a"d dropped into Ih~ "o"'illl{ .... ter in th. Ihort 

"'00<1.'11 Aum. immw'.'tly UJll!ltrPlm from Ihe .. ".I 

'ha,,,,~1. The ... te of .. nd r.....LIIlI{ ..... romroll<'<l by • 

\"I ... hl~ 8~ mol.,. .'hirb m,wf<i Ih~ ."dl_ htlt 

Ti,e ... ,. of Ie..! 01 Ih~ .. "d load ... uld be .. ariPd from 

(110 abuut 200 gt'I"" J"'r nul~ Ouri", the ex""ri. 

m~',1 Ih....., siZ8 of .. "d ,,·t ... uwd r ...... pp, A;,. 

In tl,. ~Xperi"'tbl il ..... ,m!"*ibl. to m~ .. ur~ 

I<'('ul'll.~ly Ih~ emounl of .. nd dd,,'~ to Ih ... ulillt 

h~.j" II Iht 10"'er ~nd, TIr~ I'llt~ ol ... "d I.wing could 

I ... I<,<,ul'lllel)" obtain...t by n .... _i'·~ .. mpl .. of th. dry 

",at~nlll'Omin, off Ih. rndl_ J:w,lt. We "'fr~ lol'('w 

to n-ly ·,n an inex ... 1 method of d.t~nniD'n![ "'holhor I h~ 

.~·.I.m "'1$ in "Iuilibnll m: .,,<'('_ive detprml/llhon. of 

Ih~ )o:rnJillod","1 proRle of .'01<'. aurl.N'.nd d,.,. It .... m 

htd Tt,;,. m~lhod ;"IUffifiMIdy a""UI'llI~ und .... C1l'C'um-

.tln""" .·i,,," th, I'lll •• 1 ... b,rh Iood ia intrndue.d ia 

1.'lI" ... lll,,·p to Ih~ .. olume of tht ri .. et- ehannel. lor 

.~dll">n or degradalion could be "",u",'~ly ",P"-

urtd dunn[\" Iht pTOgT?M of. run of reuon.ble durol,on, 

Til .... ,,"p,.,. the elr<:11"'"tanr..- for m",,1 runl, bulo morr 

,.,.finM mr,hod of detrmlin,ng "Iuilibrium would bto 

dl"'il'llble. 

II it important 10 .mphuin .be fart th.t Ih~ .hann~1 

de,'''op<'<l in Ih~ flulIll' ..... not. model ri .. er but ..... 

tht ptOlolyP<' of a ..... 11 ...... m, Th~ 8un .... rin .. 

adju~l..t nol only il3 oIoJ"'. but abo i1$ d""lb .nd • idtll. 

Tlril eln J:w, II/'t'II in Ihe labulll..t dlla in .pP<'ndix C. 

,\ »friO<! during "'hid, .. nd and "'''~r ... ·Ne d~Ii"ertd to 

Ihe ehlnnrl at consllnl rolH IUlro .. long .. U, houl"l. 

Dnring Ihis ""riod Ih lIow "'U inl~rruptM at int~t\·.I • 

for "'~lUure",~nt of .1"0IIII o«lions. Such "W""""- "'~ntl and ""...,.ponding nlocity and ",ope data .rp 

tabul .. t...t log ... h~r ."d 1.J:w,I..t a """d" in Ip""ndc~ C. Th~ R .. t exampl~ Ibo • .-ing Ihe de'· .. opm .... t of a 

b .. ,d..t "'I<'h IS. Ht of ""'" (&., b .nd 8) in . ·bich .ht 

,nili.1 chann" cut by Iht I~mplil. ,,'U 15 ind, ... "'ide 

.nd II; ineh ... dN'p .• ·or Ib_ ""n. Ihe ftum~ .. · .. ttt 

al I 0101'" of 0.01 t4 Tire d'lICha~ ,,'U 0.085 ct., Ind 

load " ... introduced II Ihe rate of 120 g ""r minutr or a 

ttdimpnt COnCC"II"II;O", C" of 830 pl>m by ,,·~ilthl. 

Cu.romarily, Ihe luili.1 "·,,lth of d,.nnel inc",fIIIed "~ry 

.. pidly throUgll the ... tion of the lIo ... ·ing ",al~r ."d 

attainf<ia minimum ... Iu~ .·hich .... lIable ror the ginn 

di..,h.rr· In Ibe ri .. er being ditcUSllCd, Ih. uerov 

""ble ",idlh lor I diKlrarge 01 0.08~ cis ..... 1.1 leet. 

The I.mplale dllnn" being I.U feet (l5 i"d'H). 

lIiKluly l_rrr Ihln the "';ni,num I.able ,,"Iue. 11r~ 

.. ... no .. pid adjullmtnt. During Z2 llOu .. of Aow 

(inter""pl..t for purpoetoo of ,nc .. u",rnent) a .... i .. of 

htoro .nd nd. devcloped in I t2_1001 reach bet,,· ... n 
46 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS 

stations 10-22. The lower end of the entrance box was 

at station 3, which means that the head of the braided 

reach was 7 feet downstream from the entrance. 

The sequence of stages in the development of this 

braided rcach is shown in figure 34, which includes 

sketches mudc of the patt,c?rn eLt various stvges and 

detailed cross sections at one position or station along 

the flume. A photograph of this braid looking upstream 

is shown in figure 35. At the end of 3 hours of flow 

the development of a central submerged bar had proceeded so far that its lower end had caused some deflection of the flow toward the right bank. This resulted 

STATION 

22 18 1c 

houts 

I I 7' 

*- 

>hours 

7 hoc-r 

-/---- 

Island 

, 

Incipient bar 

9 hours 

1 

PROGRESS IN DEVELOPMEN1 OF BRAID IN FLIJML c1ANia:i 

EXPLANATION 

.":*. :. 

Deposit more coarse than original sand 

m 

Deposit finer than original sand 

- - /.-..-.- 

Path of principal bed transport 

Riffle, or water flowing 

- 

in steep, thin, sheet 

"~llllllllilll~~ 

Island or area nearly 

I 

out of water 

Well-defined edge of bar 

----____ 

111.defined edge of bar 

SUCCESSIVE CROSS SECTIONS 

AT STATION 14 

Initial 

Water surface 

0.25 

w 0 

Water surface 

0 25 

-7 

10 hwm 

0.25 

0 1 2 Feet I-. -.- 

FIGURE 34.-Sketches and moss sectlons showing prowess in development of braid in flume-river (February 1642,1954, runs S-a.) (Profiles shown in fig. 38.) 
Rl\"~R CIIANNI:L 'A'lTF.RNS 

in I amlU areulte I'ftfItranl in the formerly .. nipl 

bank. The hud of Ihe ... bm~~ bu had limillrly 

","uoe<! IOm~ cUlling on Ih lelt hf.nk. The eroM teetiono .ho~·n .t Iho right of figure 34 were taken by 

melnl of the point PI!" on the tn,'elinr e.m.~ .fl<o. 

lbe load .nd .... ter .. ~,.., lemponrily .lOppM. The 

IIOpping..,d .tarting had liltle effecl nn the conliguntion of Ih bed. 

The el'Oll IeClion It ltation 14 .fttr 4 hou .... of 1I0~· 

Iho"" t he pronounced ""nlnl rid", 0' lubm""Pd bu. 

It ohould be noted. ho .. e .. er. lhat in Ihe upper left 

d~ ohowing the plln .. iew It 3 houn.. Ibe band e>f 

principoal bed t.n.nllport liel "" lOp oj ".. m ... ".,-

ctnlnd 6<1.. The grain mO"em""t in the deeper p"rLl of 

the channel adja.,.,nt 10 the centnl bar ... ·u ulu.lly 

negligible in Ihe t&rIy lla&<' of Wind de"eLopmenl 

The CO'IIIrIl bar ""nlIDued 10 build ru.tr 10 tl,e .... ter 

lunlOll yet the pnneipal ..,ne of movement rem.ined 

fo •• lime .Iong the lOp of the build"'g bar. [t "·U 

there th.t .orne of the luger P*"liclei llOppM. tr.ppinr 

omallc. part .. ]eI in tM building bar Th_ .. nalle. 

,....... C(luld hove been mO"ed by the UIAtina; Ho .. had 

they Dol h«ome pro_ted or bloek...! by lorge. ","in •. 

Th,,«nt ... l bar in thellum ... ri,·or wu «used by 10011 

.orting, til<! I."". plrtidel being devo:-ited in the eente. 

of the 11l'81li'1 lOme plaoe "-h",,, Ioeoll C(lmpetenre ..... 

imuffici.ent 10 mo,'e Ihem. But., as _plaiMd, bll' build. 

ing by IO~ dOel nol Impl~' that th3 dcpoait ~ C(IJI]-

pu.ed onl.v of gnino too I"-'F' to be moved further (_ 

app B). 'rh ~ .kelChei of the developing h ... ided r06l'h 

- .... ___ .. _~ ... _.-....... oa..l 

""" _ ... H .... """". _ .. 

... "" ... - ....... _ .......... _" ... __ f ...... ,_ 

,,, .......... _ .... ,

oho .. UI irngulu d .. lnbullOll of weU.--ted fine 111.1_ 

!«i.I, ulually dopo-ited 0 ..... tl,. toe or do"·".I"""-1II. 

...!'" of Ih ~ bar "'h~ prDgn!tl,ve bar !Invdopmcnl 

roMilted of fnrnoel bed. as ill a ddta. The C(lnlinuAi 

ihifling of the channell, Ihen. buiLdl a het~nl&tTI""u. 

bar «)II"o;ng 01 ",lChei of mlterials of difflftnl me 

and different d~ of IOrliDjl". 

By Ihe eod of 7 houn. of 1I0w !.be ~ent ... 1 bar had 

b""n buill 10 high thAt indi"iduII i"'in. rollin&, Ilong 

i~ rid", aclually "broke" Ihe ""ter IlUn .. «. Ltopold 

.. nd ~Iiller had not...! pre,;"ully (11156. p_ &) I"'t in 

.. rroyot, many 1"-'F' pebble1U1d C(lbbl00 .'ere obse .... eci 

10 roll in 110 .... 01 deplh only half Ihe di.mel .... of Ihe 

rolhng 'lone. By ,ueh .. proc_ • truo iel.nd Clnnot 

be formed in wlilonn dise/arge. Ho,,·e,·cr. Ih .. deft.,.,.. 

lion of 1108 .... Ier by the cwln1 bu ullUJJly ~IUoe<! local 

IICOU. in lOme pin of Ihe channell ... ", ... Iro by Ibe 

c~nl .... l bar, .nd Ihi. lIOOur eeulftl I low"";"g of the 

wat~. lunace whieh lell Ihe !.>ar .Ii~kin~ OUI of Ihe 

.. ·.Itr as A .... 1 illlnd. Sueh ltOu ........... ved in 

mUly of \l.e runo IUId Ihe iIIln.do . ·hkh Ire indir.ttd 

in 1108 lItekhei io fi"' .... 34 ""'errro ..... '""It of Ih;" 

~. This ~ondi ;on i, .. 110 tho"." in figure 36, • 

photograph of, de"clopin&, ill.nd. 

The arto d .. ig".ttd II "incipient b.r" in figure 34 .t 

bou.7 had enl .. rged Ind emerged .... n w.nd by hour 9. 

Fu.tbenno ... , .ft .... hour 9 of flo .. '• lin .... bor hld 

... ~,·tloped in Ihe ~hllnel.te* loCI "'""" Ihe 1.'0 iol.ndo, 
48 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS 

bisecting the flow into two parts, marked A and B. 

By hour 13, continued bar building in channel A and 

subsequent lowwing of the chmnel B diverted most 

of the water out of the old channel A and the primary 

zone of transport over the bar arw was restricted to 

charinel B. 

Similar sequeiices continued to change the configuration of the braided reach, moving the principal zones 

of transport from one place to another, and at hour 22 

there were three island areas. It should be unclcrstood 

that in the flume-river the constant discharge did not 

permit the islands to receive any increment of deposition 

after emergence so that an “is1arid~’ actually represented 

merely the highest knob of a bar most of which remains 

submerged. 7‘11~ cross section of station 14 at hour 18 

(bottom diagram, right side, fig. 34) illustrates this 

feature. 

The succession of events observed in the flume are 

analogous to those postulated to account for the characteristics of thc rcach studied on Horse C‘reck. The 

central bar built closer to the water surface and c~xtendcd 

itself downstream with time, channels were successively 

formed and abandoned, and the bars were macle up of 

the coarser fractions of tlic introduced load but mixed 

with considrrable fine material which hat1 become 

trapped. ‘l’hc similarities hetwrcn the field example 

and tlie flume can be scm by comparing the photographs in figures 30 and 35. 

Nearly all observers who have recorded notes on tlie 

action of a braided stream have reinarlied on thc shifting 

of bars and the caving of banks. Once a bar is deposited 

it does not ncccssarily remain fixed in form, contour, 

or position. Tliis can be seen in the successive cross 

sections of four stations made during the run pictured in 

figure 37. Tim(. changes at a particular position arc 

arranged sidc by side and the downstream variation at a 

particular time can be seen in tlie vertical groups. A 

reference lrrel is givtm for c~iicti scction so tliat tlic 

changes of watrr surface elevation can be compared. 

The sections grouped on tlie uppermost horizontal line 

are at station F. Comparing the sections from left to 

right it can be seen tliat station 6 underwcnt continued 

aggradation and t Ii11 shape of the cross section ctianged 

radically, murh more than did the area of the cross 

section. 

The horizontally arranged group of sketctics at 

station IO illustrate tlie varying cltvation of wntrr 

surface which rose twtwcen hours 1): ant1 4, fcll from 

hours 4 to 6, and rosc again from hours 6 to 11. The fall 

of water surface elevation is clearly duc to the scour of 

the right-hand chiinnel between liours 4 and 6. 

The initial linear nature of the central bilr is hcst 

illustratcd at 6 hours where a central ridge is present 

through an 11-foot reach between stations 6 and 17. 

This is shown on the sketch of the plan view in tho 

ower right part of figure 37 and on the cross sections 

‘or that timv arranged vertically on the figure. 

The growth and subsequent erosion of a central bar 

s also illustrated tit station 10 (fig. 37). On the leftland diagram of station 10 the shape of the initial 

:hannel molded by template is shown as a dashed line. 

4ftcf 1: hours this shape had been altered by the 

milding of a central bar and by slight degradation of 

he channrls bcsidc the bar. By the crid of 4 hours thc 

:ombination of lateral building and deposition on the 

Jar surface had widended the bar arid made a double 

:rest. Bar building resulted in a clivcrsion of most of 

[tie watcr into tlic right clianncl tit station 10 which 

:auscd loc.al scouring. 

DIVIL)EI> AND tJNl>IVIDlH> REACIIEH IN TIIF, FLUME AND 

IN NA’L’IJHAL RIVERS 

In both natural strrtims and thc flume-river the slope 

Df the divided reach provcd to be greater than that of 

the undivided reach. Tlie stecpening of thc divided 

rcach in tht. flumr is vcry marlied. Figure 38 sliows 

the watcr surfacc profile data associated with runs 

6a and b arid 8, Fc~brunry 16-22, 1954. The measurerncnts presented in tlic left part of the figure are interpreted diagrammatically on tlie right half of the figure. 

When considering the nieasurrments it must be recalled 

that tlic elevation of the watcr surface WRS nicasured 

relative to a sloping datum. Thus, water surface 

profilcs which rise downstream relative to the datum 

mean that the water surface became adjusted to a slope 

less than that of the flume rails. This can be seen by 

reference to thc diagrammatic profiles on the right of 

figure 38 where the initial profile, shown as a heavy line, 

reprcscnts the slope of the water surface when the run 

began and the water started to flow down a channel 

parallel to the sloping rails. By tlic end of 9 hours, 

aggradation had tnltcn place in the reach between station 

6 and station 12, and also downstream from station 35. 

Degradation of the initial channel liad occurred between 

stations 15 and 3.5 with the establishment of a steep 

reach in tlic divided or braided section. 

Betwrrn hours 9 and 20 of flow, continued aggradntion took place in tlie divided reach but, in general, thc 

steep slope was maintained approximately parallcl to 

that which cxistcd at tlic cnd of hour 9. Similarly, 

tbe aggrading reach downstream from station 20 maintained nearly the same average slope as that which 

existed at hour 9, this slope being much flatter than that 

of the divided or braided reach. A similar sequence 

can be observed in thr profiles presented in tlie lower 

Irft-hand part of figure 37 (associated with run 17, 

March 11-12). In figure 37 it can be seen that bctween hours 1ji and 4, the reach from station 10 to 
1050 A.M 

Ik hours 

Water surface 

O.'.-3 

we+ STATION 6 47a 

OZ5

VERTICAL SCALE 

I 

I 

I 

I 

I 

025 1 E I 

-- --I- 

\ Initial channel 

140PM 

4 hours 

4'30 P M 6 hourr 

STATION 8 

1.0 Feet 

O-LuxLLL 

== STATION 14 

830 P M 11 hours 

STATION 6 

VI PROFILES OF WATER SURFACE , 

-11 hours 

zb 

026 

8W--XT--X 

30 40 50 

DISTANCE ALONG FLUME IN FEET DIAGRAMMATIC PLAN VIEW OF BAR AFTER 6 HOURS 

I 

FIC~RE 3i.-Cross sections showing the progressive development of harp in a braided reach of the flume-river, profiles of water surface, and diegrammatic plan view of bar (March 11-12, 19! ) 
50 

0.3 

r 

vi 

- 

2 

2 0.2 

c 

I- 4 0.2 

a 

0 

3 

LL 

w 

- 

w 

2 

Q 

s 0.2 w 

Area ...-.......... ~~... 

Width --....... ~ ....-.. 

Depth. __. . . . . . . .~... . 

Velocity.. . . . . . . . . .-. . 

Slope ...-... ~~.~~.~ .... 

Uarcy-Weisbach resistancehctor .... ~ ..... 

PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS 

1.3 1.03 1.6 0.94 1.08 0.78 1.07 

1.513 1.83 2.0 1.05 1.34 1.48 1.70 

,88 .56 .79 .%I .80 -52 .63 .77 .97 . . . ~. .~ ~ 1.06 .93 1.27 .93 

5.7 2.3 1.4 1.3 1.4 1.9 1.7 

10.5 1.3 ~ ...... ~ 1.1 1.3 .63 1.25 

10 20 30 40 50 

STATIONING ALONG FLUME, IN FEET 

e 1030 Feb 16 20min Slope of rails 0 0114 0 2 10 4 hr X 1140 Feb 18 9hr 

V 330 19 17 hr L 120 grams per minute V 11 05 22 20% hr 

ACTUAL MEASUREMENTS 

--- 0 0 085 cts 

HORIZONTAL DISTANCE, IN FEET 

DIAGRAMMATIC PROFILES INTERPRETING MEASUREMENT DATA 

10 20 30 

lM~ine 38.-Measured and diagrammatic profiles of flume-river during run of February 1&22,1954. (Plan view and cross sections for these runs are shown h fig. 34.) 

station 22 steepened markedly, but from hours 4 to 1 : 

aggradation occurred at approximately the same sl~pe 

which existed in this downstream reach at hour 4. In 

the braided reach upstream from station 10, however, 

continued aggradation was accompanied by continued 

steepening between hours 4 and 11. 

It is important to notc in these runs that aggradation 

could take place at a constant slope without braiding even 

when the total load exceeded the capacity of the channel 

for transport. Braiding is developed by sorting as the 

stream leaves behind those sizes of the load which it is 

incompetent to handle. If such sorting results in progressive coarsening of the bed material then the slope 

increases progressively If the stream is competent to 

move all sizes comprising the load but is unable to move 

the total quantity provided to it, then aggradation may 

take place without braiding. Hence, contrary to the 

assumption often made, the action in thc flume rivcr 

suggests that braiding is not a consequence of aggradation alone. This is brought out in flume runs 30a to 35 

which are discussed later in relation to the adjustment of 

slope in natural channels. 

Although thn, steepening of slope in i8h: divided reach 

is one of the more obvious of tlie observed changes in 

the channel associatcd with division around an island, 

nearly all other hydraulic parameters arc also affectcd. 

D&iled comparisons of an undivid-d channel and a 

channel divided around an island, or a potential island, 

are availabl- for thee river reaches and four runs in thc 

flume-river. These comparisons are presented in 

table 1. (Complete data are tabulated in app. D) 

Comparisons are shown as ratios of the measurements 

in the divided reach to similar measurements in the 

undivided one. The width io R reach containing an 

TABLE 1.-Ratio of hydraulic factors of divided to undivided 

reaches of braided streams (natural rivers and jlume-river) 

New Fork River/ Flume at California Institute of 

Technology 

_____ 

Wyo. Reach 1 Reach 2 Feb. 15 Feb. 16 Feb. 18 Mar. 5 

(1953) (1954) Sta. 10 Sta. 14 Sta. 10 Sta. 12 1 1 ! and 14 1 and 22 I and 14 1 and 38 

island is the width of flowing water. The width of the 

undivided reach is the width of the water surface upstream or downstream from the island or where thera is 

but a single channel. 

All examples show that channd division is associated 

with increased width of water surface, increased slope, 

and with decreased depth. In the three comparisons 

from our measurements of natural rivers the sum of the 

widths of the divided channels ranges from 1.6 to 2.0 

times t,hat of the undivided one. In the four comparisons made in the flume tlie ratios vary from 1.05 to 1.70. 

Tlii.; increase in water surface width caused by 

development of a bar or an island is accompanied by a 

decrease in mean depth. The mean depth of the divided 

reach was computed by dividing the cross-sectional area 

of flowing water by the total width of water surface in 

the two channels. 'I'he ratio of dcpths in the divided 

reach to dcpth in the undivided reach varied from 0.6 

to 0.9 in natural rivers and from 0.5 to 0.9 in thc 

flume-river . 

With regard to changes in slope, the profiles of Horse 

Creek in figure 29 show tirat the left channel is more 
RIVER CHANNEL PATTERNS 51 

conspicuously divided in to pools and rimes thnn the 

right ow, but, tbe slope of each of these divided channels 

is unquestionably greater-in fact, it is three times as 

large-as the slope of the undivided part of the stream. 

The increased slope of the divided reach is wen more 

marked on the profile of the Green River neai Daniel, 

Wyo., where there is nearly a six-fold increase in slope 

after the river divides (fig. 39). In the example of the 

New Fork River (fig. 40), the steepening is less obvious 

primarily because there is a steep riffle between stations 

200 and 500 which tends to increase the average slope 

of the upper 1,000 feet of the mapped reach. If, however, the divided reach between stations 1700 and 2400 

is compared with the undivided reach from stations 

1500 to 1700, steepening of the slope in the undivided 

part is again apparent (table 1). 

In Rubey’s analysis (1952, p. 126) of the division of 

the channel of the Illinois River by islands he was 

unable to show from the maps available to liim any 

significant increase in slope in the divided reach, but 

the maps suggested that “on the average, the slope 

opposite islands is steeper by something like 5 to 10 

percent.” 

As table 1 shows, there is more variation in the ratios 

in slopes than there is in the ratios of widths and of 

depths in divided and undivided reaches. This is due 

primarily to one example in a natural river, the Green 

River near Daniel, for which the slope of the divided 

channel was nearly six times that of the undivided one. 

With the exception of this one large ratio, however, tbca 

natural rivers have ratios of 1.4 and 2.3, and the 

ratios in the flume ranged from 1.3 to 1.9 

The changes in width, depth, and slope caused by 

island development in the flume-river are of the same 

order of magnitude as comparable changes in the 

natural rivers studied. 

From plmctabla map by Leopold and Wmm. Aup. 12,1953 

FIGIJRE 39.-Mop of Green River near Dnniel, Ryo., showing a reach in which the chnnnel divides around nil island nnd is, therclore, braidrd; the indiviciunl 

divided chnnnels meandcr. 
52 

The change of cross-sectional area depends upon the 

relative amounts of change of width and depth. The 

division by an island caused the cross-sectional area to 

increase in all three reaches of the natural rivers studied 

but in the flume there was an increase in cross-sectional 

area in two instances and a decrease in two instanccs. 

The velocity in the divided channels was sompwhat loss 

in the two natural rivers for which data are available, 

but in the flume division caused the velocity to increase 

in two rcachcs and to decreasc in two others. Nonuniform changes caused by island growtli can also be 

seen in the Darcy-Weisbach resistance factor f (table 1). 

These data indicate that changes in neaily all the 

hydraulic parameters occur when a channel divides. In 

discussing this matter Franzius (1936, p. 38) assumcd 

PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS 

that conditions in channel division could be approximated by assuming that the width-to-depth ratio, 

slope, and roughncss are identical in divided and 

undivided channels. Such assumptions would apply 

only in certain cases but could not be assumed generally 

applicable. Chien (1955) computcd the charactcristics 

of divided channels, using the Einstein bedload equation 

(1950) and assuming that 110 change of grain size accompanied channel division. ‘This assumption is more liltcly 

to be fulfilled in natural clianiicls than those of Franzius, 

but both the flume data and the streams studied by US 

in the ficld indicate that selective deposition of coarsc’ 

fractions of tlie load in the braiding process tends to 

result in coarser material in the beds of the separate 

channels than in tlie undivided channel. 

EXPLANATION 

/---- 

Riffle 
RIVER CHANNEL PATTERNS 53 

The adjustment of various hydraulic factors to any 

change in the indepcridcnt factors may take the form 

of any one of inany possibilities. The adjustments are 

intrrdependen t and it is difficult to specify in advance 

how an alteratioii of caonditions will be taken up by the 

deprndrn t f ac tors. 

New islands form and channels often change too 

rapidly for complete adjustment to cqiiilibrium conditiom, but some reac1ic.s of braided rivcrs are very 

stable indeed, as judged by the size and age distribution 

of vegetation. The island shown on Peak’s map of 

the Green River near Daniel still exists 70 pears later, 

as can bc seen in figure 28. Presumably, in such 

instances, a closer approach to equilibrium is possible 

than in transitory channel division. Nevertli eless 

we interpret our obswvat ions presented above as 

indicative that a braiclcd pattern as well as other 

patterns can indeed be one of the possible conditions 

of quasi-equilibrium. 

SUMMARY: THE BRAIDED RIVER 

A braided river is onc whicli flows in two or more 

anastomosing channels around alluvial islands. This 

study indicates that, braided reaches taken as a whole 

are steeper, wider, and shallower than undivided 

reaches carrying the same flow. A mode of formation 

of a braided channel was demonstrated by a small 

stream in the laboratory. ‘I’lie braided pattern d3veloped after deposition of an initial central bar. The 

bar consisted of coarse particles, wnich could not be 

transported untlcr local conditions existing in that 

reach, arid of finer material trapped among these 

coarser particls. This coarse fraction bxame the 

nucleus of the bar which subsequently grew into an 

island. Both in the laboratory-river and in its natural 

counterpart, Horse Creek near Daniel, Wyo., gradual 

formation of a central bar deflected the main current 

against tlie channel banks causing them to erode. 

The braided pattern is one among many possible 

conditions which a river might establish for itself as a 

result of the adjustment of a number of variables to a 

set of indapendent controls. The requirements of 

channel adjustment may be met by a variety of possible 

combinations of velocity, cross-seccional area, and 

roughness. Braiding represents a pardcular combination, albeit a striking combination, of a set of variables 

in the continuum of river shapes and patterns. 

Braiding is not necessarily an indication of excesFJive 

total load. A braided pattern once established, may 

be maintained with only slow modifications. The 

stability of tlie features in the braided reaches of Horse 

Creek suggests that rivers with braided patterns may 

be as close to quasi-equilibrium as are rivers possessing 

meandering or other patterns. 

STRAIGHT CHANNELS 

In the field it is relatively easy to find illustrations of 

zither meandering or braided channels. The same 

:annot be said of straight channcls. In our experience 

truly straight channels ara so rare among natural 

rivers as to bt> almost nonexistent. Extremdy short 

segments or reaches of the channel may be straight, 

but it can be stated as a generalization thaf, reaches 

which are straight for distances exceeding ten timss 

the channel width are rare. 

THE WANDERINQ THALWEG) 

Figure 41 shows in plan arid profile a reach of Vall~y 

Creek near Downingtown, Pa. For 500 feet this 

rhannel is straight in a reach where the alluvium c,f 

the valley is 30 feet thick. Its sinuosity (ratio of 

thalweg length to valley length) is practically 1 .O. 

The thalweg, or line of maximum depth, is indicated 

by a dashed line in the upper portion of figure 41. 

‘I’hough the channel itself is straight, the thalwcg 

wanders back and forth from positions near one bank 

ad then the other. This is typical of a number of 

nearly straight, reaches which we tiavo studied. The 

wandering thalweg is easier to see in the sketch shown 

in the lower part of figure 41 in which the position of 

thc thalweg relative to a channel of uniform width 

is plotted. 

Along with the wandering thalweg it is not uncommon 

to find deposits of mud adjacent to the banks of straight 

channels. These commonly occur in alternating (as 

opposed to “opposite”) positions. A similar obsrrvation has been made by Schaffernak (1950, p. 45). The 

alternating mud “bars” are related to a thalweg which 

also moves alternately from bank to bank. In an 

idealized sense, this plan view of straightr cIianne1s 

appears to bear a remarkable resemblance to a mcander. 

In a straight flume Quraishy (1944) observrd that a 

series of alternating shoals formed in the channel. 

These lie referred to as “skew shoals” (p. 36). Sim 

ilarly, Brooks (1955, p. 668-8) called the condition in 

which low channel bars formed alternately adjacent to 

the left and right walls of his straight flume a “meandthr” 

condition. 

POOLS AND RIFFLES 

Another characteristic of natural streams even in 

straight reaches is the occurrence of pools and riffles. 

This has been noted by Pettis (1927), Dittbrenner 

(1954), and Wolman (1955). Figures 40, 42, and 43, 

respectively, the New Fork River near Pinedale, Wyo., 

the Middle River near Staunton, Va., and the Pop0 

Agie near Hudson, Wyo., present plans and profiles for 

a braided reach, a straight reach, and a meandering 

reach. Profiles of these three examples are compared 
0 

m 

\ 

i 

I 

I 

\ 

\ 

\ 

/ 

/ 

I 

I 

\ 

'\ 

\ 

/ 

I 

/ 

/ 

/ 

\ 

/ 

\ 

'\ 

\ 

\ 

/ 

/ 

/ 

/ 

\ 

I 

I 

\ 

\ 

\ 

\ 

\ 

/ 

/ 

/ 

/ 

4 

\ 

'. 
RIVER CHANNEL PATTERNS 55 

iw 

P 

0 300 Feel 

EXPLANATION 

_jc 

Rlnle 

Bedrock in channel 

through this reach 

From planetable map by Lmpola ana woln m AUBW ?w - 

STATIONING ALONG RIVER CHANNEL IN FEET 

FIG1 RE 42 --Plan and profilr of d icach of tho Middlo River lirar Stnunton, Vn 

in figure 44 which reveals a similarity in tlie profiles 

of streams possessed of very dissimilar patterns. Thus, 

a straight channel implies neither a uniform stream bed 

nor a straight thalweg. 

As demonstrated first by Inglis (1949, p. 147), the 

wavelength of a meander is proportional to the square 

root of the “dominant discharge.” One wavelength (a 

eomplcte sine curve or 2a radians) encompasses twice 

the distance between succcssive points of inflection of 

the meander wave. It is well known that meandering 

channels characteristically are deep at the bcnd and 

shallow at the crossover or point of inflection. Thus, 

twice the distance between successive rimes in a straight 

reach appears analogous to the wavelength of a meander 

and should also be proportional to Qo5. As an initial 

tcst of this hypothesis, bankfull discharge wliai I) u 

consider equivalent to “dominant dischargc” nf 111 

Indian literature, has been plotted in figur 3 45A ncn~n~+ 

wavelength of meanders. The figure Includrs dtil 

from straight reaches for which “wavchngtti ’ :\ twicv 

the distance between successive riffles. 

The data in figure 45, tabulated in appendix E, 

include measurements of rivers in India from lnglis 

(1949), our own ficld measurements, and some fiumc. 

data from Friedkin (1945) and Brooks (1955 and pcrsonal 

communication). The wavelengths In Brooks’ dtll a 

obtained in a fixed-wall flume (no. 259, appendix E> 

represent, as in the nonrneandering natural channels, 

twice the distance between the “riffles,” or low bars, 

which he observed. 
m 0 

0 

a 

0 

z 

oz 

z I 

t: 

WnlVO AWtlllEllV :1334 NI NOllVh313 

3 
57 

6000 7000 5000 

I 1 

5000 

80 

2000 3000 4000 

DISTANCE ALONG STREAM, IN FEET 

I 1 I 

DISTANCE ALONG STREAM, IN FEET 

FIGURE 44.-Profiles of three rivers including straight, meandering, and braided reaches. 
58 

Figure 45A drmonstratcs that, with considerable 

scatter, a relation between wavelength and discharge 

exists through a IO8 variation in Q. Thr data for 

straight channels do not vary from the average relation 

any more than those for meanders. 

Inglis (1949, p. 144) had called attcntion to the fact 

that since width is also proportional to the square root 

of discharge, wavclcngth is a linear function of stream 

width. Inglis did not mention the fact, illustrated in 

figure 45B, that the sctltter of points in the width-wavelength relation is Icss than that in thc. discliargc 

wavelength relation. The relation in figurc 45B is quitc 

PHYSIOGRAPHIC AND HTDRAULIC STUDIES OF RIVERS 

cmsistent though it includes straight channels as well 

as mcanders, and the widths range from less than 1 foot 

in the flume to 1 mile in the Mississippi River. The 

line drawn through the plotted points in figure 45R 

indicates that in general, the ratio of wavelength to 

bankfull width varies from about 7 for small streams 

having widths of 1 to 10 feet, up to 15 for large rivers 

having widths in excess of 1,000 feet. 

Dr. T. &I. Prus-Chacinski has told us that European 

1 engineers have a rule-of-thumb that the meander wavelength is lt5 times the channel width. That our ratio 

is 1 :15 only for large rivers may possiblybe influencjd by 

EANKFULL DISCHARGE. IN CUBIC FEET PER SECOND 

EXPLANATION 

MLANDERS 

0 

Rivers and flumes from Leapold and Wolrnan (lhlr repon) Friadkin(1945). Quraishy(1944). 

and Inglis (1949) 

-1 

1 

- 7 

D 

Rivers in Oriru India lrom lnglli (193940 p 111) 

POOLS AND RIFFLES 

0 

(this report). and Broor(1955) In straight channels fmm Leo Id and Wolman 

BANKFULL WlDTU OF CHANNEL, IN FEET 

IWL'RE 45.--\\ia! drngth of incandcrs and of riffles as functions of b;tiikfull discharge and channel width. 
RIVER CHANNEL PATTERNS 59 

the fact that our data show bankfull width rather than 

width at some lower stage. Our data indicate that the 

relation is not a constant ratio but a power function 

having an exponent slightly larger than 1 .O, specifically 

X=6. 5w1 . ’. 

Comparison of figures 45A and 45B leads us to 

postulate that in terms of the mechanical principles 

governing meander formation and the formation of pools 

and riffles, the wavelength is more directly dependent 

on width than on discharge. It is argued later in this 

paper that in general, at a constant slope, channel width 

follows from discharge as a dependent variable. We 

suggest, therefore, that wavelength is dependent on 

width and thus depends only indirectly on discharge. 

That this relation describes both the distance between 

riffles in straight channels and the wavelength of 

meanders leads us to conclude that the processes which 

may lead to meanders are operative in straight channds. 

SUMMARY: STRAIGHT CHANNELS 

The observations discdssed lead us to three tentative 

conclusions. First, pools and rimes are a fundamental 

characteristic of nearly all natural channels and are not 

confined to meanders. Second, river curves all tend to 

have a wavelength that is a function of stream width 

227 

x ;z9 

X 

233 X 

232 

128 -X 

‘125 .1: 

hi;!_ e434 

vx\ 

24 30’ 

3: 

240x 

’42 24 

and thus indirectly a function of dischargt. Third, 

even straight channels cxhibit somc t cdency for the 

flow to follow a sinuous path within thc confincs of their 

straight banks. 

THE CONTINUUM OF CHANNELS OF DIFFERENT 

PATTERNS 

The physical characteristics of the three specific 

channel patterns discussed in thc preceding section 

suggest that all natural channel pattrrns intcrgradc. 

Braids and meanders arc strikingly tlitferent but thy 

actually represent extrcmes in an uninterrupted range 

of channel pattern. If we assume that the pattern of ti 

stream is controlled by thc mutual intewwtion of a 

number of variables, arid the rarigc of thcsc variables 

in nature is continuous, then we should cxpcct to find n 

complete range of clianncl patterns. A givcn reach of 

river may exhibit both braiding arid mrandering. In 

fact, Russell (1954) points out that the hleander River 

in Turkey, which gave us the term “menridering,” has 

both braided and straight reaches. 

This conception of transition in pattern or interrelation of channels of diverse pattern is supported by the 

data in figure 46 in which the average channel slope is 

plotted as a function of bankfull discharge (data tabuEXPLANATION 

e Braided 

X 

S t r a i g h t 

V Meandering 

BANKFULL DISCHARGE, IN CUBIC FEET PER SECOND 

FIGURE 46.-Values of slope and bankfull discharge lor various natural channels and a llne defining critical values which distinguish braided from meandering channels. 
PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS 

h 

60 

lated iri app. F). Meandering, braidrd, and straight 

channels are designated by diffcrrnt symbols. ‘I’hc 

reaches which have been called meanclrrs are those in 

which the sinuosity, the ratio of thalweg length to 

valley length, is equal to or greater than 1.5. This 

value is an arbitrary one but in our experience where the 

sinuosity is 1.5 or greater, one would readily agree that 

the stream is a true meander. Many channels which 

appear to the eye to be very tortuous actually have 

rather low sinuosity ratings. The reader may be 

helped in visualizing these values by inspecting the map 

of the Pop0 Agie River near Hudson, Wyo. (fig. 43). 

Tliis meander on the Pop0 Agie, the most symmetrical 

that we have seen in the field, has a sinuosity of 1.73. 

The term “braid” is applied here to those reaches in 

which there are relatively stable alluvial islands, and 

hence two or more separate channels. 

The data in figure 46 indicate that in the rivers 

studied the braided channels are separated from the 

mcanders by a line described by the equation 

For a given tlisc.hargc, mcanders, us one would expect, 

dl occur on the smaller slopes. At the sanie slope a 

braitlcd cliaiinel will havc a higher discharge than a 

inc~nndering one. ‘I‘lic figure shows, moreover, that 

straight clianiicls, those with sinuosities less thnn 1.5, 

occur tliroughout the range of slopes. This supports 

the view that the scpnration of a true meander from a 

straight channel is arbitrary. Study of the sinuosities 

of these channels does not reveal an increasing sinuosity 

with dvcrcasing slope; that is, greater tortuosity is not 

tiec~esst~ril,y ussocmtccl with decreasing slope. A diagram 

similar to tlie one in figure 43 has been plotted by 

Nuguid.’ His clcsigrintioii of meanders was not based 

upon a particular sinuosity but was apparently an 

arbitrary designation based upon the plan or map of 

the c~hannel. Nuguid indicated that what he ,:ails 

normal, or straight, ciiannels have a smaller value of 

slope than meanders for any given discharge. The 

present data do not demonstrate such a distinction. 

In considering figure 46 it is important to keep in 

mind thaL these data tiescrihe certain natural channels. 

In natural charincls spccific variablcs often occur in 

association. For example, steep slopes are associated 

with coarse material. In a system which contains, as 

we have pointed out, a minimum of seven variables, u 

cliagram sucbh as figure 46 which treats only two of these 

cannot be expected to describe either the mechanism of 

adjustment or all theoretically possible conditions. 

Because it IS drawn from nature, however, it does _.__- 

I Nuguid, C P 1050, A .Judy of stream meanders Iowa State Univ , runstel’s 

theqls. 

dcscribe ti sr.t of conditions which arc to be expected 

in many natural channels. 

Two ideas that will be explored more fully are inherent 

in figure 46. First, at a given discharge various slopes 

are associated with varying channel shapes and patterns. Second, in considering an individual bifurcating 

channel, we are concerned with a division of discharge 

comparable to the comparison of n downstream point 

with an upstream point in a river channel system. 

Cottonwood Creek near Daniel, Wyo., is a striking 

illustration of a11 abrupt change from one stream pattern 

to another (fig. 47). Above the gaging station, Cottonwood Creek is a very sinuous meander. Immediately 

bclow the gagc it becomes a braid. The character of 

thca channel where braiding begins is shown by thc 

photograph in figure 48. As the profile in figure 47 

shows, tlie meander reach has a slope of 0.0011, while 

the braided section occurs on a slope of 0.004. ‘I’hc 

difference in slope is accompanied by a change in thc 

median grain size from 0.049 foot in the meander to 

0.060 foot in the braidctl reach. 

At n 

discharge of 800 cfs points 12a and 12b rcpreseiit, 

respectively, the meandering arid the braided parts of 

the reach of Cottonwood Creek pictured in figure 47 

In changing from a meander to a braid at a constnnt 

discharge we should expect the two conditions on 

Cottonwood Creek to bc represented by points OII 

different sides of the line of figure 46, and indced this 

expectation is fulfilled. 

It is clear that through the short reach of Cottonwood 

Creek discharge is the same in both mcantlering arid 

braided parts, for no tributaries entw The load 

curried is the same in both meandering arid braided 

parts. ‘I‘here is no indication of rapid aggradation or 

degrnclation, and to the extent that this is true, if the 

nicandrring reach is assumed to be in quasi-ccluilihriurn, 

then the braided reach is also. The braided pattern 

here is not due to excessive load but appears to be a 

channel adjustincnt causecl by the fortuitous occurrencc 

Df a patch of coarser gravel deposited locally in thc 

valley alluvium, the bulk of which was probably laid 

lowii in late Pleistocene time. 

A reach of the Green River near Daoicl, Wyo., is 

shown on tlic map in figure 39. Here thr traiisition 

from undivided to divided channel irivolvcs ti change of 

dope, and by reason of the individual channels, 11 

hngc in discharge. The river at this point has 

i drainngch urea of 600 square miles and a barikfull 

lischnrge of about 2,000 cfs. It flows in a broad 

illuvial plain about 2 miles wide. Tlierc are myriad 

Joughs mid marshes with a dense growth of sedges and 

villows. In the r~ach mapped in figure 39 the main 

~Iiannrl divicles into two channels about one-quarter 

Data for this reach arc plotted in figure 46. 
WnlVO AWtlllEW '1334 NI 'NOllVA313 
PlIl'SIOOIlAPUlC A~D HYDRAt;LIC 6TU1H~S OF RIVEIIl! 

.... , ... .. _, .... ,_ ................... ""'_ .... c .... __ .... .......... _-_ ... _ ............ _-_ .. ...... A''' ... _____ .. _ . 

Inile &bo"~ 1.:. S. ROUl8 1811. At the li n~ tlo" ",ap ..... 

n",de the undivided ch.nnel carried • d;"'h..-ge 01 

42i> do. llelo'" Ihe div;,,;on tlte lelt channel h..,] & 

<lioeharg" of 305 da and the righl IW d,. ~'o"'ing on 

a $lope 01 0.0005 the u"d"·ide.l channel h .. a grain 

oi ... of OOM 1001, "'hil~ ;n bolh Ihe ritrlu a"d J<.h 

ehan""ll .he oIo~ iA 0.0029 Ind lhegn-in we 0.18 fOOl. 

A .. um'ng th.~ Ihe proportion of the ditcha~ 

fto"'ing in ...,IL ch&rul,,1 ",maina Ihe .. me al .ILe bank· 

I<lll '1Ig~, the threfl channel. for Ihe Green !{i"eT at 

o lnielne ploned in figu .... 46 (poin'" I"-e, appendix 

F). In Ihia figuNl ille dh'ided .... uhM of the eh.nnel 

.,.., rolliidored ... pa .... I~I ... in I~rms of th"ir local oIo~ 

and diAch~. The undi~ided part ia lito <OIIIiderOO 

O,'er & ohort I"Hd,. ThuI, the oIlOrt undi ... id.d .-..eh 

01 the Groen River.t Daniel (point Ib) il@"lven th 

Iymool of • I,raigllt ri"cr in figure 46. The 1101'8 of 

the d;"ided channel •• re «]ual but Iheir di.c1,.rget are 

diff.....,nl. f rom figure 46 (poin'" 1410. e) We should 

upe<:l 1M 1"lt channel to be braided .nd the righl to 

be m"",nd~ring. A. lhe map in figuu 39 tho .... , the 

right chlnn.1 i. d.finitely meandering. TILe Ielt 

channel h •• too .,...11 • \"Alue of $inuooil)' to be called. 

rn~."der. 11 d .... include lOme ;'Iandl, but it;' nol. 

cleu ...... 01 braiding .nd should .... d,,"ifierl .. 

II .. iglu. 

Oth~r tUmplM 01 the ~tion 01 chann"!l pat~ to 

d;"dl''l!:~ .nd olo~ ean be d~n from riv" .. in ... rio", 

partl of the world. h~ great ri,'c" t""effing the 

pl.in of the G.ng .. in lhe Sille of Bihar, India, pro"ide 

illult .. tion.. Tbe K"'; Ri,'u (m .... imurn dillCharge 

.!>out 800,000 cro), rioin, M*I" :\[ount E"erelt, 110 .... 

out of lhe jftmala,.. .nd 0'""" a bl"Olld, 8&1 debn. 

rone to jo'" the Gangeo. The Kooi ia b .. ided in the 

Ii .. t • S milM .fter it I ... ,· ... the mount.in fro"t .nd thi' 

b .. iditljl ;. _iated with dtporoition of Ihe ..,. .. er 

I .. ChOu. of itl dehri. load. j .... t .. in the Hume upe.-;-

n,,,nt.l d""";M<! "",rli,.,.. The patlflrn ch.ng"", from 

b,.iding to m"",ndtritljl It the foot of the dehri. fIn 

'nd 'c"'8ill~ 1II~.,,,I"ring 10 Ihe junction wilh the 

GIn!!"". 0.11 on dillCh"'lCe .re m.., ... On the Bih.r ri .. " ... 

Tbe m ... n annual "00<1 for Ihe K"';, rourhlY"NJui,·.lent 

to tht htinkfull .Iagf', itt .boUI ZOO.OOO d.. """'" 

dec:.u.e of the peak di.cha'"l" un be ,""peeted from 

dllnnol .Iorage in Ih~ '5-mil. '<'lid, o'·.r the deb,;· 

'"ll a"d th" i. probabl.'· rompen.u",1 by an i",....,n,cnl 

pro"ided by th" !lagmlli and Kaml. Ri,'~" "'hich 

"Iller the KOlIi u tIlt foot 01 the I.... A .. I .......,. .. ble 

1I"'" .. I'u,;on .... " .... me Ihlt lit" bankfull dilCh.rge 

"'In.in. <:(Inltan, from the fOOl of the lIim.l.y .. to the 

junclion "',Ih Ihe G.n' .... . 

The ti"er olope decr ... """ from 'ooUI 0.001 " ... r Ihe 

Ip"" 01 Ihe debril fIn 10 lbout 0.00035 in the m"",nderlnr _ell. The "a1u,," of oIope ... d diocho.'l!:e on fi&:ure 

46 Ippear .. point.l 21'0.-<:, (IPP. ~'J. The I"Ilfl&ndmng 

_ell (poinl 171k) plotllOme"'hat .bo .... IILe ltntative 

lille "'e ha". d" ... " 10 .. pa .... te brlid, from meande ... 

Point 27! "'ptel(!ntl the Gil"",, Hi"er near Pl1n., 

.nd ".in the dilCl"'l!:e il ollly Ipproximate. Tllia 

poinl fa14IOn>eYIt.lt too 10 .. ' for the lille di"iding brlid.o 

from mHndt... Though Ih, data are approlimatt 

ti,e Kooi and G.ng .. ~u.mpl ... re included healu ... 

th ... n-praent cUH of b .. iding at ,·t'Y l''l!:e dilCh.'l!:". 

The Soil Rin., • north"·ard.Ao,,·ing lributary, Join. 

the Gangel ncar I'ltnl. 0"""1\" 10 the g<"ea~ bl"Hdlh 

of the Ganget;" pl.in. "'bieIL in the CCIltral portion ..... 

_ .. l"",ted principllly by tb" GIlIf!:eo, tbe Son 110 .... 

on • gradient grw,t1y in/lu"oced by lhe Gang..,. i!MII. 

Where Ihe Son joinl lhe GlIli""" both riv~ .. /I" ... u 

.pproximately t he taln" gradient. The G.ngeo, h. ";ng 

• milch llrger d'lCh'l!:8 than tbe Son, hu a b .. id",,-

J)llIern. while tbe Son m""'nd..... Thia illull .... tea the 

principle tho""11 in figure 46, lhat .t I lI'''eD olopt, tM 

braided pattern will be .....,.,iued wilD. • larp d .... 

dllrp and Ihe m","dering plUtrn ..-ith a &mill OM. 

Booideo differtnce. in olope ."d di.ach''l!:8 .... t .. ·""n 

munden and b .... id. our obo",·ationl indic.le tI,.t ilt 

len" .. I. u <OIlltan, IIope b .. id.d elt&rulel • .,.., .110 

ch.racttriuo/ by higher .. idlh : d"plb rltiollhan ...., 

rntIIndt ... 

When a eh.nnd di~id ... roultd.n ioI.nd in I bnoided 

..... d,. Ihe ... p ..... le ch.nnd. h.ve I .m.ller diAch.rge,. 

11'"1". grain lilt. Il\d. aleep" oIope Iltallihe undivided 

dllnn"l. h~.., chllgel.re not p"""liarto b .. idl Iione 

blll.re III the tame d,rec"on .. the On,," ... e ",uaUy filld 

ill • oomparioon 01 amaU and la"" channell ... ith 

lIlere"'''g d...,harp in tbe do ... "'t ....... m direction. 
RIT'EIE CHANNEL PATTERNS 63 

Tlic relation of clianriel pattern to slope and discliargc 

is of particular iritcrwt in conncction with the rcronstruction of the alluvial landscape from profiles of 

terrace remnants and from alluvial fiIls. Changes of 

climate such as occiirrcd in tlic Plcistocenr might be 

accompanied by changes in precipitation md runoff. 

Such variations in streamflow might produce changes 

in the stream pattern without any accompanying changc 

in tlic quantity or caliber of tlie load. An increase of 

flow could result in a meander becoming IL braid; a 

decrease in discliargc could nialw a braidtd channel 

a meandering one. Yet, a change in tlic character of 

tlie load, such as an increase in caliber which the 

presence of ti vallcy glacier might provide, could result 

in an incrcasc in slope and a change from meandering 

to braiding without any changc in the precipitation or 

discliarge. The presence, then, of material of different 

sizes in successivc vallcy fills suggclsts that at diff eren t 

periods in its history the river which occupied the 

valley may have had several distinctive patterns. As 

the pattern of major rivers in an area is a significant 

feature of the landscape, the application of such 

principles to historical geology may prove of somc help 

in reconstructing the past 

SUMMARY: THE CONTINUUM OF CHANNEL 

PATTERNS 

The observations descrihrd above demonstrate tlie 

hnsitional nature of stream patterns. A braided 

stream can change into a meandering one in a relatively 

short reach. Individual channels of a braided stream 

may meander. A tributary may meander to its junction 

with a braided master stream. 

When streams of diff (>rent pat terns arc considered in 

terms of hydraulic variables, braided patterns seem to 

be diffrrentiatrd from meandering ones by certain combinations of slope, discliarge, and width-to-depth ratio. 

Straight channels, liowcv(x, have less diagnostic combinations of these variables. The regular spacing and 

alternation of shallows and dccps is characteristic, 

however, of all three patterns. 

This continuum of channel typt.s emphasizes the 

similarity in physical principles which determine the 

nature of an individual cliannel. Thc next section 

discusses some aspects of these principles. #Itliough 

our understanding of them is far from complete, the 

analysis does indicate the complex nature of the 

mechanisms con trolling diverse natural cliannels. 

THE NATURE OF CHANNEL ADJUSTMENT TO INDEPENDENT CONTROLS 

Many geologists accept tlie idea that geology, cli 

mate, and interrela tcd hydrologic factors are thc ultimate determinants of river morphology. Nevcrthclcss, 

the details of how this control is exercised, pnrtirularly 

with respect to thc. Iiydraulic mcchanisrns, litilvc not bcc~n 

fully described. 

It is thc purpose of this final section of the prescnt 

report to illiistratc, from our field and laboratory 

obswvations, somc parts of the process by which tlic 

river channel is ultimately controlled by geology and 

climate tlirougli the effect of these factors on discliargc 

and bad. 

The shapc and pattwn of tlic river cliannel are detcrmined by the simultaneous adjustment of discharge, 

load, width, depth, velocity, slope, and roughness. In 

order to study the behavior of any of the variables 

separately, the remaining ones must be kept constant. 

Obviously, this seldom occurs in nature. Nevcrthclcss, 

it has been possible to makt. som~ observations in 

natural ehnnels in the field and in the flume under 

conditions in which several of the variables do remain 

constant. These observations of isolated parts of the 

mechanism of adjustment in river channels are presented in the following section. Each example is a 

simplification of the general case involving simultaneous 

adjustment of all of the variables. Segregated into a 

sequence of actions and responses, the process of 

adjustment is somewhat easier to visualize. 

DEVELOPMENT .OF RIVER WIDTH 

During a flood the process of bank caving and cutting 

takes place with relative rapidity. One high flow can 

make more change in channel shape in the direction of 

increasing width than many succeeding days of lower 

flows can alter. It is reasonable to suppose, however, 

that the quasi-equilibrium width of the channel is 

determined not by those floods which occupy the entire 

valley, but rather by discharges wliich attain or just 

overtop the banks of the channel (Wolman and Leopold, 

1957). If tlie u idth is larger than necessary for quasiequilibrium, the unused parts of tlic wide channel are 

taken over by vegetation which not only tends to 

stabilize the places where the roots are present, but tlic 

vegetation itself induces deposition. Tlic cstablisliment of vegetation in unused parts of a natural clianncl 

provides a slow but effective way of reducing a width 

which has been made excessive during high flows. The 

deposition of root-bound mud lumps seen on the bars 

of braided streams in Wyoming is one way vegetation 

tends to become established. It is well known that, 

plant seeds are frequently included in flood debris 

deposited along high-water marks. As described by 

Dietz (1952), lines of even-age vegetation can often be 

observed marking the zone of deposition of seeds on 

sloping river banks. 

We have noted in natiiral cliannels and in the flume 

that the wandering thalweg of a straight reach provides 
64 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS 

an additional mechanism for decreasing the width of 

the channel. Deposition of makrial on the insides of 

these thalweg bends tends to reduce the channel width. 

These areas of deposition may also be associated with 

the loci of vegetation mentioned above. 

The width of a river is subject to constant readjustment if the banks are not well stabilized by vegetation. 

The magnitude of the readjustment depends on the 

nature of the banks and the amount and type of vegetation they support. In the eastern United States river 

banks generally tend to be composed of fine-grained 

material having considerable cohesiveness, and large 

trees typically grow out from the bank and lean over 

the stream. Their roots are powerful binding agents, 

and under these conditions width adjustments are 

small and slow. Only the large floods are capable of 

tearing out the banks. In the semiarid West width 

adjustments appear to be greater owing to generally 

more friable materials making up the banks and to less, 

dense vegetation. Though examples for which adequate data are available are not numerous, a few may be 

mentioned. 

The Verde River in Arizona has experienced in the 

last half century several floods of considerable magnitude, The flood of 1891 widened the channel greatly 

but in subsequent years vegetation became established 

and the width gradually became restricted. The Gila 

River in Arizona has not experienced a great flood since 

1916 and vegetation and deposition have tended to 

narrow thc channel in the subsequent years 

After construction of Hoover Dam the channel of 

the lower Colorado River changed considerably. Data 

on changes of width at Yuma, Ariz., were analysed by 

Leopold and Maddock (1953) who showed that the 

new width is much smaller than existed before the 

higher flows were eliminated. 

If these lines of reasoning are correct, it might be 

supposed that if rivers from a great, diversity of geographic areas were considered, flood discharge would 

correlate more closely with river width than it would 

with any of the other channel factors such as depth, 

velocity, slope, or grain size, because the latter are 

apparently less directly controlled by discharge. Data 

from such diverse rivers as the arroyos in New Mexico, 

Brandywine Creek, Pa., the Yellowstone and Bighorn 

Rivers, and tho upper Green River indicate that such is 

is the case. There is, of course, considerable variation 

in width of streams having equal discharges of a similar 

frequency. Nevertheless, the variation between streams 

at a particular dischargc is small relative to the change 

in width with increasing discharge in the downstream direction. Tliedifference in width between streams having 

equal dischargr appears to be related to sediment concentration and to the composition of the bed and banks. 

The close relation between channel width and discharge is also shown by several runs in the flume (table 

2). Runs 23b and 30d each had a discharge of 0.033 

cfs. Despite the fact that the bed material in run 30d 

was 6 times as coarse as that in run 23,b, and the slope 

about 10 times as steep, each run developed the same 

width. 

TABLE Z.-Comparison of channel factors in two Jume-runs at 

equal discharge 

[California Institute of Technology flume, 19541 

I Run 

~ 23b 30d 

0. 033 

.0036 

.00202 

. 67 

. 0320 

1. 36 

.0117 

. 0523 

The rapidity with which the width of the channel in 

the flume adjusted to the discharge indicates the close 

association of the two. When the water was first 

turned on, if the initial channel shape molded by the 

template was not in equilibrium with the discharge, 

the adjustment of shape took place very rapidly 

indeed. More than 20 runs were made in which the 

initial channel shape was not wide enough for quasiequilibrium with the discharge, and in all of these runs 

the adjustment of the channel width by bank erosion 

and the consequent change of mean depth took place, 

on the average, in less than 5 minutes. The runs 

lasted not less than 5 hours and often as long as 30 

hours. After the initial adjustment in channel width 

within the first 5 minutes, no Subsequent change in 

width took place during the rest of the run. In interpreting this flume observation, it should be noted that 

the channel within the flume was composed of completely uncemented sand without any clay for binding 

the channel banks. An inspection of the cross sections 

of figure 37 shows that the sand banks above the water 

line stood nearly vertical for the duration of a run 

without any tendency for caving or progressive 

widening. 

When a template was used which established a 

channel wider than that which the water would have 

rut-that is, widcr than necessary for quasi-equilibrium-thcrc was little or no adjustment of the channel 

to a narrower widLh except gradually in conncction 

with teridencies for general aggradation or degradation. 

From the cvidencc presented we tentatively concludc 

that the width is primarily a function of discharge. 
RIVER CHANNEL PATTERNS 65 

The magnitude of the effective discharge to which the 

width is adjusted is considered in another paper 

(Wolman and Leopold, 1957) where we argue that it 

occurs about once a year. 

CHANNEL ROUQHNESS AND RESISTANCE 

Onz of the ways by which the lithologic character of a 

basin affects river morphology is the size of the particles 

contributed to the debris load To relate this effect to 

the hydrauli-, mechanisms by which the channel is adjusted, it is nxessary to consider the interaction of 

grain size with other hydraulic factors. 

Engineers are familiar with the concepb (Rouse, 1950) 

that at high Reynolds numbers the Darcy-Weisbach 

resistance coefficient, 

(2) 

is a function of relative roughness. Where the roughness is controlled by the grain size, relative roughness 

may be defined as the ratio of grsin size to the depth of 

flow. 

For flow in pipes empirical relations between resistance coefficient and relative roughness have been obtained, and in thess relations the “grai? size” term has 

usually been defined on the basis of a uniform sand size. 

The size of roughness elements of pipes of various materials are often expressed in terms of “equivalent grain 

size,” that is, uniform grains which gave comparable 

resistance. 

RESISTANCE CONTROLLED BY SIZE OF BED MATERIAL 

The beds of natural rivers are often characterized by a 

wide range of particle size, particularly where the bed 

matericll is gravel. Because of both organized and 

random variation of grain size-distribution over the 

channel bed, the sampling problem is in itself important. 

Furthermore, even when an adequate sampling pro 

ccdure is adopted, one must choosz some representative 

size or some characteristic of the size distribution to 

typify the bed material. 

Thus far no completely satisfactory method has been 

developed for relating grain size in natural rivers to 

resistance. Our approach to the problem has been an 

empirical one. The size-distribution of grains making 

up the beds of several river reaches was measured, using 

a method described by Wolman (1954). Some of the 

size-distribution data are included in appendix G, and 

the values of median grain size determined by the same 

method are shown in appendix H for a more extcnsivc 

list of river locations. 

In our attempt to relate grain size to resistance, the 

grain size parameter cbosen is DS4; that is, 84 percent 

of the material on the cumulative curve is finer than the 

size Ds4. The 84 percent figure is one standard deviation larger than the median size, a choice guided by our 

experience that this size gave the best corrzlation with 

resistance. 

Figure 49 shows an empirical relation between a 

1 

resistanc3 parameter - (where f is the Darcy-Weisbach 

coefficient) and relative smoothn2ss (the ratio of meau 

depbh of water, d, to grain siz3 Da4). The data in figure 

49 are for a number of rsaches of Brandywine Creek, 

Pa., (data from Wolman, 1955). The equation for the 

straight line drawn through tho points is 

$f 

sf= (d)O.B D,, (3) 

The data from Brandywine Creek include measurements of the slope of the water surface which, in conjunction with the measurements of the bed material 

size, are available for very few locations elsewhere. To 

be correct, the slope used in the computation of f 

should be the slope of the energy grade line. Our data 

indicate, however, that for tha purposes of this genera€- 

ized analysis, the differznce between the water surface 

and energy slopes is not significant. 

For streams other than Brandywine Creek, our dah 

do not include water surface slope but only the mean 

slope of the channel bed. The latter is usually a rough 

approximation to water surface slope bub its use constitutes an additional source of variance. It is not 

astonishing, therefore, that when such data arz added 

to those for Brandywine Creek as has been done ill figure 

50, the scatter is gre%ter than in figur3 49. Nsvertheless, the mass of points encompass the points for Brandywine Creek alone and these two figures indicate in a 

g2neral way how geology, through its effect on grain 

size, may influcnce the river channel properties. 

Relative smoothness d 

084 

FIGURE 49.-Relation of relative smoothness and a resistance factor for data collected 

on Brandywino Creek, Pa. 
66 PHYSIOGRAPHIC AND HYDRAULIC STUDIES C)F RIVERS 

t 

M 

in 

.- 

8 

0 

0) 

C 

m 

in 

u) 

+- 

.- 

E 

10 

5 

1 

0.5 

X 

- 

X - 

X 

X 

X 

‘x I 

0.1 

0.1 0.5 

I 

X 

8- 

X 

m 

0 

Opq 

X. 

I 

X 

0’ Maryland and Virginia streams 

X Wyoming streams 

V New Mexico arroyos 

o Brandywine Creek, Pa. 

5 10 50 100 

Onc reason the empirical rclation prcscntcd abovo is 

defined only poorly is that the computed resistance is 

probably not solely a function of thc size of thc brd 

material. Although the data largely reprcscnt streams 

with coarse beds in which tlic ratio of width to dcptli is 

usually greater than 20 to 1, the resistance in somc of 

thcm may be affected by vegetation, channel alinemcnt, 

or otlicr factors riot attributable to grain rouglincss. 

In the event that grain sizc is not tlic dominant factor 

controlling the rcsistancc, thc relation sfiowri in figiircs 

49 and 50 would not apply. 

RESISTANCE RELATED TO BED CONB’IGURATION 

In many natural channels with beds of fine material 

tho roughness of the channel is rclated to the dunes 

and ripples which form on thc bcd rather than to the 

size of the djscretc particles themselves. This relation 

is illustratcd by an csamplc from tlic flume. 

The photoginph (fig. 51) of the bed of thc c~liann~l 

in run 23b shows the size and spacing of dunes. Thcse 

dunes were characteristic of all runs in which tlic bcd 

was composed of fine sand, D,, equal to .00059 foot. 

As tnblc 3 shows, in run 30d t,hc grain sizc was 6 timcs 

as largc 8s it was in run 23b. Figurc 57 shows the bctl 

in riin 30d. When cadi was espcriencing tlic same 

discharge, howcver, the resistance factor in ru11 23b 

was approximately cqual to that in run 3Od. Thus, 

tlic ndjustmcnts in velocity, depth, and slopc which 

accompanied the changes in the configuration of thcb 

bcd of fine sand resultccl in a rwistancc in the bcd of 

fiiic material cquivaleiit to thaL in the much coarser 

channel. Where bed configurntion is important, the 

chaiinel roughness can no longer be considcred cven 

partially inclepcndcn t. Roughness is controlled by 

changes which take plaw in velocit.y, depth, and sloptl 

in rcsporise to changes in discharge and load. Dctailctl 

st,udics of sediment transport by Rgopks (1955) support 

this conclusion. 

SEDIMENT TRANSPORT, SHEAR, AND ItEHlHTANC’K 

‘l’lir cbomplcsity of the problem indimtcd hy thr brkf 

observations on bcd cw~figuration arid resistancc lcads 

directly to a consideration of somc illustrations of t lie 

intcrrclation of rcsistancc, shear, ni\d sediment transI,ort. 

111 sonic of tlic ruiis rnude in tlic Numc~, a dccp 
HI,' EH CJ'A"".:L PATT~H"S 67 

tra[l<!z.oi,lal chan,wl (template ~;. run t-;(). 20a, h, c, 

WM m()I,lrd in t j'e on",1. Though th6 diecharge "early 

filled tho chan nd. tho ... ,,,1 making up the bcd 61 tho 

flun," ,.. ... "61 mo\·",g. I..olld fed a t the uppcr cnd 

of II,,, Aumu w,d",1 to mo,'o do"'"strcam ... II fro"t , 

oediment dCplnileti in ,. I(i" e" reach building up the 

bed ... d JV"dullliy .-wncing tho dep tl, and incre ... i"g 

Ih6 "docity in th" reach. When thc deplh wu ,Ie_ 

creaoed ."ffici"ntly, the grAins I'"W)<I Over lh ~ new 

de!"'Ait ."d wc,e e .... ' i..,] downotream .... Ioe, .. (hey ronod 

o" cr the end of th6 ne .... deposit liko foreset bcd.being 

,l e"""il".1 ,,' a della. 

III run 20. (tahle J ) stuio"s \I li nd 13 are upstream 

lrom the dcplnilional front, an,l .taUon 26 i. ,IO"'n_ 

~Ire&m lrom tl' " front. The dua in Ihe table . how 

IhaL passage of t),o front through II given reach w" accomp~ni I h." an inc,." .. e in vdocity and 810pe and 

• 

T .. e. ~. Co .. ,..ri .. " '" ,,~ .. ; .. ,,' ,.\a •• <1 "", ... .. d o.fl" 1""_ oj ,.d,,.,., I' •• , 1,·. ~::'. ... . tT~~ ,, ~ '""' __ _ 

~~. 

......

_ ... . .... . .... " -, ..... , .. " , ...... ... ,_ '-'.. .... .. "' 

,_ 

... -...... .... -- H, ....... ,... .-..... ~ 

._"_... ~ 

- . ....... , ... ,"",. ,-, ....... _-_. 

---,--""'-r--:::- ~ ~ - ... . . . .,-_ "" ..... .. . 

--

,." ... . 

-... .-. . 

.. 

.

""' ........ ..... ."" "-.. 

':, -... . .... ' .. . " .. . .. , . 

.. 

. ......... .~"- •N•._ • 

-, •,. • 

• • •.. • ~-~~' 

by a (Iecr ~ .... , in hy,l .... uli ~ r.d;u.. The "Ion. (rom_ 

I'ul~d ... .,.110) a~ 8lat.ion 26 i" which no "",lim ~nt wu 

"",..;ng. !'''''',wcr, "ory nearly equabl lhe 81o".r a~ 

s!.aLio" 13 Ihrough .... hid, "",limenL ....... ,,"o,·illl:. Th~ 

movemen t of sedimcnt. how~'·"r. Rt >tation 1:\ ....... 

M80Ciated will, a much lower C$ ", a.n . 

At tho oUlsd 01 run 17 no oedimcnt ....... bei"g 

removoo from th e bed of the cI,a,.nd until .. nd inlrod,,~.,.) at lhr. hea,l of the flume moved down the channel. 

As tho run progr-oo the oedi",,,nt loatl i"tro<.j uced 

i"to Ihe flow Ino,'",) progr_ive!y uo .... ".tr"a,n .... thin 

gl, • .,. of ",aterial along the 1H.~1. Alter I'~e 01 th" 

sheel., mO"CmN,t on the bed wu ronti""ou •. Verlical 

"elocity profil .. ("ken at OIalio", 36.8 belo,"" and after 

1'_1:" of Lhe ah.,.,t nrC .hown in figuro 52. TIo" grain 

. i.e re"'ained c<"'SIRnt ."d Ihe ruo of d""'go of 

,'elocil }" wilh d"pth wu great er when sediment was not 

moving on tI, e be,1. A. Ihe rate of chang<! of "clocity 

with depth is directly proportional 10 the shear velocity 

Rnd tlot Von K".ma" kapp., it i. tentatively _ umed 

tht lho "an'porl of "",limo"t aIle", the "Rlu~ 01 kappa 

... lound loy Vanoni (1946). 

. ... , .. . ... _ , .... "'" ........ of _ . .. ,ho ",-.. ............ "'" .... ,_ ........... _,_,~_, .. _ ......... ' .... "01 .... 

--
" 

, . ...",,', .. _ .. _ .. _ .... _'-,---" , .... ~,.- ............ .., 

a",1 I~Jnpl&I~ .,U-. T .... ",i\;..1 clwlntl ..... molded 

"'jtb • u·"I"'KOidal....,'ior> lining" lOP width or 9 jt>Cb .. 

Mild" d~plh of ~I; I,,~h... K~p"ri~"tf! 1 .. 01 1Iho.'" that 

" diN'hllrg.. of o,oaa d. "''lul.l "'..,u,"" no r .. ;Jj".tm.1ll 

or th" ... idth, Th .. i"itial rhannol ill Ill)O"" in filfUrc! J;3. 

TIlt' nu,,", <10".. ,,'11''''1 U O.GLOJ. In th~ fin! run in 

lilt otfteo no load ..... intrOd.......J 11,orf .... IIl!T"dU1I1 

.';"no"';,,!!' of lilt bNJ dunnl whi.b Illtn' .... aclin 

mo.-rllle"t o,'rr lilt tent .. l as i".h ... Clf Ih. un,t hed 

"',dtl! or 7 ind,,,". T il ..... nl .. J hoi".! of Nnd tnO'·~m."L 

III 1111 ion :!O afltr I hour ."d :!O millUl"," """ I ... -.. in 

liplnt M ..\f'tr IS boW'll of no ... wllh no le."l bem,: 

mtrodLll:f<l. h~ ... hole .,h.."ntl ~ ... ,,"10,",,' of 

finK! (mI;'" "hl furlhr, ,ll'j(Nduinn liD!! in ~fl'~.\ 

~....-d_ Th """dilion III Itlllio" 2(1 .hr. 18 hou", is 

.1>0 .. ." in ~ .... :.5. 

Durin", 1m. d~II'''' lhf 110['" II.Umttl oI~tl~· 

and lilt' "' .... <'Oa,*,n<'<i unlil 1itll~ QI' no mOYeDlttll 

",-""WT1'IL At t!,,, d",,!,"'W' Ih~ .,t •• m I ...... m. ,m.bl~ 

Ie> nKl,'t lh. ma l~rl.l ou ilA 1 ... ,1; thu", thi. 'liJ!'h.l1!~ WM "".UI Ie> kI .. U"... in • PAw",1 ri,·~t "'jllo • ("<NIIW 

bo:ol. n.... ..... tb. dll('~ wu lIN! Jo.... 10 .... ~If""ti,·~. 

Ihe elope could nol be alt..n.l. 

, ............ ' . ...,'~'., -' .. -...... . ""---... , (A ...... ' ............ IO.l Ru" ... ·.re m.d~ l ' Iht "PIe diM:h~ .",1 ipilial 

1101'" h'lrodudog load ., tI,~ rRlI' of 2~ 1l""I1$ pc:r 

A oen.,. of rorut u, d •• Dun, ....... dfSlltOt'd 10 -'>0 .... 110 .. 1 miu"\~ Ind 65 1(Ho"'" pc:r 'UIIl"le. In c ... ~h run tw,..., ~""l of .-.rio ....... teo or mlrodU(IKln .. f R<iimenl to.d ..... ""me .tN'pI'fllu@:of ,h. fflIch futhfsl up Ilro&l1l U 

un dtr con.taul coadiuolW of diloobltp, flUIWl ilope, on p .... ,·ioua i"I\.m:~ on ... b",h • b ... "It'd rn.~1 
1I11':ER ClIANN[L PATTF.Rl<S 69 

developed. The principal part 01 the Hume, hO""""~r, 

through which moved the bulk 01 oediment minu. pan 

of the coar'!le Iraction deposited in the dO"e\oping island. 

remained relat",el~' otabk The slope 01 this low.r 

reach bee.me 0.01t7 in the run (No.:rod) during which 

55 gram. per minute "' .... introdu~. and 0.01t2 in Ihe 

run (11;0. 31) 0124 gram. per minute. 

The moat otriking difference betw~n these two ruu. 

(Nos. 30.1 and 31) in which different qu.ntitica 01 10ftd 

were introduC<!d .... 8a the width 01 the band 01 m""iug 

sediment in the long reach below the d.,·eloping b .... id. 

As can be lOOn hy compariu, the phot~p,," in figur"~ 

56 Bnd 57, the larger introduced lORd (run 30<1. fig. 57) 

wM _iate<! with mo"em."t of the load o,'cr moo! 

01 the bed width. With the .maUer introduced load the 

movement on the bed W,"" confined to a nUr(lW band in 

the center 01 the <lIBnne!. 

Thi . ... ma "ff""l "."" shown by another ""ri ... of run. 

in which .ll partid ... C04""'" tllBn 3.32 mm had bee" 

sieved out of the introduced ... nd lond (app. A). The 

width 01 the moving band of ot't.Iiment appeared 10 

depend on the ,Me of introduclion of load, .. aho"'" in 

table 4. 

In .urnmary, the bed oediment mo,'emenl in the 

lIume tended to con""ntra!O in the center of the bed, 

not only when the bed wu lIat, but .,'en after a central 

rid", began (0 del·.lop. \\'lwn nO central ridge "."" 

beiTlg built. the width of the bnlld of mO"ing sediment 

.... , ...... -....... _ ... ".... ---" ........ --... -

• ., .... r.,_ .... _ .. ..... ........... _. _" .... " ........ _ 

in"",alled will, Ihe amount of load coming into (he 

reach. 

1''' .. ,.- -" .". .r.) li"""') 

" ~ 21. 

" '" " "' lT~ ., 

Another """<'0 of runs in the nume w"" d""igued to 

t""tlhe ....,Ialion bet""~n _Iimen~ load .. nd .Iope at a 

con.t"n~ dischorg<'. The or""" section remained p .... clically OOU6tal)t during Ihe ""i.... The following 

data (table 5) were obtained under oonstant initial 

conditions except rat" of introduction of load. All 

material co r thon 3.32 mm had been screened lrom 

the introduced load, ."d "" a ..... ul~ no island or bar 

appeB,ed. Whell the load w ... introduced a~ various 

rat .. at the .... me discharge (runs 32 to 35) the . Iope 

beeamc adjusted to nearly tho ... me valuo whelher th 

reach w .... stahle or aggrading. Aggradation w ... 

characterized by a gnldual and uniform rise of Ihe bed 

all along the lIume. 
70 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS 

Elkhorn River near Waterloo, Nebr., March 26 to 

April 9, 1952 

TABLE 5.--E$ecl of changing load on stream slope, all other conditions being kept constant 

[California Institute of Technology flume, 19541 

Load inDischarqe troduced 

(cubic feet (grams per 

Rim per second) minute) Slope Condition of channel 

32 0. 033 56 0. 0105 Nearly stable. 

33 .033 115 .0105 Slow aggradation 

34 . 033 175 . 0109 Aggradation. 35 . 033 212 . 0110 Rapid aggradation. 

Despite a .fourfold increase in load, slope remained 

essentially constant. Although this appears to conflict 

with Gilbert’s conclusion (1914), analysis of Gilbert’s 

data shows that the increase in slope which took place 

with increasing load in his experiments was also accompanied by an inc,rease in roughness. In our experiment t>lierc was but a relatively small change in either 

slope or resistance. 

Though slope was little affected by changes of total 

load in the flume experiments, there was some indication 

that at constant grain size, relatively steep slope is 

associated with small discharge and flat slope with large 

discharge. The data do not permit a definite statement 

on this relation. Considering the downstream rate of 

change of velocity, depth, and width with discharge in 

an average river (Leopold and Maddock, 1953, p. 26) 

under tho assumption of constant roughness (f), slope 

must dec.rease with discharge as 

(4 ) (x Q-na 

The part which changing cross-sectional area downstream plays in this relation is unknown. Tentatively, it is believed that at constant grain size, river 

sections having diff crent effective discharges should 

differ in slope, larger discharges being associated with 

flatter slopes. 

Section A-2, Rio Grande at 

Bernalillo, N. Mex., April 

to June, 1952 

OBSERVATIONS OF ADJUSTMENTS IN NATURAL 

CHANNELB 

Measurements in the flume are complemented by 

examples drawn from larger rivers illustrating the same 

principles of adjustment. Table 6 indicates the nature 

of the adjustments which accompgny changes in sediment load at constant discharge. Unfortunately, 

there are few rivers for which data on the flow parameters, including slope, are available and the data for 

these few suffer because suspended load but not bed 

load was measured. 

In table 6 the flow characteristics of the Elkhorn 

River, which are compared at a discharge of 6,000 cfs, 

represent the rising and falling sides of a hydrograph. 

The rising stago was typified by a lesser depth and lesser 

slope, and a greater velocity and greater load than the 

falling stage. The elevation of the bed remained the 

srtme. The larger load of the rising stage was associated 

with lessar roughness. This lower resistance led to a 

greater velority and a lesser depbh despite the slightly 

lesser slop-,. The product of depth times slope, which is 

directly proportional to the shear, was less in the rising 

stage, and thus tlie larger load was associated with the 

lesser shear. It is presumed that the increase in velocity associated with the lesser roughness was of greater 

importance than the relatively small diff erencc in shear 

in promoting equilibrium with the large load. 

Also in table 6, the data on tlie Rio Grande at Bernalillo show another type of adjustment. The rising 

stage was characterized by a lesser depth, greater 

velocity, and greater load than the falling stage. In 

the falling stage, slope was somewhat less, and thus the 

smaller load was associated with the lesser shear. 

Here, then, the greater shear was associated with the 

larger load, but, as in the Elkhorn River, the total 

resistance was less when the load was large. 

TABLE 6.-Examples from river data of adjustments of depth, velocity, and slope to changes in suspended load at constant discharge and width 

Stage 

Rising Falling Rising Falling 

6, 000 

255 

4. 90 

4. 8 . 00038 

06, 000 

7. 8 . 114 

.o1n 

6,000 

263 

4. 56 

5. 0 

. 00046 

74,000 

7. 8 . 143 

.028 

.04 

__. 

4,700 

275 

5. 5 

3. 1 

.00094 

46,000 

3. 2 

. 182 

. 025 

13 

3 2 

4,700 

275 

5. 0 

3. 4 . 00084 

21,000 

3. 2 

. 178 

.029 

. 13 

. 32 
RIVER CHANNEL PATTERNS 71 

SUMMARY AND INTERPRETATION 

From these diverse observations on the nature of 

channel adjustments to independent controls we draw 

several tentative conclusions: 1. Channel width is 

largely determined by discharge. The effective discharge we believe to be that corresponding approximately to bankfull stage. 2. Where resistance is controlled by the roughness provided by discrete particles 

on the bod of a channel, the resistance factor may be 

correlated with the size of the particles. 3. Where the 

configuration of the bed enters into the determination 

of roughness, the resistance is a function of the discharge 

and load and represents a simultaneous adjustment of 

velocity, depth, and slope. 4. The load transported at a 

given discharge is riot solely a function of shear and 

grain size. At a constant shear decreased resistance 

appears to be associated with greater transport. The 

resistance is not necessarily governed by caliber of the 

load but may be determined principally by bed configuration. 5. In the flume-river the width of th? band 

of moving sediment was often less tlian the width of the 

channel, and width of the band was related to the 

quantity of load being transported. If such bands 

exist in natural channels, errors might result from estimates of total load based on computations of load per 

foot of width multiplied by the total width. 6. Where 

no change in roughness occurs at constant discharge, a 

large increase in load is not accompanied by an ap 

preciable increase in slope. Both aggradation and 

degradation may occur, therefore, without change in 

We shall now attempt to construct a general though 

oversimplified picture of the way in which the shape and 

pattern of a natural channel may be determined by the 

river itself within the framework provided by the 

climate, rocks, and physiography of the region in which 

it lies. 

In a given region the magnitude and character of the 

runoff are determined by climate and lithologic factors 

quite independent of the channel system. The amount 

and distribution of precipitation, and characteristics 

which affect the runoff, are functions of the climate. 

The topographic and lithologic character of the drainage 

basin helps to determine, in conjunction with vcgetation, not only the characteristics of the runoff, but of 

equal importance, it greatly helps to determine the load 

of debris delivered to the channel systcm from the 

interstream areas and from the stream margins. Both 

quantity and nature of the load are greatly influenced 

and often are primarily governed by geologic factors. 

Exceptional runoff is accompanied by conditions 

which increase the movement of soil and rock debris. 

Of particular importance are datively large amouncs 

of rainfall, often at high intensity, and saturated soils. 

slope. 9 

Moreover, large volumes of runoff are associated with 

relatively large depths of flow both in rills and in overland flow. These depths are accompanied by relstivsly 

high flow-velocity and increased transport of debris to 

the chsnnel system. For such reasons large flows are 

usually accompanied by large loads. 

In a given period of time there are far fewer large 

AOUW than small or moderate ones. An intermediate 

range of discharge includes flows that occur often 

enough in time and possess sufficient vigor to constitute 

the effective discharge (Wolman, 1956). During these 

flows the river can move the material on its bed and in 

its banks and thus is capable of modifying its shape and 

pat tern. 

It is within the framework of these characteristics of 

runoff of water and sediment that channel systems 

develop. The water and load, including their time and 

space distribution as well as quantity, that are delivered 

to the channel system are functions of the climate and 

geology. The water and load carve the channels that 

transmit them downstream. To the water and debris, 

therefore, the channels ultimately owe their shape and 

pattern, but processes within the channel itself effect 

specific modifications. 

Channel width is primarily, determined by discharge. 

Widening is rapid relative to other changes and the 

channel generally tends to become adjusted at the 

width provided by large flows near the bankfull stage. 

The roughness of any reach of a channel is governed, 

initially at least, by the geologic character of the bed 

material supplied by the drainage basin. Although 

abrasion and sorting may modify the material on the 

bed, the rock character partly determines the extent of 

such modification. The roughness may be primarily 

grain roughness. Alternatively, owing to the size 

distribution of the particles and their movement, the 

rugosity may be due to the configuration of the dunes. 

ripples, or waves in which the particles on the bed 

arrange themselves. 

The roughness of the boundary affects the stress 

structure and the velocity distribution in the flowing 

water. In addition, turbulent eddies near the bed 

produced by the roughness elements lift particles of 

debris off the bed. These alternately move forward in 

the current and ,settle back to the bed under the 

influence of gravity. Not only the resistance then, but 

also the movement of debris through turbulence and 

shear is related to roughness. 

At a given discharge, with width fixed thereby, 

velocity, depth, and slope become mutually adjust'ed. 

To visualize the nature of this adjustment, one may 

assume temporarily a value of slope. With slope given; 

velocity and depth must mutually adjust to meet two 

requirements: The first is that the product of width, 
72 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS 

depth, and velocity is equal to tlie valiie of discharge, or 

Q=wda (1) 

Tlie second is the relation of resistance to depth, slope, 

and velocity, which is expressed by the equation for tlie 

Darcy-Weisbach coefficient, 

Tlie resistance f can be assumed to be fixed by the 

materials in the bank and on the bed. 

These two equations must be satisfied. They contain 

six factors, but where four of the factors are fixed or 

temporarily assumed, these two equations fix the 

remaining two variables. 

At a given discharge width is considered fixed. 

Resistance is determined by the nature of the material 

in bed and banks, channel configuration, and bed 

condition. Slope has been temporarily assumed. 

Hence, velocity and depth become deternmined by thest. 

two equations. 

If this combination of depth, velocity, and slope constitute a channel that will transmit the given dischargc 

and load without erosion or deposition, the slope is not 

altered. If the hydraulic factors of the channel are not 

in equilibrium with the imposed load, erosion or deposition will occur. By such action the slope of relatively 

long reaches of the channel is altered and as the alteration occurs, the velocity and depth also are changed. 

This explanation provides a perspective of how tlic 

several variables interact to make the channels which 

are observed in nature. These variables are interdependent, but their relative order of importance is 

believed at this time to be generally as outlined above. 

If correct reasoning about the relations of geologic and 

other factors to fluvial processes is to be achieved, it is 

necessary to determine the relative independence of 

these variables. 

In further explanation we reason that if, for example, 

a river is able to mova the size of material in the load but 

is unable to transport the total quantity of load brought 

into the reach, deposition may take place along the 

reach with little or no change in slope. During a flood 

in an alluvial river if deposition occurs 00 the bed, this 

deposition at a constant width is customarily accompaiiied by a decrease in depth and consequent increase 

in velocity through reduction in cross-sectional area. 

The increase in velocity at the expense of depth implies 

that deposition on th3 bed does not cause an equal rise 

in elevation of the water surface and of tlie bed. 

Our studies indicate that an increase in load at a 

constant discharge is usually accompanied by a decrease 

in bed roughness which serves to increase the velocity. 

The adjustment in depth then, and the smoothing of 

the bed are inextricably related. It is, of course, 

possible that the increase in capacity resulting from the 

increase in velocity is still inadequate to transport the 

total load, in which event both the bed and the water 

surface will rise. 

If a stream can move only some of the sizes in tlie load 

provided to tlie reach, the process of adjustment is 

similar to the one described above save for the fact that 

by winnowing from the bed certain sized fractions only, 

the mean size of the bed material is increased. This 

increased size will be associated with an increased slope 

over the entire reach, thereby increasing the total 

capacity for transport of all movable sizes. 

APPLICATION OF OBSERVATIONS ON CHANNEL 

ADJUSTMENT TO THE PROBLEM OF CHANNEL 

PATTERN 

As explained, eight and possibly more variables enter 

in a consideration of natural stream channels : discharge, 

amount of sediment load, caliber of load, width, depth, 

velocity, slope, and roughness. Each of these factors 

varies as a continuous function; that is, within the 

limits of observed values, any intermediate value is 

possible. The factor having the largest range of values 

is discharge, for in natural channels it can vary from 0 

to any amount less than 10,000,000 cfs. Load, expressed as concentration by weight, varies from nearly 0 

to about 500,000 ppm. (:aliber of load, expressed as 

median grain size, may vary from a value near 0 to 10- 

foot boulders. Width of natural channels varies between a few tenths of a foot to about 20,000 feet, mean 

depth from 0 to an amount less than 80 feet, mean 

velocity from near 0 to less than 25 feet prr second, 

slope from near 0 to 1 .O, and resistance, expressed a? the 

dimensionless Darcy-Weisbacli number, from about 

0.001 to about 0.30. 

Combinations observed in nature are far more 

restricted than the permutations of the values of the 

eight variables. To our knowledge, for example, rivers 

capable of discharging more than 1,000,000 cfs do not 

have slopes in excess of 0.0009 and usually less than 

0.0002. 

Channel patterns, braided, moandering, and straight, 

each occurs in nature throughout the whole range of 

possible discharges. Some of the largest rivers in the 

world are braided; for example, the lower Ganges and 

Amazon. More are meandering, of which the lower 

hfississippi is the best known example. Meanders an 

cornlnon in very small creeks, and braids are common 

in many small ephemeral streams. Both meanders and 

braids have been observed in the laboratory at discharges less than 0.1 cfs. The straight pattern occurs 

at all discharges. 

a. 
RIVER CHANNEL PATTERNS 73 

Our observations iiitlicatc that brsicls terld to occur 

in c~lianncls having certain combinations of values of the 

flow factors, and tliat mpanders occur in diffcrcrit 

combinations. ’l’lie straight pattern can occur in 

either. Specifically, at a given discharga, braids seldom 

occi~r in clianiic~ls linvirig slopesa less i liaii t~ certain 

value, wIiil(1 meantlers stxldom occur at slopes grcxatcr 

than that same valur. 

’I’liesc considciatioris t ogetlier with thc tictails discussctl carlier in this study lead to oiic of tlic principal 

points of tlic prtserit discussion : Tlic~rr IS a continuum 

of natural stream channels having diffrrcnt cliaracteristics that are rcflectetl in combinations of values of tlir 

hydraulic factors. The channel pattrrns, braided, 

meantlcring, arid st raigli t, oacli is associated with 

certain of tlicsc. combinations. Tlic combinations of 

liydrniilic factors that exist in most natural channels 

are those which represent quasi-eqiiilibrium between 

the iiitlrperideiit factors of discharge and amount and 

caliber of load, uiid the dcpentlent factors of form and 

liytlrwlic cliaract wistics of the cliannel. Braided, 

meantlcring, uiitl stloiglit patterns, in this concarption, 

mc‘ among tlic forms of cliannels in quasi-equilibrium. 

This conception fits tlic observntioris that a given 

clianncl can clriauge in n short distance from a braid 

to a nicmider or vice versa, that tlic divided cliaiiriels 

of ti braid mnj- mcander, and that a meandering 

trihutarj- may join a brnidcd master stream. Such 

clit~nges in a givcii channel or such tliffcreiit channels in 

juxtaposition can bc attributcd to variations in locally 

intlcpcridcnt factors. 

REFERENCES CITED 

Brooks, A’. IT., 1055, hlerliariics of streailis with rriovable beds 

of fine sand: Ani. Sor. Civil Nngiiieers l’roc., v. 81, p. (X8-1- 

668-28. 

Chicii, A’iiig, 1955, Graphic dcsigii of alluvial chaiinels: Am. 

Soc. Civil Engineers l’roe., v. 81, 1). 611-1-611-17. 

Diet,x, R. A,, 1!)52, The evolution of a gravcl bar: Mo. Bot. 

Gardens Annals, v. 39, p. 249-254. 

Ditt,breiiiter, 15. F., 1954, Discussion of rivcr-lmi scour during 

floods: Am. Soc. Civil Ihginccrs hoc., v, 80, p. 479-1;<- 

479-16 (separate pub. no. 470). 

Eiiisteiii, H. A,, 1950, The bed-load friiictiou for scdirnent 

transportat,iori iri open chaniiel flows: U. S. Ilept. Agr. 

Tech. Bull. 1026, 71 p. 

Fraiiziiis, Otto, I!G6, Waterway engineering: Canibridge, Mass. 

Inst. Tcclinology Press, 527 p. 

Friedkill, J. F., 1945, A laboratory study of thc inearidering of 

alluvial rivers: IT. S. Waterways I‘lxpt. Sta., Vicksl)lirg, 

Miss., 40 p. 

Gilbert, 6. K., 1914, Tlic t,ramport,atiorl of debris by runliilig 

water: IJ. S. Gcol. Survey Prof. Paper 86. 

Iiiglis, C. C., 1940, Cerihal Board Irrigat,ioii Aliliual Itept. 

1949, The behavior and coiitrol of rivers a~itl callals: 

Central Waterpower Irrigat,iori arid Navigat io11 I<csearch 

Sta., Poona, India, v. 13, pt. 1, 283 p. 

Jacksoii, J. It., 1834, Hints on t.lic subject, of gcographical 

arrangement aiid nomeiiclat urc: Royal Geog. SOC. ,Jour., 

Leopold, I,. B., and Maddock, Thomas, Jr., 1953, IIytlraulic 

geonictry of st.reani ctiaiiiiels and wine physiograpliic 

implica(ioiis: U. S. Gcol. Survey Prof. Paper 252, 57 p. 

Leopold, I,. U., arid hfiller, J. I’., 1956, Ephenicral strcainInydrarilic factors and their relat,iori t,o t,he draiiiagc net : U. S. 

Geol. Survey Prof. Paper 282-A. 

Peale, A. C., 1879, Report on the geology of tlic Green 1tivc.r 

dist,rict, in Hayden, F. V., [J. S. Geol. aiid Geog. Survey 

Tcrr. !Mi Aiiri. Itept., 720 p. 

Pcttis, (2. R., 1927, A new theory of river flood flow: privately 

printed, 68 p. 

Quraishy, M. S., 1944, The origin of curves in rivers, Current Sei., 

Rouse, H., edit,or, 1950, Ihgineeriiig hydraulics: New York, 

.Johri \\‘iley I% Soiis, 1013 11. 

Rubey, W. IV., 1052, Geology ad niiiieral resources of the Ilardiil 

and Brussels quadrangles (Illinois) : U. S. Geol. Siirvcy Prof. 

Paper 218, 179 p. 

ltusscll, It. J., 1954, Alluvial nlorphologp of Aiiatoliaii rivcrs: 

Assoc. Am. Geographers Arinals, v. 44, no. 4, 11. :363-391. 

Schafferiiak, F., 1950, (;rrindr der Flusstnorphologic uiid des 

Flrissbaues: Wieii, Springer-Verlag, 115 p. 

Vaiiorii, 1’. A,, 1946, Transportation of suspended sediincnt 1)y 

water: Ani. Soc. Civil Eiig. Trans., no. 111, p. 67-133. 

iVolinati, RI. G., 1054, A method of sampling coarse river-bed 

material: Am. Geophys. IJnion Trans., v. 35, no. G, p. 951-956. 

~_- 1955, The natural chaniiel of Brandywine Creek, Pa. : 

IT. S. Geol. Snrvey Prof. Paper 271. 

1956, Frequency aiid effective force in geomorphology: 

Am. Geophys. Union Trans. (in preparat,ion) . 

Wolnian, hI. G., and Leopold, L. B.. 1057, River flood plains; 

sonic observations on their forination: U. S. Geol. Survey 

Prof. Paper 282-C (in press) 

1939-40, I’uhl. 110. 24. 

V. 4, 11. 72-88. 

v. 18, p. 36-39. 
A PPENDlX 

36 

37 

44 

48 

32 

44 

APPENDIX A -Analyses OJ stzes of sand used in flume experiments and fed into Jlume-river, 1954 

[California Institute of Technology flume] - __ ~- - 

I 

Mcdiari 

bize (inm) I I 078 I 156 

fercrnt finer than given sile (millimetem) - 

61 80 64 83 6iJ 8fi 73 89 

56 78 68 85 

Medium sand: I 0.90 

1.00 

.a2 

.72 

.65 

.73 

Run I. February 12 ....................................................... 

Rull10 Februxry2F ........................................ 

Run 12: March 5. ..................................................... 

Riiri17,MurchIl .............................................. 

Ruri18,March15 ...................................................... 

............ 

............ 

........... 

.......... 

........... 

Run20,AtarchlE ...................................................... ........... 

Run 22, March 24. ......................................................... 

Run34,AprilIB ........................................... ...I 

Fine mud: 

Medium sand screened of all particles >3.32 mm: 

G9 

.......... 

......... 

......... 

......... 

................... 

3.nn 4.20 1.75 3.60 

.48 1.30 .75 2.2s 

.I7! .R1 I. ......... 

- 

7 

3 

1 

7 

2 

3 

42 

6 

,312 

___- 

IS 

15 

17 

17 

12 

17 

93 

20 

98.G ... ......... 

49 

APPENDIX B.-Data on size characteristics of sand on channel bed and on bars in flume-river, 1954 

[California Institute of Technology flume] 

1 1 Percent flner than given size (millimeters)- I j Size in niillinieters 

Median 

Station 6. February 12 ............................. 2.10 .......... 

Station 10, February 12 .......................... 1.45 .......... 

Station 16, February 12..~ :... ..................... 1.30 .......... 

Bar or island in braided reach: 

Channel hed, unbraided: 

RUN 12, MARCH 5 

Braided reach: 

,156 

__ 

1.2 

3 

S 

....... 

.. 

.... 

,312 

7 

14 

19 

........ 

........ 

........ 

........ 

........ 

......... 

.R2S 

20 

28 

35 

......... 

......... 

1.2s 

__ 

35 

45 

49 

........ 

........ 

........ 

........ 

........ 

........ 

58 

65 

......... 1.80 3.75 

......... 1 1.251 3.20 

.................. 

................... 

........ 

1. 7s I. 55 2 74 2.21 

.33 2. ti0 

57 2. 56 

3x ~ 2. 90 

75 

APPEN~IX D.-Comparison of hydraulic characteristics of undivided and divided reaches of braided streams 

-- 

Reach 1 (1953) I Reach 2 (1954) 

i Green RivgF Daniel, 

I .~_______~- 

Feh. 15 i Feb. 16 

Hydraulic factor 

Braided reach 

~ 

Right 

1 Braided reach 

Undivid. -I ed reach 

Undivid. 

ed reach 

Area .............................. square feet .. 

Discharge.. ........... ..cubic feet per second.. 

Width. ................................. -feet.. 

Mean depth .............................. feet.. 

Velocity ...................... .feet per second.. 

Slope. ......................................... 

Resistance factor ............................... 

Shear velocity.. .............. feet per second.. 

Jndivid- 

!d reach 

0,0657 

,085 

1.32 

,050 

1. 29 ,0079 

,050 

,102 

152 

305 

65 

2.3 

2.0 ,0029 .43 

.46 

Braided Undivid 

reach ed reach 

0,0684 0.0631 ,085 ,085 1.60 1. 19 ,050 ,053 1.24 1.34 ,0133 .0095 

,083 , ,064 

,126 ~ .119 

-~___ 

Right 1 

70 

120 

.44 

1.6 

1. 7 ,0029 .41 

.41 

169 

425 

70 

2.4 

2. 5 ,0005 .04 

.49 

New Fork River near Pinedale, Wyo. 1 Flume at California Inqtitute of Technology, 1954 

,085 

1.90 

,029 

1.53 

,0157 

,044 

.085 

1.28 

.055 

1.20 

.00*1 

.070 

Left 

25 

35 

35 

.7 1.46 ,00286 .24 

.25 

______ 

Sta. 10 

Undivid- .___ 

Braided 

reach 

ed reach 

i - 

Braided reach 

Left 1 Right 

82 

290 

64 

1.3 

3.5 ,00286 

....... 

....... 

105 

325 

54 1.94 

3.1 ,00125 

,065 ......... 

52 

i.:aa2g4. ~ .:oozsl- - - .:ooii4- 

.......................... 

........................... 

0.0619 ,085 

1.38 

,045 

1.37 

.0104 

' , ?!: .." 

Sta. 14 j Sta. 14 1 Sta. 22 

Feb. 18 

Sta. 14 I Sta. IO 

____ 

Braided 1 Undivid 

reach i ed reach 

~~ 

Mar. 5 

Sta. 12 1 Sta. 38 

_- 

Braided 1 Undividreach , ed reach 

0.0748 ,093 

2. 15 .035 

1. 24 ,0165 

,0865 

,129 

0.0699 ,093 

1.27 

,055 

1.33 

,0095 

.OM7 

,123 
PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS 

Serial 

No. 

21 

23 

24 

25 

27 

30 

32 

36 

42 

43 

44 

45 

48 

49 

51 

51 

51 

54 

65 

67 

B8 

71 

84 

259 

259 

260 

260 

2Fo 

260 

260 

260 

261a 

261h 

261c 

261d 

I1 

I2 

I3 

I4 

I5 

I6 

I7 

I8 

I9 

I 10 

I11 

I12 

I 13 

I 14 

I 15 

I 16 

APPENDIX E.-Data on wavelength of meanders, bankfull discharge, arid bankfull width 

[e estimated, pattern: M meander, S pool-and-riffle spacing in straight channcls] 

Location 

Duck Creek near Cora Wyo.. ................................. 

Buffalo For& near Jae&on Wyo. (Flybox reach)--. ............ 

Wind River,'near Dubois, Wyo. (Dumb Cowboy reach) ........ 

IN Noir Creek, near Dubois, Wyo .............................. 

Pop0 Agio River, near Hudson. Wyo. (Joyful reach) ............ Watts Branch, Viers pasture near Rockvillc Md ................ 

Crooked Run, near State College, Pa. (Save'the Meander reach) 

Mississippi R., near Blytheville. Ark. (Tamm Bend reach) -. .- 

Baldwin Creek, near Lander, Wyo ............................ 

Brandywine Creek, near Cornog, Pa.. ......................... 

At Seven Springs, Pa- ...................................... 

At South Downingtown, Pa ................................ 

Wawaset, Pa..-- ........................................... 

Friedkin flume .................................................. 

Embreeville. Pa ............................................. 

uraishy flume .............................................. 8 hristians .. Creek near Staunton, Va. (Orange bridge reach) ___~ 

Barterbrook Creik Route 254near Staunton Va .............. Middle River at dethlehem Church near Staunton, Va ...... 

South River, hear Lipscomb, Va. (Black Bull reach) ............ 

Slab Cabin Creek, near Lamont. Pa.-. ......................... 

Brooks' flume ................................................... 

.... do ........................................................... 

Meander model, Central Board Irrigation Expt. Sta., Poolla, 

India. 

bran do ........................................................... .... do ........................................................... 

.. do ....................................................... 

Mississippi R., above Cairo, Ill. ................................ 

Below Tiptonville, Ill.-. .................................. 

Near Blytheville, Ark ....................................... 

Missouri R., at Bismark, N. Dak.. ............................. 

RIVERS IN ORISSA, INDIA 

Mahanadi, helow Jobra--. ...................................... 

Berupa. below weir.. ...................................... 

Mahanadi, below Chitertola.- ................................. 

Pyka ............................................................ 

Nuna .......................................................... 

Chitertola, below Nuna.. .................................... 

Katiuri. helow Surua head-. .................................... 

Bhargovi ........................................... 

Daya-. ..................................................... 

Bhargovi. below Achhutpur ..................................... 

Dnya. below Belmora escape- .................................. 

Brahmini..- .................................................. 

Kharsua ....................................................... 

Bnitarani ....................................................... 

Estimated 

hankfull 

discharee 1 

(cubic fert per second) 

~~ 

I, 200 

340 

470 

1, 700 

1, nno, non 

I xn 

I, 400 

1, nnn 2, 2nn 2,500 .15 

.10 

. 05 

,021 

2x0 

no0 

.28 

240 

r 45 

780 

680 

560 

230 

.21 

. 175 

.175 

.175 

.175 

.40 

.IO 

610. om in, no0 

237, oon 338. 000 112,000 

155 0 0 

159,000 

111: 080 

47,500 

29,000 

34, ooo 

650, OOo 

162, OOO 

260,000 

Wavelength 

(feet) 

. 110 

I, :<no 

800 

1,400 

34, ono 

290 

120 

50 

160 

400 

no0 

1, 200 

ROO 

800 

2n 16. 2 12. 4 6. 8 

I2 215 

190 

380 

3. 4 

c zoo 

240 

4.0 

14 

12. 5 14. 5 

14 

24 

16 

29, WO 41,700 

32, 700 

20.600 

21.600 

7. ,500 

lfi, 200 

16,800 

8,000 

10,500 

8,400 

10,800 

14,400 

7,200 

7. 500 

5,700 

4, KJo 

21,600 

8,000 

10,800 

Bankfull 

width (feet) 

_____ 

8 

150 

30 

BO 

22 

8 

25 

53 

78 

72 

92 

74 

2.1 

1. 5 2. 3 

.92 

31 

3 1 

29 

60 

e 15 

.66 

1 no 

3,400 

2.270 

3, mil 

2,800 

1.320 

............ 

............ 

............ 

............ 

............ 

............ 

........... 

............ 

............ 

............ 

............ 

............ 

............ 

............ 

Pattern 

nt 

M 

M 

M 

M 

M 

M 

Mz 

M 

S 

S 

S 

S 

S 

M 

M 

M 

iM 

M 

M 

M 

M 

M 

S 

S 

M 

M 

M 

M 

M 

M 

M 

M 

M 

nf 

......... 

....... 

.......... 

......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

Source of data 

Authors no. 

110. 

Do. 

T)o. 

110. 

DO. 

110. 

1)o. 

Do. 

DO. 

110. 

I)o. 

Friedkin (1945). 

Quniisliy (1944). 

Authors. 

no. 

N. H. Brooks, personal commnnic:iInalis (1949, p. 150). 

tion. 

no. 

no. 

Do. 

Do. 

Do. 

Do. 

DO. 

Do. 

Do. 

Corps of Enginecrs maps. 

Inglis, (1940, p. 111) 

Do. 

Do. ' 

Do. 

Do. 

Do. 

DO. 

Do. 

DO. 

Do. 

Do. 

Do. 

Do. 

Do. 

Do. 

DO. 

I For method of estimating bankfull discharge see footnote to corresponding serial number in appendix F. 2 At gage height, M It. 

w 
Serial 

No . 

... ........................................................... ~ ~ ~~~~~~ 

.. do.-.----- 

(rixht cliannel).-.--~ ................................... ................... 

(lrftchanncl) ................................................................... 

Dock Creek, ncar Cora . Wyo ............................................................... 

Snake R . below mouth of Hohack R.,.ncar Jackson, Wyo ....................................... 

Buffalo F&k Flyhox rearh nwtr Jackson, Wyo .............................................. 

Wind R .. Idmb Cowhoy reach above Dubofs, Wyo .......................................... 

Du Noir Creek, above Duhois, Wyo .......................................................... 

Pop0 Agio R . Joyful reach near Hudson, Wyo ........................................... 

Litt1ePipcC;eekncar Avondale, Md ...................................................... 

Watts Branch, Viers pmtnre, ncar Rockvillr, M(1- ........................................... 

Srnrcn Creek at Dawsonville, Md 

Scnwa Crrek: at Rifaeford near Rockville, Md ................................................... 

Mississippi R., at Tamm Bend nrar Rlythcville, Ark ......................................................... 

Raldwin Creek ncar Lander, Wyo. Brandywine Creek, at Cornog . pa^ .......................................................... 

-at Emhrecville, Pa Christians Creek, at Oranarbridgenear Staunton, Vn ......................................... 

MiddleR . atBethlehemChurchnear Staunton, Va ......................................... 

South R., black Bull reach south of Mt . Vernon Church near Lipscomb, Va.~ .................... 

YellowstoneR.,at Rillings . Mont-----.-.- ............................................. 

WindR nearRurris Wyo Middle Piney Creek'helow South Forknear Big Piney, Wyo.--.- ....................... 

Little Sandy Creek, near Elkhorn, Wyo .................................................. 

-at Ogden, Kans ........................................................... ......... 

-atWamngo,Kans ..................................................................... 

Fall Creek near Pinedale, Wyo .......................................................... 

West Pork' Rock Creek helow Basin Creek, near Red Lodge, MonL ........................... 

Rock Crrek, near Red Lodge, Mont ...................................................... 

ClarksFork,nearEdgar,Mont ........................................................... 

ClearCrwk nearBuffalo Wyo ..................................................... 

RedFork,nearBarnum, Wyo .......................................................... 

RockCreek atRoherts, Mont ........................................................... 

BullLakc Creek,ncarLenore, Wyo ....................................................... 

Smke R.,ncar Wilson, Wyo ......................................................... 

Big Sandy Creek, ncdr Leckir ranch, Wyo ................................................. 

Hams Fork, near Frontier, Wyo ................................................................ 

NorthForkPowderR .. nearKaycer.Wyo ............................................. 

Bagmati R., above Dhang, India ............................................................................. 

- below Dhang, Ind is ...................................................................................... 

Kosi R., above Dhamarghat,. India ............................................................... 

- above Dhamargbat, India ................................................................................... 

-belowDhamarghnt,Indi:~ ....................................................................... 

QangesR.,nearPatna India.~~ ............................................................................. 

ChenaR ..nearFairbsnk s.Alaskn. ............................................................................. 

OroenR ..atI)anirl,Wy o.(undivided) ..................................................... 

New Fork R., at American Gothic Iteacli nwar Pincdale, Wyo ................................... 

- 

- 

............................................................. 

........................................................... 

...................................................................... 

. .................................................. 

KansasR.,at Lemmpton.Kans--~-~- ................................................... 

North Fork'Clcar Crcek, hear Rangor station near Ruffalo, Wyo .............................. 

Pole Creek,').$ mile below Little Half Moon Lakenear Pincdale, Wyo~-~- ................... 

Yukon R., ncar Holy Crrss, Alask:% ......................................................................... 

6 

7 

8 

9 

llh 

12b 

14a 

14h 

14c 

18h 

21 

n 

23 

24 

25 

n 

28 

30 

31 

33 

36 

42 

43 

48 

65 

68 

71 

89 

Bo 

125 

128 

151 

152 

151 

a7 

229 

230 

231 

232 

233 

234 

235 

256 

2bl 

266 

267 

268 

269a 

269b 

moa 

270b 

noc 

271 

286 

287 

in 

im 

24o 

204 

660 I 

............. 

............. 

372 5 

345 

55 

93 

700 

8 

4 

15 

21 

26 

117 

24 

18 

69 

1i.m 

34 

21 58, 420 

45, 240 

55, 240 

37 

60 

in0 

2, 115 

120 

29 

142 

4 270 

87 

222 

2, nnn 

95 

298 

980 

3, 440 

inn 

I, 220 

B, no0 

RIVER CHANNEL PATTERNS 

APITXDIX F.-Data on estimated bankfull discharge at various stream sections 

[Pattern: €3 hraidcd. M meander. S straight] 

Stream and location Drainage area (squarc miles) 

Little Pom .. Aeie R . niw Lander .... . Wvo ........... ~~ ....... -.I New Fork R., Jenkins Ranch nehr Cka. Wyo ...................................................... 

Green R., at Warren Bridge neiir Daniel, Wyo ............................................ 

Reaver Creek, near Ihniel . Wyo ............................................................... 

New Fork R .. below New Fork Lake ncar Cora . Wyo. ........................................ 

Horsecrock. ncar Daniel. Wyo .............................................................. 

Cottonwood Creek.near Daniel . Wvo ................................................. 

108 

45 

46M 

141 

36 

124 

204 

~- 

Pattern 

S 

B 

S 

B 

S 

B 

M 

B 

S 

M 

R 

B 

M 

B 

M 

M 

M 

M 

M 

M 

S 

S 

M 

M 

S 

S 

M 

M 

M 

R? 

S 

M 

S 

M 

M 

M 

S 

S 

S 

S 

S 

S 

S 

S 

S 

S 

B 

S 

M 

S 

13 

M 

B 

B 

M 

B 

M 

M 

. 

. 

Slope 

0.0049 

. 0047 

. 0034 

. 0066 

. 0051 

. 0073 

. no1 1 . 0041 

. on05 

. nom 

. nom 

. wnig 

. no21 

. wn45 

. no37 

. onnm 

. on184 

. 00473 

. no31 

. nom 

. no21 

. nnooag 

. 0038 

. 0015 

. no21 

. 000x4 

. oonB 

. on4 

. nin 

. 000370 

. 000379 

. 000316 

. 035 

. 021 

.nom 

. 0038 

. 0086 

. on81 

. no43 

. 00425 

. 0013 

. no38 

. oonig 

. no038 

. noon95 

.eons 

. 0029 

. 00093 

. 00068 

. 0091 

. 036 

. 024 

. 028 

. 0018 

. 00057 

. 00095 

. 00038 

. 000066 

79 

Estimated 

bankfull 

discharge 

per (cubic seond) feet 

I Estimated from generalized regional relations of discharge of 1.1Gycer recurrence 

1 From rating curve; value of hankfull stage estimated in field . 

3 Interpolated in regional curve relating known bankfull discharge to drainage area . Interval plotted against drainage arra . 4 Estimated . 
80 

Little Popo Agie R. ncar Lander Wyo ..... 

Ireen R., at War& bridge ne& Daniel, 

Eorse Creek near Daniel, Wyo _______..._.. 

:ottonwood’ Creek, near Daniel, Wyo. (meander) -. __ .. _________ _._. __ Danicl, Wyo. (braid) _._.____.......___. 

3reen R. at Daniel Wyo __._.....___...... 

New Foik R.. at American Gothic reach near Pinedale, Wyo __.....____.....____-.. 

Buffalo Fork, Flyhox reach ncar Ranger station Jackson Wyo .____.._______...... 

Wind R.: Dumb bowboy reach near Sheridan Ranger station above Dubols, Wyo.. Du Noir Creek, above Dubois, Wyo ._....._ 

Vorth Pop0 Agic R. near Lander, Wyo ...- 

Watts Branch, Vicrs’pasture near Rockville. 

wyo ....................................... Beaver Crcek. near Daniel, Wyo .._..______. 

Serial 

No. 

......-- --..... 

........ 5 

3 3 ._.___.. __.___. 

.-. _ _ _ _ . 10 .._._.__ 10 .......- -...... 

......-. 

____._._ 

........ 

....-... 

__.___.. 

6 

8 

9 

1 la 

1% 

12b 

14h 

18s 

23 

24 

25 

26 

30 

31 

33 

37 

43 

44 

45 

48 

49 

65 

GG 

67 

68 

69 

8s 

w: 

121 

1B 

18: 

1% 

1 84 

18! 

18( 

18: 

1 8! 

2z 

28 

28 

23 

23 

23. 

23 

23 

241 

25 

26 

~ 

. . . . . 

100 

. . . . . 

. . . . . 

. . . -. 

. . . . 

PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS 

. . . . . . - - - -. - 

-.. . . - -. -. - . . . . . . . --. . 

. . . . . . -. - - - 

. . . . . . . -. . . . 

. -. -. . . . . . . . 

APPENDIX G.-Distribution of bed-particle size in various stream cross section8 .. 

I Perccnt Aner than (millimeters’ 

ACCornog, Pal .__..... - __.. . . . _____._. 

At Seven Springs, Pa ..__._....______._. 

Near South Downingtown. Pa .______... 

At Embrecville, Pa ._...._.__........_._ 

At Wnwasct. Pa .____...__.__...._._--.. Christians Creek, at Orange Bridge near 

Staunton Va ___.....__...._.__._......--- 

At Rt. b54 near Staunton Va ....____... 

Barterhrook Creek, at Rt. 254 near Staun- ton Va _..._______.______..-..----........ 

Middle River, at Bethlehem Church near Staunton Va ___._.___..__......_._._ 

Eidson Creek. near Mt. Tabor Church near Staunton, Va. ________...__......_.--..... 

Yellowstone R. at Billings, Mont.. - -. ____. 

Wind R. near kurris Wyo.. _._.....______. 

Middle hey Creed. below South Fork near Big Piney Wyo ..____...._..__...... 

Littlc Sandy Cr&k, near Elkhorn, Wyo .... 

Rio Galistco, at Cerrillos (Lamy), N. Mer.- Rio Santa Fe, at Old Albuquerque Rd., 

Arroyo de 10s Chamisos, near Mt. Carmel 

Chapel (Sunmount) at. Santa Fe, N. Mer- Cafiada Aneha (Eulcr), near El Rancho Montoso near Santa Fe N. Mex ..._.___.. 

Anch Chiquita, near EI’Rancho Montoso south of Santa Fe N. Mex _____.._._._____ 

Tributary t.0 Herdanas Arroyo, near Las Des, northwest of Santa Fe, N. Mex _____. 

Rio Oa!isteo, at Domingo, N. Mex ..._.__... 

Fa11 Creek, near Pinedale, Wyo .__._...____. 

Green R. Fontcnclle Wyo ____....____...._ 

West Fo;k Rock Crkk, near Red Lodge, Mont ______..._______._..____. .- __ ._____. - Rock Creek, near Red Lodge, Mont Clear Creek near Buffalo Wpo _______. -... North Fork’Cleer Creek,’near Ranger Station, Buffalo, Wyo .____......_.____._..-.. 

Red Fork, near Barnum, Wyo ._.______.... . 

Rock Creek at Roberts Wyo .___.__._..... 

Polo Creek,’J‘r mile heldw Little Half Moon 

Lake ncar Pinedole. Wyo ._..___.____..... 

Bull Lakc Creek near Lenore Wyo- .._.___ Big Sandy Creed, at Leckie rjnch, Wyo __._ 

west of Ssnta Fe, N. Mcx ...._.___.._.... . 

Stream and location 1-7; 

. . . . .. .. .-...- 

........ ....-. 

..... ... .-..-. 

......-. .- .-. ...._.__ ...... 

6.5 7.‘ ~ ....... ....-- 

5 II 

........ 15 

..~ ._.._ 13 .-. -.- ...-.-_. _.__._.. .-.-._ 

.....-.. ...... 

.-...-...-... 

27 42 

1 4 

. . . ..-~. 6 

9 17 

2 14 

1 11 11 36 -..-......... ........ . ..-.- 

. . __._. . ---. - ......-. .-.... 

....--.. --.-__ 

... _.._ ----_. .-~.-. .- .---_. ._____.. ...... 

....---. -..-. ........ .___.. ._..._._ .__._ 

Md ..---..-....---.-..~-----..------.-.... 

Seneca Creek. at Dawsonville, Md .......... 

At Riffleford near Rockville, Md -.-.-.. 

Brandvwine Creek, at Lenape, Pa ._.....__. 

- 

1 

- 

-.-. 

6 

5 

18 

10 

4 

2 

3 

3 

6 

11 

4 

9 ..__ 

..._ 

14 

.--. 

24 

16 

16 

1 .___ 

._.. 

1 

46 

34 

20 

30 

48 

37 

71 

..-. 

.-.. 

.___ 

-.-. 

.... 

--.. 

___. 

..-. 

___. 

.-. 

- 

2 

5 

8 

F 

2 

21 

11 

2 

12 

._._ 

4 

10 

5 

6 

19 

17 

7 

5 

11 

5 

4 

21 

4 

36 

.... 

m 

25 

1 

_.__ 

.... 

4 

60 

81 

52 

59 

78 

51 

91 

-... 

..__ 

_.__ 

_.__ 

._. 

.-. 

-.. 

-.- 

... 

__ 

4 

- 

9 

9 

6 

6 

29 

17 

2 

15 

--.. 

4 

23 

5 

9 

2 

31 

18 

9 

0 

11 

7 

5 

21 

11 

52 

27 

31 

1 

1 

7 

87 

(js 

72 

83 

87 

70 

96 

..-. 

.-.. 

.-.- 

.__. 

1 

-... 

._._ 

._.. 

2 

1: 

--.. 

__ 

8 

13 

9 

13 

7 

34 

27 

2 

16 

- 

.___ 

5 

37 

8 

14 

3 

48 

26 

14 

9 

12 

14 

9 

29 

23 

66 

32 

37 

1 .._. 

3 

9 

79 

76 

86 

93 

R3 

81 

9: 

____ 

-.. 

..- 

-.. 

... 

... 

1‘ 

- 

18 

- 

22 

9 

24 

22 

52 

42 

2 

23 

2 

20 

82 

8 

31 

29 

70 

40 

21 

13 

14 

40 

17 

41 

37 

78 

3’3 

51 

E -__. 

11 

RE 

O( 

94 

Of 

9; 

8s 

1M 

.-__ 

.-__ 

1 

.-.- 

..-. 

1 

-. 

32 

- 

46 

10 

49 

53 

71 

77 

12 

31 

25 

41 

100 

12 

46 

69 

92 

61 

32 

26 

24 

64 

33 

58 

61 

94 

59 

74 

lfi 

12 

16 

04 

96 

97 

08 

98 

97 

4 

8 

1 

1 

E 

IC 

m 

-.-- 

42 

, 

I( 

2: 

64 

._ . 

83 

16 

82 

88 

92 

96 

58 

88 

83 

73 

17 

72 

97 

1M) 

89 

48 

49 

39 

91 

66 

74 

82 

97 

81 

02 

39 

35 

29 

31 

100 

I00 

99 

Loo 

98 

95 

E I( 

5 

f 

1( 

2: 

SI 

3: 

.___ 

.... 

2; 

31 

- 

(2s 

96 

48 

96 

100 

99 

100 

96 

100 

100 

96 

42 

93 

_- 

..- 

ion 

--. 

99 

75 

77 

64 

1W 

92 

91 

97 

1W 

9F 

9E 

71 

6€ 

65 

71 

..- 

... 

IO( 

... 

IO( 

1M 

21 

8‘ 

2 

31 

4 

4 

9 

81 

5 

2 

6 

-__ 

._ . 

!58 

100 

84 

100 

100 

100 

___ 

.. 

--. 

... 

100 

90 

99 

100 

97 

94 

86 

100 

100 

100 

.-. 

--. 

... 

.-. 

___ 

100 

99 

99 

98 

100 

82 

.-. 

-.- 

... 

... 

.-. 

.... 

.-. 

6t 

lo( 

4f 

6: 

61 

71 

1M 

m 

7r 

6 

81 

percent 

ier than 

feet)- 

0. I1 

.46 

.IO 

.09 

.05 

.OB 

.18 

.I2 

.14 

.I3 

,035 

.49 

,082 

,075 

,026 

.22 

.21 

.34 

.I6 

,075 

.085 

.0125 

.07R 

.049 

.27 

.27 

.31 

.29 

,0038 

.0046 

.006F 

,0016 

,0033 

,0057 

,0021 

.69 

.29 

.88 

.67 

.58 

.47 

.12 

.27 

.42 

.69 

.25 

,072 

,072 

percent 

ier than 

feet)- 

n. 24 

.m 

. R4 

.21 

. I6 

.12 

.Go 

.20 

.21 

.27 

.056 

.79 

.31 

.15 

,079 

.lR 

.48 

.49 

.R4 

.17 

.33 

.29 

.21 

.069 

.24 

.15 

.47 

.Go 

.58 

.95 

.042 

,039 

,0227 

.0132 

.OlOl 

,037 

.0046 

1.25 

.42 

2.4 

1.93 

2. 15 

1.0 

.21 

.46 

.51 

1. 92 

.72 
RIVER CHANNEL PATTERNS 

ton, Va ........................... Picnic rcsch near Stsunton, Ye. Below Nash Va ............... Campbdl Crud, above Tyro, Va.. Stony Run, above mouth at Little R. near Staunton, Va ___.._.__ _.._ 

81 

1. 1 

APPENDIX H.-Values of hydraulic factors at various stream cross sections 

[e, Estimated. For deflnition of b, f, and m see page IV; for discussion see Leopnld and Maddock, 19531 __ 

J 

_- 

n. 48 

.34 

.50 

.65 

.65 

.4n 

...... 

.34 

.40 ...... 

.42 ...... 

...... 

.26 ...... 

...... 

...... 

...... 

...... 

...... 

...... 

...... 

...... 

...... 

...... 

.20 

...... 

...... 

...... 

.47 

.50 ...... 

...... 

...... 

.42 

....... 

.4? 

.48 

.35 

.45 

....... 

....... 

....... 

....... 

. - . . --. 

....... 

. -. -. 

....... 

....... 

.... 

....... 

.... 

~..~.~ 

__._._ 

...... 

_.___. 

~ 

m 

__ 

n. 18 

. zn 

.21 

.28 

.31 

.47 

..... 

.52 

.5n 

..... 

.43 

~.~~. 

..... 

.44 

..... 

..... 

..... 

..... 

..... 

..~.. 

..... 

.~.~. 

..... 

..... 

..... 

,6C 

..... 

..... 

...... 

.M 

.3( ...... 

...... 

~~.. 

.4: 

...... 

.!M 

.4: 

...... 

.3: 

. 3( ...... 

..... 

..... 

..... 

..... 

..... 

..... 

..... 

-.~.. 

..... 

..... 

~.~~~ 

..... 

..... 

..... 

At mean annual discharge Slope awe 

height 

rt hankfull 

stage 

(fcet) 

____ 

......... 

......... 

......... 

......... 

......... 

R 

......... 

......... 

......... 

......... 

......... 

......... 

......... 

......... 

......... 

......... 

......... 

......... 

......... 

......... 

......... 

......... 

..~.~ ..-. 

......... 

......... 

......... 

......... 

5. 5 

......... 

3. 3 

5. 1 

......... 

.......... 

......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

__ 

Jelocity 

(feet 

per 

second) 

Field 2 

___ 

Width 

(feet) 

540 

340 

310 

160 

400 

39 

......... 

120 

42 ......... 

61 ........ 

......... 

43 ......... 

......... 

........ 

........ 

........ 

........ 

........ 

........ 

........ 

........ 

........ 

41 

........ 

........ 

........ 

13. 1 

53 ........ 

........ 

........ 

26 

........ 

38 

50 

112 

45 

______ __ ........ 

........ 

........ 

........ 

........ 

........ 

........ 

......... 

. - . . - - -. . . - - -. - -. 

- -. - -. -. ......... 

. -- - . - - -. 

__ 

Depth 

(feet) 

1. 7 

.92 

1. 35 

1. 7 

2.0 

1. 1 

...... 

1. 8 

.88 

.61 

...... 

...... 

...... 

.8 ...... 

...... 

...... 

...... 

...... 

...... 

...... 

...... 

...... 

...... 

...... 

1. 75 

...... 

...... 

...... 

.52 

1. 06 

...... 

...... 

...... 

.92 

.-.__. 

1. 5 

.8 

1. 5 

.5 

...... 

.--.__ 

...... 

...... 

...... 

.__._. 

...... 

...... 

...... 

-.-._ 

... 

...... 

...... 

.._.._ 

...... 

Drainage 

rea (square 

miles) 

32, 000 

31,300 

26.900 

14,300 

2, 320 

108 

45 

408 

141 

36. 2 

124 

124 

204 

204 

680 ............ 

............ 

372 

vledian 

led size 

(feet) 

Serial 

No. b Stream and location Discharge 

(cubic feet per second) 

2,300 

537 

1,137 

1,493 

1. 108 e 100 

............ 

509 

32. 1 50 

63. 2 

............ 

............ 

67. 4 ............ 

............ 

............ 

............ 

............ 

............ 

............ 

............ 

............ 

............ 

............ 

in3 

............ 

............ 

............ 

e 4.2 

93 ............ 

............ 

c 580,000 

21. 5 

............ 

70 

60. 5 

1m 

447 ............ 31. 7 

............ 

............ 

............ 

............ 

....... 

............. 

............. 

............. 

............. 

-. - - -. -. -. ............ 

Map 1 

0.00135 

,00115 

,00105 

. m5 

......... 

......... 

......... 

. - - -. . -. - 

,0066 

......... 

......... 

......... 

......... 

......... 

......... 

. . -. - . -. .

........ 

......... 

......... 

......... 

......... 

......... 

,00071 

........ 

......... 

......... 

......... 

......... 

......... 

......... 

.00133 

......... 

......... 

........ 

........ 

......... 

. m947 

. onlati 

,000947 

. oniin 

. onin9 

......... 

......... 

......... 

......... 

......... 

......... 

. . --. -. - - 

......... 

......... 

......... 

. - -. - - -. 

......... I::::::::. 

2. 4 

1.7 

2. 1 

3. 6 

2. 7 

3. n 

...... 

2.4 

.86 ...... 

1.6 

...... 

...... 

1. 8 ..-.. 

...... 

..... 

..... 

..... 

..... 

..... 

..... 

... 

...... 

1. 5 

...... 

...... 

...... 

.62 

1.7 

...... 

...... 

...... 

.84 

...... 

1.4 

1.8 

2. 7 

1. 4 

...... 

...... 

...... 

-.-.-. 

...... 

-.---. 

...... 

...... 

-..-.. 

-.-.-. 

---__. 

...... 

...... 

..... 

0.0014 

,0011 

,00125 

.no095 

,0049 

,0047 

,0034 

.MI14 

,0038 

. 0051 

,00227 

,0073 

.M)11 

,0005 

. 0029 

.00m 

,00125 

.00286 

.on286 

,000193 

,000455 

.0037 

.on405 

. on21 

. no098 

.007n 

.00184 

. w473 

........ 

,0031 

. no06 

,0005 

,0023 

. onon89 

n. 0006 

.n2 

,0005 

,0016 

.16 

.ll 

,023 

.46 

,097 

.017 

. 09 

.049 

.06 

,056 

........ 

. in 

. in 

. 121 

........ 

........ 

' ,004 

........ 

. 14 

.I31 

. a35 

.48 

.10 

,049 

.I3 

,082 

,075 

........ 

. 0% 

,002 

........ 

. ny 

........ 

........ 

. - -. - - - - ........ 

. . -. - -- - 

n. 35 

.n5 

.n4 

.48 

.% 

.05 

...... 

.12 

. in ...... 

.12 ...... 

...... 

.30 ...... 

...... 

...... 

...... 

...... 

...... 

...... 

...... 

...... 

...... 

...... 

. 13 

...... 

...... 

...... 

.03 

. 16 ...... 

...... 

.~~.~. 

. 15 

-..--. 

.3( 

. 1f 

.3f 

.3( 

...... 

...... 

-..-.. 

...... 

._.._ 

... 

_____ 

..... 

...... 

.-..-. 

._.___ 

...... 

._____ 

._.___ 

-..-.- 

I 

2 

3 

4 

5 

6 

7 

8 

9 

10 

lla 

llb 

1% 

12b 

14a 

14b 

14c 

1% 

18b 

18C 

21 

2: 

z 

24 

2: 

2f 

2i 

2! 

z 

3( 

31 

3: 

x 

3t 

3s 

4: 

5; 

5t 

5s 

61 

6: 

6: 

64 

6: 

G( 

6: 

61 

61 

71 

7 

7 

7 

? 

7 

7 

North Platte R., North Platto, Nnhr -. 

Near Sutherland, Nebr- .... .~ .. 

Near Lisco, Ncbr ............... 

Near Douglas, Wyo ............. Wind R., at Riverton, Wyo ........ Little Pop0 Agie R., near Lander, W"n 

NeGYork R., Jenkins ranch near 

Green 'R., at Warren Bridge near 

Beaver kreek, near Daniel, Wyo. . 

New Fork R., below New Fork 

Horse Creek, near Danlel, Wyo.-.. .... do.3 .............................. Cottonwood Creek near Daniel, 

... -do.a-. ............................ Green R. at Daniel, Wyo ............ .... do.3 .............................. .... do.3 .............................. New Fork R. at American Gothic 

.... do.3 .............................. . .--do.3 .............................. Duck Creek near Cora Wyo ........ Snake R., &low mouth of Hoback R. near Jackson, Wyo. 

Buffalo Fork, Flybox reach near Jackson, Wyo. Wind R Dumb Cowboy reach near Sberidan Ranger station 

above Dubois Wyo. 

DuNoir Creek, &ve Dubois. Wyo. 

North Fork Pop0 Agie R., near 

Lander, Wyo. 

Pop0 Agio R., Joyful reach near Hudson, Wyo. Little PiDe Creek. near Avondale, 

Cora Wyo. 

Daniel Wyo 

Lake near Cora, Wyo. 

wyo. 

reach near Pinedale, Wyo. 

........... 

5 

3,440 

345 

55 

93 

140 

700 

n 

7. 4 

4. 2 

.53 

15. 5 

in0 

1,000. no0 7 

21 

21 

I, ,710 

2, %Q 

7,210 

1.400 

........... 

............ 

2. 1 

24 

82. 5 

6. n 

18 

2. 2 

1. 6 

69.2 

14. 2 

G. 4 12. 3 

31.4 

1. 1 

Md. 

Rock Creek. Rt. 115 near Redland. 

Md. Watts Branch. Viers nasture near 

Rockrille Md. 

near Blvtheville. Ark. Mississippi' R., at Tamm Bend 

,00093 

......... 

......... 

......... 

wyo ............................. 

At Hnlett Wyo ................. 

At Wydming-South Dakota 

State line ..................... Near Elm Springs S. Dak Near Fruitdale S.'Dak ..... 

Arikaree R. at Haigler Nebr ....... 

Seneca Creek, near Wdodfleld, Md. 

(1 mile north of Woodfleld) ........ 

Christians Creek, at Grange Bridge near Staunton Va ................. Christians creek, at Rt. 254 near Staunton Va ..................... Barterbrook Creek, at Rt. 254 near Staunton. Ve ..................... Middle R., at Bethlehem Church near St,aunton Va ................ Eidson Creek ' mar Mt. Tabor 

Tributary to Christians Creek near St. James Church near Fisheiville, Va. - -. -. -. -- - - - - - -. -- - __ - - - -. - - South R. Blnek Bnll reach south of Mt. Vkrnon Church nenr Lips- . comb Va ......................... South +ark Tyc R. above Naeh Va TYC R.. culvcrt-bridge near St&- 

Church near'Staunton, Va. ..... 

......... 

......... 

. OWJ2 

,0015 

on30 

. nn23 

0021 

,0083 

no07 

,051 

,00034 

.O67 

.068 

. 0% 

.I1 

.om 

.06 

,075 

,0125 

,049 

.085 

.076 

.0032i 

1. 15 

1.31 

1. 65 

.75 

1.77 

..... .31 

See footnote at end of table. 
82 

........ .010 

,00947 ........ 

,00374 ........ 

. woo95 

.00237 ........ 

,00108 ........ ,00252 _.___.-. 

. MX)G&7 ......... . ooO142 ......... . m19 ......... 

,033376 ......... . m95 ......... ......... .ooo63 

............... A. 

................. 

................. 

................. 

. -. -. _. 

................. 

PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS 

APPENDIX H.-Values of hydraulic factors at various stream cross sections-&ntinued 

.......... 

.......... 

.......... 

.......... 6 

- 

- 

..... 

._._. 

... 

..... 

-..~ 

.... 

0.55 

.4R 

.47 

. aa 

.8& 

.37 

A .33 

.31 

.45 

.24 

.49 

.37 

.55 

.44 

.52 

.4c 

.s 

.2f 

.7: 

.% 

.6! 

.3; 

.2: 

.2: 

.3! 

.5( 

.3! 

.2! 

.4: 

.4: 

.4 

. 5! 

.5l 

.4 

. 41 

.4 

. 41 

.4 

.4 

.2 

.4 

.3 

.6 

.2 

.4 

.4 

.2 

.6 

.3 

.5 

.5 

.I 

.a 

.5 

.3 

.4 

.z 

.4 

vPedian 

led size 

(fect) 

- 

m 

- 

..-. 

.... 

.... 

.-.- 

.... 

..- 

0.35 

.40 

.46 

.62 

.5u 

.M 

.16 

.57 

.5: 

.4? 

.4i 

.4: 

.5t 

.4: 

.5( 

.4( 

.4( 

. 2: 

. I! 

.2 

.2 

.2 

0 

At mean annual discharge 1 

0.22 

.25 

.2G 

.38 

.43 

Slope 

....... 

....... 

....... 

....... 

....... 

Gage 

height 

at bankfull 

stage 

(feetj 

. MI 

-- 

eloc- ~ 

ity 

feet 

seeind) 

per 

~ . .~~ I 

....... 

........ 

......... 

.... 

......... 

......... 

......... 

......... 

........ 

....... 

........ 

..... 

........ 

....... 

......... 

......... 

........ 

......... 

~~ . .~.. 

......... 

......... 

......... 

......... 

......... 

Ncbr .............................. 

Near Odessa, Nebr ............... 

Near Overton Nebr .............. 

Below Whalen, Wyo ............. 

Platte R., near Grand Island, Nebr. 

North Platte R.', near Mitchell, 

Nehr .............................. 

Below Casper, Wyo .............. Pop0 A ie R near Riverton, Wyo.. 

Near Meeteetse, Wyo ............ Owl Creek, near Thermopolis. WYO. 

Missouri R., at St. Joseph, Mo ...... 

At Hermann, Mo ................ At Pierre S. Dak ................ 

At Kand City. Mo-..-- ........ 

At Bismark, N. Dak ............. 

East Fork R., near Big Sandy R., wyo ............................... North Piney Creek, near Mason, 

Bou der Creek, below Boulder Lake 

near Boulder, Wyo. ............... 

Silver Creek near Big Sandy Wyo.. 

Middle Piniy Creek below' South 

Fork near Blg Piney, Wyo ........ New Fork R. near Boulder Wyo ... 

Fontendle Cieek, near Fohenelle, wyo ............................... 

Little Sandy Creek, near Elkhorn, wyo ............................... Pecatonica R at Freeport, 111 .______ 

Iro uois R lkar Chebanse Ill-..--. 

Caaeys C;eek near Brevaid N. Cwatauga R ndar sugar Grovl N. C. 

Davidson $1, near Brevard, NI C---- 

Noland Creek, near Bryson City, 

N.C .............................. Tennessee R. at Knoxville, Term-. French Rrosd R., near Newport, Te nn .............................. 

At Calvert, N. C ................ At Rosman N. C.. ............. At Bent CGek, N. C ............ Buttahatcbee R., near .Caledonia, 

Miss- ............................. Tombigbee R., at Aberdeen, Miss-- 

Near Columbus, Miss ........... Sipsey R., near Elrod, Ala ____ ~ ___._. 

Oreybufl R..'hear Basin, WYO ....... 

wy" ............................... 

Near Leroy, Ala ................. Near Coatopa, Ala. ............. 

Serial 

No. 

.12 

.32 

.20 

.62 

.37 

.35 

.58 

.50 

.47 

.37 

.45 

.50 

.42 

.47 

.27 

.48 

.30 

.50 

.33 

.43 

.35 

.67 

.50 

.53 

.65 

.28 

.Fk, 

.45 

.45 

.47 

.75 

.m 

.35 

.52 

.3u 

.5n 

.3n 

Drainage 

miles) 

Strcam and location area (square 

.......... 

.......... 

......... 

.......... 

.......... 

.......... 

.......... 

.......... 

. ~~..~~ 

~~.~~.~ 

......... 

.......... 

~.~ ~ .~.~ 

.......... 

.......... 

..~~. ~~.. 

7. 7 .......... 

~~~ ~..~~. 

......... 

.......... 

15 .......... 

.......... 

.......... 

.......... 

.......... 

10 .......... 

.......... 

.......... 

.......... 

.......... 

.......... 

--. _.__. .- 

.......... 

.......... 

Discharge 

.cubic feet er second) 

.00118 

.a0111 

,00126 

. on6a 

,00947 

.ooono 

Nidth 

(feet) 

~.. ,~~. ........ 

....... 

........ 

........ 

lepth 

(feet) 

,000227 

,00018Y 

,000146 

. oonm 

.oonim 

Asp 1 

.............. 

.~ ~. . ~. ~ 

....... 

........ 

....... 

....... 

Field 2 

____ 

n. 038 

,025 

,0048 

. no81 

,015 

,0032 

.00083 

......... 

......... 

......... 

......... 

......... 

......... 

......... 

........ 

. ~ ~-~. 

......... 

........ 

......... 

........ 

........ 

......... 

......... 

......... 

........ 

..~~~. . 

........ 

..~~~ .~ 

................. 

.......... 

................. 

......... 

................. 

ooon 

.no91 

........ 

.......... 

e 66 

......... 

.31 .......... 

......... 

.29 .......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

78 

79 

an 

81 

82 

84 

86 

87 

89 

90 

91 

92 

93 

94 

95 

86 

97 

98 

99 loo 

in1 

102 

103 

104 

105 

106 

107 

108 

in9 

110 

111 

112 

113 

114 

115 

116 

117 

118 

119 

120 

121 

122 

123 

124 

12: 

1% 

12i 

1% 

1Z 

1X 

131 

13: 

13: 

134 

131 

13f 

13; 

11 

13< 

1 H 

141 

14: 

14: 

14 

141 

Mines Run, at mouth near Staun- ton Va ............................ 3kidmore Fork, Rt. 95 near Staun- ton Va ............................ Little( R., Grooms Ridge near Staun- ton Va ............................ Norti) R. near Stokesvillc Va ______ North River Gap ne& Stokesvillr Va ....................... Slab Cab& Creek, west. of Lamont, Pa- ............................... BIK Horn R. at Mandenon, Wyo-- Wind R. ne& Crowheart, WYO ..... 

Yellowsthe R. at Billings, MontL- Wind R,. near Burris, yo ......... Near Dubois, Wyo .............. Little Righorn R., at Statc line near Wyola. Mont ..................... North Platte R. at Wyoming- Nebraska State !:ne. Wyo- ........ 

At Samtorra Wyo ............... Medicine hdgk Creek, Hyattville, wvo ............................... 

Ooodeberry Creek, near Grass Creek, 

wy[, ............................... North Fork Owl Creek, near An- chcr Wy o. ....................... 

Yello\;stone R., at Corwin Springs, 

2. 8 

4.8 

16 

2% 4 

66.4 

16 

11, !wo 

1.920 ii,wn 

1,220 

233 

199 

22,100 

2,880 

ne 

58.1 

155 . 

2, &XI 69,450 

1, 190 

20,800 

4,600 

429 

23,700 

30,000 

59,500 

58,800 

~,4on 

24,300 

16,350 

12,600 

2, nin 

1,130 

690 

484 

424,300 

528, mn 

243,500 

489,200 

186,400 

79. 

58 

130 

45. 

34. 

552 

224 

20. ' 

1,330 

2, 120 

11. 

90. 

40. 

13. 

8,934 

1,858 103 

67. 

676 

823 

2,210 

19, loo 15, 500 

4,490 

51 5 

... 

...... 

...... 

........ 

.... 

. . -. -. 

....... ...... ...... 

........... 

1,950 

1,315 

6,331 

853 

179 

........ 

258 

155 

420 

130 

68 

29 

270 

210 

25 

19.5 

17 

242 

308 

57 

96 

230 

60 

140 

670 

....... 

550 

780 

280 

. . -. -. 

2. 5 

2.4 

4.6 

2. 7 

1.4 

2.0 

1. 4 2. n 

.9 

.6 

.58 

3.4 

11.9 

1.5 

1.2 

1.7 

1.4 

1.5 

...... 

3.0 

3.6 

3. 2 

2.5 

1.9 

2.5 

2. 1 

2.0 

I. 7 

1.9 

1. 7 

3.6 

3.2 

2. 4 

2.5 

1. 8 

2.2 

2.0 

.._.. 

00004: 

00152 

0063 

0095 

00118 

00146 

..-.. 

on4 

........ 

.27 

.27 ... 

......... 

.05 

.o 

.22 

. 10 

.15 

. OD 

.31 

. OF 

.n2 

,134 

.o: 

.04 

.at 

. 1; 

.a 

.% 

. O! 

. 2: 

.o 

.3 

.4: 

. 2! 

.o' 

. 11 

. 21 

. 21 

.0 

.o 

. 11 

.0 

.n 

.o 

.I 

.n 

.1 

.1 

.2 

.2 

.2 

.2 

.o 

.1 

.1 

.u 

.u 

.a 

.c 

.c 

.I 

.c 

.' 

.I 

.I 

.I 

.I 

152 

767 

1. 204 

3i 

19 

16 

2,950 

11,860 

202 

294 

724 

185 

438 

340 

960 

937 

2,583 

3. 4-3.9 

........ 

7.3- 8.8 

,0099 

0114 

. onzx 

. on118 

. onm 

,0012~ 

.00018 

,00316 

. OOORF 

.00167 

. OOllE 

,0012f 

.0012( 

Mont .............................. 

Near Sidney Mont ............. 

Little Bighorn ' R., below Pa.% 

Creek near Wyola Mont .......... 

Republican R., near Bloomington, Near Crow Agency, Mont ...... 

16 Nehr.-. ........................... 

Laramie R. near Ft. Laramie, WyO. South Platle R. at Paxton, Nebr.-. 

North Platte 8.. near Keystone, 

.......... 

......... 

.......... 

.......... 

.......... 

.n 

.96 

1.55 

2. 0 

1.9 

3.3 

.96 

1.4 

.9 

11.5 

14. 5 

9.1 

11.7 

G. 1 

1.3 

.94 

1. 8 

.a 

1.8 

.9: 

1.5 

6. 2 

3.2 

.9 

1.6 

1.9 

14.4 

5.3 

1.8 

2.0 

2.8 

13.0 

11.5 

22.3 

11.9 

7.0 

..... 

.n 

1. n 

26. n 

1.8 

1.8 

2.2 

2.6 

3.0 

1.7 

2.4 

1.9 

3. 6 3.0 

2.5 

3. 4 

2.9 

1. 15 

2. 2 

1.9 

2. 0 

2.2 

1.7 

..... 

3. n 

.84 

.7G 

1.03 

1.5 

1.5 

1.3 

1.4 

1.0 

1. 5 

2.0 

1.5 

1.9 

.5 

2.0 

2.2 

1.8 

1.1 

.n 

1. n 

1,495 

1,111 

1,358 

fi83 

200 

364 

45. 

35,440 

69,170 

22, nao 43,710 

20,320 

....... 

250 

123 

90 

87 

26 

863 

1,578 

962 

1,093 

1, 202 

70 

29 

29 

21 

98 

42 

19 

140 

.330 

25. : 64 

55 

30. ' 

933 

346 

92 

77 

296 

130 

103 

60. 

196 

43. 

26. 

403 

64. 

22 

906 

34 

154 

125 

42. 

12,820 

2,764 

335 

229 

1,589 

1,066 

2,863 

26,250 

21.450 

5,791 

715 

1,mfI 

See footnotes at end of table. 
RIVER CHANNEL PATTERNS 

APPENDIX H.-Values of hpdraulic factors at various stream cross sections-Continued 

~. ~ 

3.7 

4.3 

3. 1 2. 1 

1.6 

1. a 

83 

I. 1 

~. 

f 

_- 

.45 

.58 

.% 

. 17 

.45 

.70 

.55 

.61 

.55 

.32 

.40 

.4(! 

.4c 

.42 

.a 

.27 

. 3s 

.34 

.N 

.44 

.4E 

.5i 

.34 

.L 

. 5: 

.a 

.4: 

.5: 

.32 

.4! 

.a 

.4 

.6' 

. 31 

. €1 

.% 

.31 

. 3! 

. 3, 

.x 

.fr 

.4 

.fr 

.4 

.2 

.5 

.5 

5 

.5 

.6 

..... 

..... 

..... 

..... 

.6 

.5 

.4 

.4 

.5 

.4 

..-.~ 

K ... 

.. 

.& 

... ..... 

rlap I 

000541 

~ 

m 

.20 

.30 

.20 

.72 

.48 

.25 

, 40 

.30 

.25 

.38 

.55 

.50 

.44 

.51 

.77 

.69 

.36 

.34 

.20 

.38 

.45 

.15 

.56 

.5Ei 

.42 

.30 

.46 

.36 

.57 

.49 

.29 

.35 

.2E 

.2! 

.3: 

.4: 

.3f 

.24 

.34 

.4: 

.4t 

.a 

.34 

.2: 

.41 

.3( 

.4! 

.1' 

. l! 

.2 

____ 

Field 2 

_____ 

.......... 

At mean annual discharge 

Stream and location 

Drainage 

area (square 

miles) 

mgc 

height 

It hankfull 

stase 

(feet) 

le ublican R., at Clay Center, 

&!arts.. -. -. - - - - -. -. . - - - ___. - -. 

At Lindshorx, Kans ............. At Enterprise, IEans ............. Cansas R.. at Bonncr Springs, Kansmoky Hill R.. at Elkader, IEans .... 

At Lccompton, Kans ............ At Ogden, ICans ................. At Topeka, Kans ................ At Wamego IEans ............... 

Mond .............................. 

At Columbia Falls, Monk ...... Near Polson Mont .............. :lark Fork R., kt St. Regis, Mont..- Above Missoula MonL .......... Below Missocla,' MonL ._ - -. -. - Near Plains, Mont ,.. ............ Near Heron Mont .............. 

near Metaline Falls, Wash ........ Embarrass R.. at St. Maric, Ill ...... 

Lock R. at 6omo Ill ................ jangamdn R. at hiverton III ....... 

Plathead R., ndar Columhia Falls, 

'end Orcille Jil, below Z Canyon, 

Cankakee R. at Mcmence, 111. ___~. 

2onneoticut k., at First bonnecti- cut Lake near Pittsburgh, N. >I.. . 

At North Stratford, N. H ....... 

Near I)alton, N. €I............ 

At White River Junction, Ver- mont ........................ 

At Montague City, Mass ........ 

Arkansis R. at Salidn Colo. - --.. ~. 

Rio Santa Fe at Old Albuquerque 

Rd. west oi Santa Fe, N. Mex --.. 

Arroyo de Ias Chamisos, near Mt. Carmel Chapel (Sunmount) at Santa Fe N Mex.-. .............. 

Catiada Akcha (Euler), near El 

Rancho Montos:, near Santa Fe, N.Mex ........................... 

Ancha Chiqnita, near El Rancho Montoso. south of Santa Fe, N. Mex ............................... 

White R., near Bethel, Vt ...... At Wet Hartford, Vt ........... 

Rio Oalistco: at Cerrilios, N. Mex. .. 

_- 

elocity 

feet 

Per 

ind) 

jet- 

- 

2.0 

1.5 

I. 5 1.9 

1.8 

2.3 

1. 9 2. 1 

i. 9 

4.0 

2.9 

3.4 

3. 5: 2.4; 

2. 2 

2. 6 5.3 

7. G 2. 3 1.8 

2.8; 

2. 5 

2.6 

2.7 

2.0 

3. 5 2.6 

2.3 

1.2 

3.0 

..-- 

..~- 

..~. 

.... 

..~. 

..~. 

.... 

~..- 

..... 

..... 

1. 1 

.8 

2.3 

2.0 

1.6 

1.3 

1. 1 

1.7 

2.3 

2. g 

..... 

..... 

..... 

..... 

1. i 

2. ( 

1. : 

1. 

1. f 

2. ( 

1. i 

l.I 

3. 1 

., 

2. 1 

000545 

000303 

000379 

000379 

000379 

0430 

000316 

00158 

00079 

- 

epth 

eet) 

- 

2.0 

. 6 2. 4 

7. 2 

5.9 

4. A 3.8 

4.6 

4.1 

2.5 

7.1 

7.6 

6.0 

4.7 

5.8 

L4.3 

12.0 

11.7 

4.8 

2. 3 3.6 

6.0 

1. 25 

3.7 

4.0 

4.2 

11.5 

1.3 

4. 1 2.0 

..... 

..~-. 

~~~-. 

.-.-. 

.... 

.... 

.~.~ 

~~.. 

.... 

.-.- 

1. 21 

1. 5 2.8 

4.7 

8.1 

1.3. 

1.9 

2. 4 1.6 

2.3 

.... 

... 

.._. 

..... 

3.6 

5.0 

3.7 

2.8 

5.4 

1.5 

................. .......... 

.......... 

.......... 

.......... 

.......... 

.~- -. _. . - .......... 

................. 

.................. 

................. 

................. .......... .................. 

.................. 

___. -. --. 

rledian 

w?d size 

(feet) 

~ 

........ 

........ 

........ 

- - -. -. -. 

-. -. -. -. 

........ 

- - -. -. -. 

........ 

........ 

........ 

. - . - -. -.

... 

.... 

.... 

... 

....... 

........ 

........ 

.... 

....... 

. . -. -. 

........ 

........ 

........ 

....... 

....... 

........ 

........ 

........ 

........ 

.0038 

.OM6 

,0066 

,0046 

.0033 

.0057 

,0022 

........ 

........ 

........ 

........ 

........ 

........ 

........ 

........ 

........ 

........ 

.-.2.--. 

........ 

. -. - -. -. 

.w 

.os 

,074 

,037 ....... 

....... 

....... 

-. -. - - - ....... 

....... 

....... 

........ 

....... 

.................. 

.................. 

.................. 

.................. 

.................. 

Serial 

No. 

,01136 

. ooin9 

00189 

.......... 

.......... 

.......... 

b 

.37 

.I7 

.x? 

.I0 

. 06 

.07 

. 02 

.07 

.17 

.30 

.04 

08 

.09 

.05 

. 03 

.04 

.20 

.30 

.!XI 

.15 

.10 

.35 

.10 

.15 

. OR 

.04 

.08 

. OH 

.05 

.c4 

.I8 

.2E 

. 0s 

.31 

.1: 

.3: 

.2i 

.3: 

.3: 

.2: 

.2 

.a 

.% 

.4l 

.01 

.a 

.2 

. 2, 

.o 

0 

. 00063 

,00034 

. ooing 

,00114 

Discharge 

cubic feet cr second) 

.......... 

.......... 

.......... 

.......... 

Nidt.h 

(feet) 

.. 

........ 

........ 

........ 

--- I 

,025 

.0175 

,0286 

,032 

,0055 ................. 

................. 

................ 

146 

147 

148 

149 

150 

151 

152 

163 

154 

156 

157 

159 

160 

161 

162 

163 

164 

167 

168 

169 

172 

173 

174 

1 75 

176 

178 

179 

180 

181 

182 

183 

184 

i5n 

185 

1 86 

18i 

186 

181 

1K 

191 

19: 

19: 

194 

19f 

1% 

19; 

198 

1sI 

m 

201 

20: 

20: 

XI. 

201 

201 

m 

201 

20' 

211 

21 

21 

21 

21 

21 

211 

Iowa .............................. 

Turtle Creek new Austin Minn.-.. 

Cedar R.. at 'Cedar Rapid. Iowa ____ Near Conesville, Iowa ........... 

Iowa R., at Wapello, Iowa .......... Cedar R., near Austin, Minn ........ Lime Creek at Mason City Iowa.-- West Fork Shell Rock R., & Finchford, Iowa ......................... Cedar R., at Janesville, Iowa.-. ..... At Waterloo Iowa- ............. 

Tributary to Seieca Cr. at Hawkins 

Creamery rd. near De'mascus, Md. 

Seneca Creek at Holstein pasture near Wooddeld. Md ............... 

At Poison Ivyreach. Brunt road 

bridge near Woodfield, Md -..- 

At Pretty Flooa Plain near 

Prathertown, Md.. ............... Kankakee R at Davis, Ind ......... At S held;, Ind-.- ............... Auglaize R. near DeEance Ohio--.- Near Fdrt Jennings, Ohio ........ Blanchard R., near Dupont, Ohio-.. 

Near Findlay, Ohio. ............ At Glendorf, Ohio ................ 

Maumee R., at Antwerp, Ohio ...... 

Near 1)eflance Ohio ............. At Waterville 'Ohio .............. Ottawa R., at Allkown, Ohio __.___ 

At Kalida, Ohio .................. 

.. _. 

15 ......... 

......... 

......... 

......... 

-. - -. -. 

......... 

21 ......... 

................. 

................. 

................. 

................. 

................. 

................. 

................. 

2pv 570 3,555 

8.110 

19,200 

59,890 

58.420 

45,240 

56,710 

55,240 

1,553 

4,464 

7,096 

10. 500 5,740 

8, GW 19. A00 21, no0 

25, 200 

1.540 

2,340 

8,700 

2,560 

798 1,514 

4,092 

7,865 241 

6W 

1,218 

e 100 

e 175 

83.0 

2.5 

1. 5: 

. 0! 

.M 360 e 600 

..... 

........ 

......... 

1,093 36 

292 1.419 

5,874 

7,836 

2.514 

4,655 

4,114 

................. 

................. 

................. 

................. 

.00467 

.00345 

.W16 .................. 

272 

41 

8n 

102 

563 

7% 

342 

481 

525 

450 

444 

340 

232 

370 

495 

328 

293 

110 

4311 

500 

125 

57 

160 

380 

485 

450 

160 

235 

104 

290 

.000189 

. W13 

.000090 

,000237 

,000146 

. ooo2/1 

. 000189 

.Mw)947 

. ooo631 

,000473 

.................. 

......... 

......... 

......... 

......... 

......... 

......... 

......... 

......... 

......... 

......... 

2,855 

9.112 

11,330 

4,897 

18, 6!IO 

7,341 

2.659 

20,400 

......... 

......... 

......... 

......... 

......... 

......... 

......... 

26,190 

1.239 

1, 8lf< 5,174 

1,806 

198 1.570 

2, W2 

......... 

18 

7,217 

13.670 487 1,169 622 

......... 

12 

......... 

......... 

......... ....... -1. .:oo5B.. ........ 

.. --I .0151 

...... 

... 

.......... 

......... 

.......... 

........... 

........... 

.......... 

.......... 

... 

.. 

... 

380 

144 

?E 

:E 

12,480 425 

535 

860 

0.8 

7.9 

141 

65 3,093 

4,259 

6,135 172 

209 

461 

675 2,988 

100 

46 

460 

430 

480 

94 

94 

112 

190 

440 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

10 

..... 

..... 

..... ... 

....... 

..... 

.2 

.1 

.o 

.2 

.0 

.1 

.I 

.1 

.2 

..... 

0 

..... 

..... 

.1 

.2 

.4 

.2 

.3 

.2 

.3 

.5 

.2 

.4 

..... 

26 

5of, 

1. wo 

2,329 333 

749 

343 

643 

2,049 

5,530 

6,314 168 

315 

........... 470 

1,598 278 

452 

219 

548 

1.547 

3,612 

4,269 119 

141 

1.m 

...... 

75 

130 

285 

100 

120 

92 

77 

202 

620 

670 

52 

80 

8 

17 .......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

....... --. 21'. 

See footnotes at end of table. 
84 

m 

PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS 

APPENDIX H.-Values of hydraulic factors at various stream cross sections-Continued 

Gage 

height 

at bankfull 

stage 

(feet) 

__ 

b 

Map 1 

At mean annual discharge 

Median 

bed size 

Field * (feet) 

Slope _____ 

.53 

.Fd 

.46 

.40 

.50 

.42 

.43 

.m ....... 

................. 17 .......... 

.......... 

.......... 

.......... 

.......... 

................. 

.......... 

8.5 

7. 1 

__ 

Jelocity 

(feet 

per 

ond) 

scc- 

.00021n 

.000316 

. Ow271 

.ooo473 

.OOO94, 

,000316 

,000237 

.nonio5 

.wo189 

........ 

......... 

Serial 

NO. 

................... 

................... 

................... 

................... 

................... 

................... 

................... 

................... 

................... 

,036 .69 

no02 . 29 

Drainage 

rea (squar 

milos) 

........ 

........ 

,0316 

....... 

........ 

,0038 

........ 

,035 .88 

,021 . 67 ,00295 .21 

,024 .58 

.028 .47 .......... .l2 

,0086 .27 

Stream and location 

.54 

.35 

.46 

.4n 

Discharge 

(cuhic feet 

ier second) 

................. 

................. 

................. .......... 

.......... 

.......... 

.......... 

I 

........ 

Width 

(feet) 

.Gill8 .42 ........................... 

........................... 

........................... 

Depth 

(fect) 

.52 

.35 

.54 

.59 

.38 

.60 

.50 

.31 

.57 

.50 

.34 

....... 

....... 

....... 

.40 

.48 

.53 

.42 

.47 

.56 

.43 

.59 

.XI 

.30 

.52 

.3n 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... ................. 7. 5 ................. 

5.5 

3.8 

4.e5.1 

.......... ................. .......... 

.......... ................. 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

.......... 

...... 

........................... 

........................... 

........................... 

........................... 

........................... 

........................... 

,0038 

. 00271 

.m47 

,00114 

,000847 

. Wl8D 

,000947 

,000842 

.......... .15 ............................ ................... ............................ ................... 

................... ............................ 

............................ 

............................ 

............................ ................... 

................... 

................... 

................... 

............................ 

-1- /-- 

369 

3,847 

2,635 

I, 624 

988 

255 

571 

766 

444 

37. 

3,970 

inn Ro 

2,115 

120 

292 

3.289 

1,815 

I, 386 

797 

198 

489 

448 

292 

1,838 

85 

166 

36. 2 

1. no8 

70 

16 

29 ........ 

14,220 

11,6711 

20,950 

4, no9 

in8 

86. 7 

368 

575 

1.671 

1,264 

217 

146 

e 74 

258 

285 

126 

1, om 

30.7 ........ 

95 

200 

280 

280 

130 

205 

90 

85 

77 

24. ! 

250 

33 

28. t 115 

42 

21 

21 

600 

620 

....... 

wn 

840 

60 

60 

160 

275 

315 

86 

78 

70 

72 

92 

90 

43 

iin 

in9 

.... 

2.8 

9. 2 

3.7 

3.8 

2.5 

3.9 

5.6 

3. 2 

1.25 

2.4 

4.2 

.9 

.R 

.97 

in. 8 

2. n 

.35 

...... 

15. n 4.1 

11.5 

2.4 

1.23 

1.1 

2. 7 

2. 4 

3. 2 

4. 7 

2.9 

1. 5 1. 4 

1. 2 

2. 7 

1.65 

.a 

.53 ....... 

1. 1 

1.8 

.6 

1.35 

1.95 

.6 

1. 5 

1. 4 

.69 

.42 

2.3 

2. n 

2. n 2. 3 

1.8 

.8 

1. 34 

1. B 4. 5 

1.9 

...... 

2. n 

1.4 

1. 2 

1.2 

1. 5 

1.9 

1.9 

1. 8 

1.34 

.9 

1.3 

1.9 

1. 9 

1.4 

.87 

...... 

.12 

.IO 

.18 

.13 

.n2 

. na 

.n5 

n 

. n8 

...... 

.20 ...... 

.04 

.14 

.... 

.30 

.21 

.52 

.40 

.32 

.50 

.32 

.35 

.36 

.29 

.31 

.37 

.... 

..... 

218 

219 

220 

221 

m 

223 

214 

225 

226 

m 

228 

228 

230 

231 

232 

233 

234 

235 

236 

237 

238 

239 

240 

245 

247 

248 

249 

250 

251 

252 

253 

254 

255 

254 

257 

258 

264 

266 

267 

268 

212 

273 

274 

215 

276 

277 

278 

279 

280 

281 

282 

m 

284 

285 

3t. Joseph R., near Blakeslee, Ohio.. 

At Columbus, Ohio ............. 

At La Rue Ohio. ............... 

Bcioto R., at Chillicothe Ohio ....... 

Near Dublin, Ohio.-.. ........... 

Near Circleville, Ohio ............ 

Near Prosbet Ohio.. ........... Tiffin R., near Brhnerhurg, Ohio .... At Stryker. Ohio ................. 

Fall Creek near Pinedale, Wyo.. -. .Green R. hear Fontenelle Wyo .... 

West Fork Rock Creek, beiow Basin 

Creek near Red Lodge, Mont ...... Rock Creek near Red Lodge, Mont. Clark Fork 'near Edgar Mont.. .... Clear Creei near Buffaio Wyo.. ... North Fork'Clear Creek,'near Buffalo (near Ranger station), Wyo. .. Red Fork R. near Barnum, Wyo ... Rock Creek 'at Roberts Mont ...... Illinois R. it Kingston'Mines, Ill-.. 

At M&eilles, Ill ...... bt Meredosia Ill ..... Kankakee R., neir Wilmington,.Ill.. Pole Creek, % mile below Llttle 

Half Moon Lake near Pinedale, wyo .............................. 

Cedar Creek near Winchester, Va.- North Fork bhenandoah R., at Mt. Jackson. Va ....................... Near Strasburg Va .............. South Fork Shedandoah R., at Front Royal, Va ................... Near Luray, Va ................. 

.58 .......... :; I..... ~3:o. 

.48 ......... 

..... 

-..-.. 

. 16 

.03 

.04 

. n8 

...... 

.06 

. in 

.n4 

.n6 

. in 

. 13 

.04 

.04 

.m 

,135 

.14 

.I3 -.-..- 

.... 

.32 

.M 

.57 

.50 

.... 

.58 

.33 

.52 

.42 

.33 

.53 

.30 

.43 

.45 

.35 

.33 

.53 

..... 

.... 

................... 

........ 1 .......... 1. ........ 

........................ 

87. 

in1 

509 

772 

1,638 

1,377 

1,076 

m 

144 

76 

281 

222 

7,134 

2,070 

2, 000 

95 

298 

Va ................................. 

Ant.ietam Creek, near Sharpsburp, Md ................................ Bull Lake Creek, near Lenore, %'yo 

Cheyenne R. at Edgemont, S. Dak. 

Snake R. ne'ar Wilson, Wyo ____. ~.. 

Big San(dy Creek, near Leckie 

ranch Wyo ........................ Hams F'ork R. near Frontier Wyo.. Middle Fork Powder R., ne& Kayw, wyo .......................... Bighbrn R. near Custer, Mont 

Missouri R. at Toston Mont ...... 

At Moorhead Mont ........... 

North Fdrk Shenandoih R., at Cootes Store Va .................. 

Shenandoah R., at Millvilfe, W. Va Bighorn R., at Kane, Wyo ......... At Thermopolis. Wyo .......... 

Powder R., at Arvada, Wyo ........ At Sussex, Wyo ................ South Fork Owl Creek, above Curtis 

ranch at Thermopolis. Wyo. ____. 

Lance Creek 'at Spencer. WYO.-. .... 

Near St. Xavier, Mont .......... 

Powder R., ;ear Locst& Mont .. 

Middle R. nesr drottoes Va ....... 

Passage Creek'at Buckton Va ..... 

........ ,00055 ......... ........ 1 ,0081 1 .69 ........ ,0013 e.ooO16 

........ ,00073 e.0099 

,0043 I .......... 1. ....... 

........ 1 :E;5 I ...... ... .25 ..... ,086 .--..- 

...... 

. in ..--.- 

.04 

.28 

.15 

.30 

.26 

.06 

.44 

.44 

.21 

...... 

.n4 

. ne 

._.~.. 

...... 

.50 

.47 

.42 

.34 

.28 

.28 

.40 

.51 

.35 

.27 

.m 

. 24 

...... 

...... 

........ ....... 

........ 

390 

264 

3i0 

165 

124 

84 

73 

40 

.tm 

175 

112 

100 

21 

210 

..-.-. 

4.65 

4.9 

4. 5 

1.6 

1.7 

1.4 

1.75 

3.85 

3.8 

2. 7 

1.27 

3. n 

. 82 

.84 

.-.-.- 

2. 4 2.8 

3. 2 

2. 8 

2. 5 

1. 3 

1.8 

.95 

1. 4 

3. 35 

3. 33 2. 77 

1.85 

1.65 

980 

22,350 

e m,Ow 

4,441 

3,758 

5,322 

727 

511 

314 

........... 

12,900 

8, 030 

360 

215 

87 

15, 900 

8,080 

3, om 

6, n,w 

3, n9n 

139 

187 

70.1 

2, 561 2,413 

1.900 

410 

134 

29.1 

1 Slope measured from topoprghic map. 

1 Divided channel. 

Elope determined by field survey. 
INDEX 

Acknowledgments .......................................................... 40 

Aggradation, relation to slope of water surfam ......................... 48-50,6 9-70 

Bedconfiguration, relationofresistance to--..^----.- ......................... 66 

Bed.materia1, data on size distribution of .................................. 

resistance controlled by size of ........................................ 6546 

Braided channels, valws distinguishing meandering from ..................... 

Braidedreaches, development inflgme ..................................... 45-48 

develo-ment in Horse Creek ....................................... 4344,48, 53 

proflle of typical ........................................................ 57 

ratio of hydraulic factors .................................................. 

Braided rivers, general discussion- ....................................... 40-53 

data on divided and undivided reaches. ................................. 

Brandywine Creek . Pa ....................................................... 65, 66 

b (width-to-discharge relation), values at various cross sections ................ 81-84 

80 

59 

50 

77 

Channel adjustments, relation of dependent hydraulic variables ............ 71 

Channel division, hydraulic factors affccted ................................... .W .53 

Climate, influonce on channcl patterns- ...................................... 63.71 

Cottonwood Creek, Ryo .............................................. 60,61, 62 

Darcy-Wcishach resistance coefficient. ...................................... 65 

Depth, values at various stream cross .sections-.--.. ........................ 81-84 

Channel patterns, relation to hydra!ilic variahlcs. ............................ 59-63 

Discharge, data on hankfull .............................................. 78, 79 

values at various stream cross sections ................................... 81-84 

Elkhorn River, Ncbr.-- ............................................... 70 

No . 2, Darcy-Wieshach resistance factor .............................. 65, 72 

No . 3, rclation of resistance to depth: sizr ratio ......................... 

No . 4, relation of slope to dischargr 

Equations, No . 1, relationofslope to discharge ............................... 60 

65 

70 

/(depth-to-discharge relation), values at various cross sections ................ 81-84 

..................................... 

Flume experiments, development of braided reach ............................ 45-48 

flume described-..- ..................................................... 4M5 

sizes and distribution of sancl .......................................... 

slopeofaatersurface.~~.~ ....................................... 48-51 

summaryofdata .................................................. 76 

Ganges River, Bihar, India ................................................ 

Green River, Wyo ............................................ 40,41,50,51,53,60, F2 

Horse Creek, Wyo ..................................................... 4044,48, 53 

IIydraulic factors, values at various stream cross srctions ..................... 81-84 

75 

62 

Inglis, C . C., wavelength-discharge relation plot. tcd ........................... 

Kosi River, Bihar, Indk .................................................... 

Lithologic factors, influence on channel patterns .............................. 

Load, hydraulic adjustments related to suspended ............................ 

sediment band in relation to introduced. ................................. 

58 

62 

71 

50 

69 

slope in relation to introduced ............................................ 69-70 

m (velocity-to-discharge relation), values at wrious cross sections ............. 81-84 

Meanders. profi1coftypic;rl ............................ 

wavelength ................................................ 

Meandering channels, values distinguishing hraided fro!n ........ 

Meander River, Turkey ....................................... 

MiddleRiver,Va.- ................................. 

Mud bars, relat. ion to thalwcgs .................. 

New Fork River, Wyo ....................... 

Pcale, A . C., quoted ............. 

Pools .................................................... 

Pop0 Agie River, Wyo ........................................ 

Purpose of study .......................................... 

Quasiequilihrium . in braided stream pattcrns 

Resistancc, relation of bcd configuration to ......... 

relation of hed-material sizc to .. 

Rimes ............................. 

Rio Clrande, Bernaliilo, hT . Mes .. ~ ~ ~ ~ ~ ~ ~ 

Roughness, definition of relative ....... 

relation of load movement to channcl .... 

Runoff, inflncncc on channel patterns- . . ~ 

Sedimcnt, influence on channd patterns 

Scdimcnt transport ................. 

Shcar ............................... 

Sinnosity, defined .......................... 

Skewshoals~ ..................................... 

Slope, relation to braids .................. 

relation to changes in load..-.----^---^- 

valucs at various streem cros 

Son Itivrr, Ritiar, India .................... 

~ ~ ~ ~ 

value defining meandering channels . ~ .. ~ ~ 

Straight charuicls .............................. 

Straight reach . profilcoftypicni ................... 

Symbols cqil.tined.. ................................. 

Thal\r.eg, ~wndering .................................. 

Valloy Crcck, Fa ............................... 

Vcprtation, influence on channel \vidtti-----.-~. ~ ~ 

Velocity, nteofchangeu,ithdepth ................. 

values at variousstream cross sections ................ 

\..avrlengt. 11, data .............................. 

plotted against channel width ........................ 

plotted against dischargr.- ........................ 

ratio towidth ........................................ 

relative effect of width and discharge on ............... 

factors, influencing ............................ 

interpretation ............................................ 

valnes at. varions cross sections~ 

defined ......................................... 

Width . data on bankfull-.--- ............................... 

................... .. 

........ 57 

........ 55, 57 

........... 59, 60 

.......... 59 

....... 53,55, 57 

~~~~~~~ ~53 

53. 57 

...... 40 

....... 53-59 

....... 53,5F, 57 

......... 40 

53 

...... 66 

~ ~~~~ 65-66 

53-59 

.70 

.. 65 

. 71 

~~7

~7~~~~ 

~~ (i7-69 

t17 

53 

~~ 60 

........ 53 

~~ 48-51 

~~~ ~ ~~ lis-i0 

......... 81-84 

~~ ~~ ~~ ~~ 02 

53-59 

.... 51 

......... iv 

......... 53,54, 64 

~~ $3, 54 

....... (14 

.......... lii 

........... 81-81 

......... 78 

.......... 5.5 

.......... 58 

............ 

............ 5X.5!) 

............ iR 

............ 63-65 

......... 71 

........... 81-XJ 

85 

0