Channel Movement of 

Meandering Indiana Streams

GEOLOGICAL SURVEY PROFESSIONAL PAPER 732-A

Prepared in cooperation with the 

State of Indiana Department of 

Natural Resources
Channel Movement of 

Meandering Indiana Streams

By JAMES F. DANIEL

PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS

GEOLOGICAL SURVEY PROFESSIONAL PAPER 732-A

Prepared in cooperation with the 

State of Indiana Department of

 J J- tj

Natural Resources

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1971
UNITED STATES DEPARTMENT OF THE INTERIOR 

ROGERS C. B. MORTON, Secretary

GEOLOGICAL SURVEY 

W. A. Radlinski, Acting Director

Library of Congress catalog-card No. 74-175750

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

Washington, D.C. 20402 - Price 35 cents (paper cover)

Stock Number 2401-1221
CONTENTS

Abstract .........................................................

Introduction .................................................

Concepts .........................................................

Movement defined ...............................

The sine-generated curve ...........

Moving reference axis ...............

Observed modes of movement 

Theoretical mechanics of movement .

Impulse momentum ........_...._..

Channel-forming discharge .......

Page.

Al

1

2

2

2

2

3

5

5

6

Concepts Continued

Theoretical mechanics of movement Continued 

Channel-forming discharge redefined .........

Field investigation ..........................................................

Study sites .................................................................

Data analysis .............................................................

Interpretive discussion ...................................................

Individual sites .........................................................

General conclusions ...................................................

Summary ............................................................................

Selected references ...........................................................

Page

A6

7

7

9

14

14

15

17

17

ILLUSTRATIONS

Page

FIGURE 1. Graph showing sine curve of the best fit to data for the White River near Worthington site ................... A2

2. Diagram showing general mechanism of meander loop movement ................................................................ 3

3. Diagrams showing effects of stationary and (or) translating end points on general mechanisms of

meander loop movement .............................................................................................................................. ..... 4

4. Sketch identifying elements of the momentum concept .................................................................................... 5

5. Graph showing traveltime for the East Fork White River between U.S. Geological Survey gages at

Columbus and Seymour ...................................................................................................................................... 7

6. Map of Indiana showing location of investigated meander sites and gaging stations ............................ 8

7-12. Plan-view channel patterns for:

7. Paw Paw Creek near Urbana ...................................................................................................................... 9

8. Carpenter Creek near Egypt ...................................................................................................................... 9

9. White River near Martinsville .................................................................................................................... 10

10. White River near Worthington .................................................................................................................... 11

11. East Fork White River near Vallonia...................................................................................................... 12

12. Muscatatuck River near Austin ................................................................................................................. 13

13. Map showing definition of actual end points from theoretical loop, plotted on 1937 loop, for the White

River near Worthington site ............................................................................................................................ 13

14-20. Graphs:

14. Path-length increase versus flow volume for the White River near Worthington site .............. 13

15. Path-length increase versus flow volume for the White River near Martinsville site .............. 13

16. Path-length increase versus flow volume for the East Fork White River near Vallonia site..... 13

17. Accumulated flow volume versus water year for the White River near Worthington site .......... 15

18. Probable relation of path-length increase to silt-clay percentage .................................................... 15

19. Dimensionless relation of path-length increase and flow data to silt-clay percentage ................ 16

20. Dimensionless relation of path-length increase and flow data to width-depth ratio .................... 16

TABLES

TABLE 1. Selected site characteristics ......................................................................

2. Suspended-sediment loads for East Fork White River at Seymour

Page

A7 

14

in

PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS

CHANNEL MOVEMENT OF MEANDERING INDIANA STREAMS

By JAMES F. DANIEL

ABSTRACT

The process of channel movement in a meander system 

involves rotation and translation of meander loops and an 

increasing path length. The amount of path-length increase 

is directly proportional to the impulse supplied by discharge 

and is inversely proportional to the silt-clay percentage of 

the material composing the channel perimeter.

Comparable paths have been obtained by standardizing 

measurements with a sine-generated curve and a moving 

reference axis. Analysis of previous investigations and timeof-travel data indicates that the discharge effective in channel formation consists of the range beginning just higher 

than the average and continuing throughout all higher discharges. Of six field sites investigated, three meander systems had path-length increases of sufficient magnitude to 

correlate with above-average discharge volume, one had no 

discernible change over a 30-year period, and two had 

changes which were too small for correlation owing to the 

short period of time covered by the available data.

Because of the consistency of yearly above-average discharge volumes, it was possible to develop a general relation 

between path-length increase per thousand cubic-feet-persecond-days per square mile of drainage area above average 

discharge and the width-depth ratio of the channel. Little 

progress was made toward defining relationships for rotation and translation.

INTRODUCTION

For many years the planimetric meander form has 

both intrigued and perplexed geomorphologists. Each 

investigation has added some facet to the knowledge 

of meanders. Today, while no one will claim that all 

the answers are known, the state of knowledge is 

such that the physical characteristics of meanders 

can be described in mathematical models with a 

reasonable degree of accuracy. Laboratory and field 

investigations, such as the one by Toebes and Sooky

(1966), have provided information about the mechanics of flow within a meander, while theoretical 

investigations, such as those by Langbein and Leopold (1966) and Scheidegger and Langbein (1966), 

have delved into statistical concepts related to the 

development of meanders.

Much information is available about why meanders 

begin and about meanders in a static situation. However, a meander is not a static entity. It is dynamic 

in every respect. Valuable farmland in the flood 

plains of meandering streams is lost or changes 

ownership, and powerplants next to eroding banks 

require expensive bank stabilization, as do highway 

bridges and other structures which are in the path 

of moving, meandering channels. Investigations are 

needed regarding how, how much, and at what rate 

meanders move. Relationships need to be developed 

with which movement of meanders can be predicted. 

It is to these factors, which are of practical importance after the initiation of meandering, that this 

report is addressed.

Many persons have provided assistance to the 

author during this project, especially Richard F. 

Hadley, U.S. Geological Survey, Denver, Colo., who 

performed the field reconnaissance and made many 

suggestions about data collection. This investigation 

was conducted with financial cooperation by the 

Indiana Department of Natural Resources, Division 

of Water, whose personnel also contributed by supplying the field surveys for two of the sites investigated. Most of the personnel of the Indiana District 

at one time or another aided in the field surveys, 

often under adverse climatic conditions.

Al
A2 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS

CONCEPTS

It is the thesis of this report that the process of 

channel movement in a system already in a state of 

meandering involves rotation and translation of the 

loops and an increasing path length. Any one or any 

combination of these forms of movement may occur, 

depending on the boundary conditions of the loop. 

Each of the components of movement must be known 

in order to predict movement. Direction of movement is related to the impulse required to change 

flow direction, and rate of movement is related to 

discharge and grain size of the bed and bank 

material.

MOVEMENT DEFINED

The Sine-Generated Curve

Historically, the meander pattern has been described as either a sine curve defined by amplitude 

and wavelength or a series of semicircles defined by 

radius and wavelength. Many authors have correlated these parameters with discharge in an attempt 

to discover regional or universal relationships between them. Upon cursory examination of a topographic map showing meanders, it is apparent that 

measurements of their amplitudes, wavelengths, and 

radii would be very subjective. Each investigator 

would undoubtedly have a slightly different interpretation of each of these parameters. The result is 

that there are many slightly different but similar 

equations relating these parameters in existing 

literature. The work of Carlston (1965) did much 

to rectify some of the discrepancies between equations.

Langbein and Leopold (1966) provided a method 

to remove at least some of the subjectivity from the 

description of meanders. They showed the best description of a meander loop to be a sine-generated 

curve described by the equation:

o

<t>=<>> sin p 2* (1)

where tf>=the angle of deviation of a tangent at the 

end of s from the mean downstream 

direction.

<"=the maximum angle of deviation of path 

from the mean downstream direction 

(usually in degrees). 

s=a segment of P (in feet).

and P=the path distance through one wavelength (usually in feet).

By inspection of the example (fig. 1) for the 

White River near Worthington, it can be readily seen 

that a sine curve is the best fit for the data of this 

meander loop. Although a complete wavelength does

120

-120

5 10 15 20 25 30 35 

ASSUMED STATIONING OF BANK, IN HUNDREDS OF FEET

FIGURE 1. Sine curve of the best fit to data for the White 

River near Worthington site, July 5, 1937.

not exist, the meander is uniquely defined by the 

parameters » and P. This method has been used to 

describe the path length of the concave bank for 

movement comparison of the meanders under investigation in this report.

Moving Reference Axis

This study was begun using the procedure that 

cross sections would be surveyed at each site, steel 

pins would be set within the cross sections, and 

measurements of erosion and deposition at these pins 

would be made. After obtaining these movement 

data, correlations would be made with discharge. 

This procedure was in fact followed. However, after 

some insight was gained about the mode of movement, it was found that this type of data had little 

applicability to the problem under investigation.

For example, figure 2 shows a theoretical meander 

for two instants in time. At time tl} the loop is 

defined by w, and PI, while at at time t2 , it is defined 

by "2 (w2 ^: Wl ) and P2 (P2 ^ Pi). If, between *i and 

t2 , measurements of erosion were periodically made 

at section A, the data obtained from each measurement would represent the end point of different 

fractions of the total path length. Therefore, any 

correlation of these data would not represent the 

movement of a point on the meander loop but would 

represent the time at which different points on the 

dynamic loop would reach a fixed reference. The 

data obtained would have little application to prediction of future movement of this meander or comparison to movement of another meander.

Let us consider, however, the result of using the 

concepts of a sine-generated curve and a dynamic
CHANNEL MOVEMENT OF MEANDERING INDIANA STREAMS A3

FIGURE 2. General mechanism of meander loop movement.

system. At time t { the meander loop is denned by «i 

and PL Therefore, we can determine the stationing 

of the maximum deviations of the channel from the 

mean downstream direction, ^^SP^ and 3/4Pi. The 

mean downstream direction is the line connecting1 

those points. We can then set our reference axes 

along this line (labeled d±) and perpendicular to it 

(labeled Z t ) with the origin at y^Pi. At time tz the 

same operations are performed, resulting in coordinate axes d2 and 12 and points y&Pz and %P2 . We can then define the movement of the meander 

by measurements of the length and direction of the 

line from y^Pi to ^P2 , the rotation of the axes, and 

the change of « and P. These measurements of 

equivalent points and parameters of a developing 

loop would have value in prediction of future movement and comparison with different loops.

We have, in effect, made our measurements with 

reference axes which translate and rotate with 

time. This concept leads to a number of methods by 

which meander development could be described, and 

the method used in this report will be described 

in a subsequent section.

Observed Modes of Movement

Implied in the construction of figure 2 is the idea 

that the meander is evolving by two mechanisms. 

At time tz, P2 ^ Pi, W2 ^ «i, and dz =£ d^. This is one 

mode of change which has been observed for the 

meanders under study for this investigation. Observed movements constitute five general classes of 

expansion (increasing P) and rotation (d2 =£di), depending on the boundary conditions of the loop. One 

class of movement is shown in figure 2 and the other 

four general classes are illustrated in figure 3. These 

five modes are applicable to vertically stable (little 

or no aggradation or degradation), alluvial channels investigated in this study. Channels incised in 

bedrock would have the meander pattern imposed 

by the stream when degradation began. Because of 

the abrasive effect of bedload, their mode of movement is basically vertical rather than lateral.

The concept of increasing path length (AP), a 

contributing factor to the movements shown in figure 3, was inferred by Langbein and Leopold (1966, 

p. H2) :

In the context of the whole river system, a meandering 

segment, often but not always concentrated in downstream 

rather than upstream portions of the system, tends to provide greater concavity by lengthening the downstream portion of the profile. By increasing the concavity of the profile, 

the product of discharge and slope, or power per unit length 

becomes more uniform along a stream that increases in flow 

downstream. Thus the meander decreases the variance of 

power per unit length * * *.

The conclusion is reached that meanders provide 

a greater path length which makes energy dissipation more uniform. It is reasonable to extend this 

conclusion to say that, unrestricted, the path length 

would continue to increase until energy dissipation 

is uniform. In the field, natural cutoffs or chuting 

(Friedkin, 1945) would occur before uniform energy 

dissipation was achieved. Therefore, in the dynamic 

system, increasing path length is a requirement.

Figure 3 illustrates an extension of this concept. 

In figure 3A, points a± and a/, are essentially fixed. 

Such a condition exists when dense vegetation or 

"clay plugs" restrict movement of the banks at 

these points. In this situation, erosion results simply 

in a path-length increase. In figure 3B, point % is 

fixed while ai is not, and in figure 3C the reverse is 

true. In either situation, the two mechanisms, change 

of downstream direction (rotation) and increasing 

path length, are more equal in effect. Figure 3D 

shows a loop whose condition is very near dynamic 

equilibrium in a uniformly erodible medium. Such 

a condition is approached in laboratory experiments 

(Friedkin, 1945) in which the whole meander system tends to translate downstream.

Not shown are conditions which might result if 

the less erodible parts of the loop constituted other 

segments of the loop. Many possible combinations 

are obvious. The significant point is that a meander 

system works toward equal energy dissipation by
A4 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS

a,i has stationing lAPj 

a'i has stationing %Pi

D. Translation (dynamic equilibrium)

FIGURE 3. Effects of stationary and (or) translating end points on meander loop movement.
CHANNEL MOVEMENT OF MEANDERING INDIANA STREAMS A5

increasing the path length, and where erosion rates 

within a loop differ greatly, rotation also occurs.

These mechanisms of movement should have application to all forms of free meanders when they 

are viewed throughout a period of time. Boundary 

conditions at the end points of and within each loop 

can result in the dominance of any single mechanism 

of increasing path length, rotation, or translation, 

but the usual condition would be some combination 

of the three.

THEORETICAL MECHANICS OF MOVEMENT

That meandering is a stochastic process has been 

established by previous studies. One can reasonably 

expect, however, that cause-effect relationships govern the movement of an individual meander.

Impulse Momentum

Friedkin (1945, p. 11) wrote, "The rate of bank 

erosion depends upon the force of the water against 

the banks as well as the toughness of the banks." It 

is a small step from this idea to the concept of 

impulse-momentum change, which seems to offer 

the most reasonable basis for an explanation of 

movement.

Assume a segment of channel with constant curvature as shown in figure 4. The mean velocity 

vector of the fluid, which has a discharge of q and

FIGURE 4. Identification of elements of the momentum

concept. - 

flows in the channel between points A and B, can 

be represented by the unit vector v which is parallel 

to a tangent to AB at any point.

At point A, q has momentum pqvA and at point 

B, q has momentum pqvB where p is the density of 

the fluid. The difference in the two values is the 

change of momentum in the intervening reach and 

ideally is equal to the force applied by the bank to

the water. Of prime interest, however, is the force 

applied by the water to the bank that is, the impulse of the water on the bank.

The mechanism of bank movement can be explained in terms of the applied impulse on the bank 

and the resulting momentum of dislodged bank 

material. The following equation expresses this 

mechanism :

Fqdt= (mvB ) b - (mvA ) (2)

where Fq is the force supplied by the water, tA and 

tB are the times at which q pases points A and B, 

(mvA )i> is the product of mass and velocity of the 

bank at tA , and (mvB ) b is the same product at tB. 

The bank material between A and B has no momentum at tA . However, in an credible material the impulse dislodges individual grains of bank material 

which are moved by the flow and do have momentum 

at tB. Equation 2 can then be rewritten for the 

grains affected by q as:

rtB

/ Fqdt=(mgvB ) b (3) 

J tA

As AB -» 0, equation 3 represents the impulse at a 

point where the left side of the equation is the force 

of the fluid on the bank, the time interval of force 

application has end points tA and tB, and the direction of the force is always tangent to the channel. 

In the real situation this direction of force tends to 

increase the path length.

The foregoing expression does not take into account the process occurring on the opposite bank 

where material is being deposited and hence losing 

momentum. For the streams investigated and for 

most streams with similar climatic and physical 

conditions, the channel characteristics are relatively 

stable; that is, even though meanders move with 

some rapidity, widths, depths, and width-depth 

ratios remain fairly constant so that the amount 

of material deposited very nearly equals the amount 

of material removed. Therefore, equation 3 is an 

adequate, albeit gross, means of representing movement of the concave bank if it can be assumed that 

the force effective in removing bank material is 

directly proportional to the total flow in the stream, 

Q. This assumption has been made, and it is the 

movement of the concave bank which has been analyzed.

The next steps are to put equation 3 in a form 

more easily analyzed with available data and make 

the necessary real-world substitutions. For a constant force, equation 3 can be rewritten as :
A6 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS

(4)

Movement is another way of expressing material 

removed, (mgvB )b- Because the direction of force is 

always toward increasing path length (AP), the 

right side of equation 4 is proportional to AP. Force 

is proportional to Q. Different materials erode at 

different rates, depending on the cohesiveness of the 

material. The more cohesive the material the slower 

it erodes, so AP is inversely proportional to cohesiveness. A convenient measure of cohesiveness is the 

percentage of silt and clay in a material, M, as 

defined by Schumm (1960). Substituting in equation 4 results in the relation: 

Q(tB -tA )

M

ocAP (5)

This expression lends itself to the use of flow-duration data.

Duration data are compiled in tables listing the 

number of days for narrow discharge ranges. The 

product of the number of days for each range (N) 

and the average discharge of that range can be 

used as a constant discharge for a definite period 

of time with little error being introduced by using 

the average discharge of the range. All such products can then be accumulated so that relation 5

becomes:

^/n \r\

(6) M

which is the basis for the analysis of data obtained 

in this investigation.

The development of relation 6 gives a macroscopic 

view of the mechanics of meander expansion. This 

explanation does not take into account the many 

microscopic processes which take place in a meander, 

such as bed or bank shear, superelevation, eddy 

currents, or transverse flow. The contribution of 

these factors is unquestionable, but they do not 

always have to be considered in determining direction or magnitude of channel movement. The important consideration is the net effect, and the impulse-momentum concept applied to the concave 

bank supplies just that. It is a measure of the net 

effect of flow on an erodible material. The work 

done (or energy expended) in changing momentum 

from one value to another is the same no matter 

what process effects that change.

Channel-Forming Discharge

All discharge within an alluvial channel has some 

effect on the channel-shape parameters. Because of 

this it is impossible to relate these parameters to 

only one discharge. Several investigators have alluded to this premise.

Carlston (1965) found the most significant relationships for meander wavelength to involve average discharge and the mean discharge for the month 

of maximum discharge. Schumm (1968, 1969) found 

that when average, bankfull, and mean annual flood 

discharge are each correlated with the percentage 

of silt and clay in the channel perimeter and channel 

properties, the results are, to nearly equal degrees, 

very significant explanations of meander wavelength and channel cross-sectional properties. Stall 

and Fok (1968) found that hydraulic geometry was 

best explained using the discharge at 10-percent 

flow duration. These relationships show that there 

is a range of discharge from at least the average 

to the mean annual flood which controls the dimensions of meanders.

The position of the main-velocity thread in a 

meander loop at varying discharge has been shown 

by Friedkin (1945, pi. 9). He indicated that low 

flow attacks the upstream part of the concave bank, 

half-bankfull flow attacks the mid-part, and bankfull flow attacks the downstream part. At discharge 

greater than bankfull, the meandering velocity pattern is not destroyed, and the turbulence effective 

in erosion may be increased (Toebes and Sooky, 

1966).

Channel-Forming Discharge Redefined

Consideration of all the relationships developed 

indicates not only that all discharge affects channel 

dimensions, but that there is a threshold discharge 

at and above which the major part of channel formation occurs. Channel dimensions should depend upon 

those flows for which the channel acts as a unit. 

At low flows (less than average), the pool and riffle 

sequence within channel limits is effective, resulting 

in a low-water channel which often meanders within 

the confines of the bankfull channel. At some discharge the pool and riffle sequence is drowned out, 

and the channel acts as a unit at all higher discharges. The point is probably reached near average 

discharge as the relationships discussed have indicated.

Some further evidence can be gained from study 

of traveltime data. Figure 5 presents the results 

of several traveltime determinations for the East 

Fork White River. The break in slope occurs near 

average discharge and is characteristic of unpublished traveltime curves for most of the streams 

in Indiana which exhibit a pool and riffle condition 

at low flows.

Channel formation can be considered, then, to 

begin at just above average discharge and continue
CHANNEL MOVEMENT OF MEANDERING INDIANA STREAMS A7

10,000

Q LlJ

W*

o: O

m D 

o " 

^2

§°

LjJ O

O ^ 

Q<

1,000

100

15-11-67

BREAK ABOUT 2400 CFS 

AVERAGE 0 =2346 CFS 

^ (40 YEARS, 1928-67)

>r

)4-19-68

7-27-6

10 100

TRAVELTIME, IN HOURS

FIGURE 5. Traveltime for the East Fork White River between U.S. Geological Survey gages at Columbus and 

Seymour.

for all higher discharges. This range can also be 

considered to be directly related to the expansion 

of a meander loop.

The remainder of this paper is an attempt to test 

the conclusions reached up to this point namely, 

that path-length expansion is directly proportional 

to the volume of flow for above-average discharge 

days and inversely proportional to the percentage 

of silt and clay in the bed and bank material.

FIELD INVESTIGATION

STUDY SITES

The sites investigated for this project are shown 

in figure 6, and some pertinent physical characteristics are listed in table 1. All sites were within a 

reasonable distance from a U.S. Geological Survey 

stream-gaging station (fig. 6) except for Paw Paw 

Creek which is ungaged. As shown in table 1, a 

wide range of characteristics is represented.

The surficial geologic characteristics were formed 

during the Wisconsin Glaciation in the Pleistocene 

Epoch. At the maximum glacial advance, the northern two-thirds of Indiana was covered by Wisconsin 

ice. The two sites on the White River and the site 

on the East Fork White River are south of the 

maximum Wisconsin glacial advance, but the material filling the present river valleys is outwash from 

the melting of this last continental glaciation. The 

Muscatatuck River site is also south of the Wisconsin boundary, but the predominately clay material 

at the site was deposited in a lake whose basin was 

formed during the previous Illinoian Glaciation. 

The lake sediments of the Carpenter Creek site and 

the morainal features of the Paw Paw Creek site 

were deposited during glacial retreats of the Wisconsin Glaciation.

The weighted silt-clay percentage (fine fraction) 

was computed by a method described by Schumm 

(1960), but a diameter of 0.062 mm (millimeter), 

instead of 0.074 mm, was used as the dividing point

TABLE 1. Selected site characteristics

[Depositional environment: After Wayne (1958)]

Drainage

Name and location (

Paw Paw Creek near Urbana........

Carpenter Creek near Egypt ......

White River near Martinsville....

White River near Worthington....

East Fork White River

near Vallonia ................................

Muscatatuck River near Austin.....

area

sq mi)

8.60

48.0

2,520

4,390

2,530

.. 367

Period of

record

(water

years)

1949, 1951,

1953-67

1930-31,

1946-67

1929-67

1928-67

1933-35,

1937-43

Average

discharge

at gaging

station

(cfs)

33.7

2,258

4,459

2,346

387

Channel

slope

(ft per

ft)

0.0018

.00064

.00035

.00023

.00024

.00025

Widthdepth

ratio

7.2

8.0

27

20

14

5.8

Weighted

silt-clay

percentage

7.9

29

2.2

2.6

6.9

87

Depositional

environment

Ground moraine.

Lake sediments.

Valley-train sediments.

Do.

Do.

Lake sediments.
A8 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS

87°

38°-

FIGURE 6. Location of investigated meander sites and gaging stations.
CHANNEL MOVEMENT OF MEANDERING INDIANA STREAMS A9

EXPLANATION FOR FIGURE 6

Meander sites

Map No. Name and location

1 Paw Paw Creek near Urbana, Wabash County, 

sec. 12, T. 28 N., R. 6 E.

2 Carpenter Creek near Egypt, Jasper County, 

sec. 22, T. 28 N., R. 7 W.

3 White River near Martinsville, Morgan County, 

sec. 7, T. 11 N., R. 1 E.

4 White River near Worthington, Greene County, 

sec. 28, T. 8 N., R. 5 W.

5 East Fork White River near Vallonia, Jackson 

County, sees. 19, 30, T. 5 N., R. 4 E.

Meander sites Continued

Map No. Name and location

6 Muscatatuck River near Austin, Scott County, 

sees. 33, 34, T. 4 N., R. 6 E., and sec. 3, 

T. 3 N., R. 6 E.

Gaging stations

National No. Name

5-5240 Carpenter Creek at Egypt.

3-3540 White River near Centerton.

3-3605 White River at Newberry.

3-3655 East Fork White River at Seymour.

3-3670 Muscatatuck River near Austin.

for fine and coarse fractions. A dividing-point diameter of 0.062 mm conforms to the Wentworth grade 

scale and results in only a slightly smaller percentage. The difference is not enough to destroy 

comparability. Material for these analyses was collected at several locations on both banks within 

each study reach, and the results were averaged 

for each reach. The variability within each reach 

was considered sufficiently small that a reach could 

be treated as having fairly homogeneous lithology 

throughout.

The field investigations were carried out from the 

spring of 1966 to the spring of 1969. Channel locations were identified from aerial photographs and, 

except for those from 1939 and 1958 for the Martinsville site, were obtained from the files of the 

Indiana Department of Natural Resources. The two 

exceptions were obtained from the files of the Soil 

Conservation Service, U.S. Department of Agriculture. Plan-view channel patterns for all sites are 

shown in figures 7 through 12. The method of 

analysis will be illustrated with the White River 

near Worthington site (fig. 10).

100 200 FEET

I_____|

No trees on either bank

FIGURE 7. Meander system at the Paw Paw Creek near 

Urbana site. Surveyed by J. F. Daniel and J. W. Tucker, 

April 3, 1969.

DATA ANALYSIS

Field surveys at the White River near Worthington site were made June 7, 1966, and July 23, 1968, 

by Indiana Department of Natural Resources personnel. The results of those surveys and the bank 

locations based on aerial photographs taken July 5, 

1937, and April 16, 1962, are shown in figure 10. 

Any further usefulness of this site was destroyed 

when a natural cutoff formed in late June 1968.

50 FEET

EXPLANATION

Concave-bank locations 

June 20, 1966 

May 26, 1969

FIGURE 8. Meander development at the Carpenter Creek 

near Egypt site. Surveys by J. F. Daniel and others.
A10 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS

Each path location was analyzed independently as 

follows:

1. The direction angles with an assumed mean 

downstream direction were measured for equal, 

short tangents of the cut-bank path length.

2. The direction angles and the stationings were 

plotted, and a sine curve was fitted to the 

points. (See fig. 1.)

3. The path length, corrected mean downstream 

direction (obtained by adjusting the vertical 

coordinate scale), and amplitude of the sine 

wave were determined from the graph.

4. The theoretical loop was then compared with 

the actual loop by plotting the positions of 

both, beginning at the midpoint stationing of 

the actual loop.

EXPLANATION

Concave-bank locations

July 17, 1939 (aerial photograph) 

 June 29, 1958 (aerial photograph)

March 21, 1964 (aerial photograph)

June 2, 1966 (survey)

April 17, 1967 (survey)

July 18, 1968 (survey)

End point

Barren 01

FIGURE 9. Meander development at the White River near Martinsville site. Surveys by State of Indiana Department

of Natural Resources.
CHANNEL MOVEMENT OF MEANDERING INDIANA STREAMS All

5. A line joining the *4- and %-wavelength points 

on the theoretical loop was extended to the 

actual loop, as in figure 13. This method objectively defines y^P and %P on the actual 

loop, and the path distance between these two 

points was measured.

Using duration data which were computer-compiled by class interval, the total flow volume of all

days having discharge greater than the effective discharge was accumulated. It has already been shown 

that this effective discharge occurs at a discharge 

slightly greater than the average. Therefore, accumulation was begun with the first class interval 

greater than the average. Volume for each class 

interval was computed by taking the product of the

-Continuous trees

EXPLANATION 

Concave-bank locations

 June 7, 1966 (survey) 

July 23, 1968 (survey) 

End point

July 5,1937 (aerial photograph) 

April 16, 1962 (aerial photograph)

FIGURE 10. Meander development at the White River near Worthington site. Surveys by State of Indiana Department

of Natural Resources.
A12 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS

average of the class and the number of days in 

the class. While this is not an exact measure, the 

class intervals are small enough that very little error is introduced.

The effective-discharge volume was then plotted 

versus the accumulated path-length increase as in

figure 14. It appears that the few points available 

define a straight line, which was fitted by eye. Using 

the same technique, the same relations were developed for the White River near Martinsville and the 

East Fork White River near Vallonia sites (figs. 

15,16).

Continuous trees

EXPLANATION 

Concave-bank locations

August 4, 1937 (aerial photograph)

 September 1, 1949 (aerial photograph) 

April 19, 1966 (survey) 

April 5, 1967 (survey) 

April 24, 1968 (survey)

 April 8, 1969 (survey) 

End point

FIGURE 11. Meander development at the East Fork White River near Vallonia site. Surveys by J. F. Daniel and others.
CHANNEL MOVEMENT OF MEANDERING INDIANA STREAMS A13

Flow

0 100 200 FEET

I i I______I

\ Trees are continuous on both banks

FIGURE 12. Meander system at the Muscatatuck River near 

Austin site. Surveys by J. F. Daniel and R. J. Southwood, 

April 28, 1966.

EXPLANATION

o Computed point

® End point

- Theoretical loop

 Actual loop

FIGURE 13. Definition of actual end points from theoretical 

loop, plotted on 1937 loop, for the White River near 

Worthington site.

2000

FLOW VOLUME FOR DAYS ABOVE AVERAGE DISCHARGE, 

IN MILLIONS OF CFS-DAYS

FIGURE 14. Path-length increase versus flow volume for the 

White River near Worthington site.

r 800

600-

o

LJI- 

_ILJ

I £400

July 17, 1939,and March 21, 1964

200-

FLOW VOLUME FOR DAYS ABOVE AVERAGE DISCHARGE, 

IN MILLIONS OF CFS-DAYS

FIGURE 15. Path-length increase versus flow volume for 

the White River near Martinsville site.

600

April 8, 1969_ 

April 24, 1968 

April 5, 1967-

April 19, 1966

400 -

300

200

100

FLOW VOLUME FOR DAYS ABOVE AVERAGE DISCHARGE, 

IN MILLIONS OF CFS-DAYS

FIGURE 16. Path-length increase versus flow volume for the 

East Fork White River near Vallonia site.
A14 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS

INTERPRETIVE DISCUSSION

INDIVIDUAL SITES

The differences between bank locations at different times at the sites on Paw Paw Creek near 

Urbana, Muscatatuck River near Austin, and Carpenter Creek near Egypt were small; therefore data 

obtained from studies at these three sites were not 

adequate for analysis.

Bank locations of Paw Paw Creek for 1941 and 

1962, as determined from aerial photographs, are 

not significantly different from those mapped by 

surveys in 1967, 1968, and 1969. There is field evidence of erosion and change, as identified by measurements of steel pins set in the channel, but the 

scale factor of the photographs in combination with 

such slight changes in bank location makes the 

data unreliable for developing a mechanism applicable to other sites.

The bank location of the Muscatatuck River near 

Austin site has not changed during the period 1940- 

66, as determined from aerial photographs in 

1940, 1949, and 1956 and a field survey in 1966. Rotation of steel pins in the channel indicates that bank 

creep moves earth material toward the bank face 

where it is loosened by freeze and thaw cycles and 

carried away by high flows. This indicates that the 

channel is widening, but at such a slow pace that it 

is not readily measurable. Another valuable insight 

learned at this site is that, for this particular relation between silt-clay percentage and discharge 

volume, the increase of path length is virtually nil.

There was also no significant change at the Carpenter Creek at Egypt site. However, field surveys 

for a longer period than 1967-69 would probably 

yield information that would allow analytical results. Aerial photographs for 1939 could not be used 

to obtain a comparable path because of uncertainty 

of reference-point location.

The studies at the East Fork White River site 

yield information which is reliable. The data on 

expanding path length were collected for a 33-year 

period when the site was not directly affected by 

man. The author believes, however, that any further 

data collection at this site would not be worthwhile

because the loop is moving into a prior channel 

location. Data obtained will no longer be applicable 

to a singly defined loop.

In conjunction with the field investigation at this 

site, measurements of daily suspended-sediment load 

were made at the gaging station upstream. The 

suspended loads measured during the field-survey 

period are presented in table 2. Russell F. Flint 

(written commun., 1966) estimated the average 

yearly load on the basis of an indirect method of 

analyzing periodic samples collected during the 

period 1963-65. Because the daily load record is 

short and the estimated yearly load seems disproportionately high, no reasonable relation of sediment 

load to expansion rate has been found. The data 

herein are presented for future reference.

Some discussion of the White River near Martinsville site is needed to explain the two curves in figure 

15. Between 1958 and 1964, the middle part of the 

loop was stabilized with riprap and the upper part 

of the loop was apparently straightened. This channel alteration appears to have resulted in an increased rate of path lengthening owing to increased 

erosion in the downstream part of the loop. It seems 

likely that this increased rate will be temporary 

and that there will be a return to the prealteration 

rate. For this reason the author believes that the 

previous rate can be used for comparison with rates 

of other sites.

General relations can be developed from the 

studies at the Vallonia and Martinsville sites, which 

were just discussed, and at the Worthington site,

TABLE 2. Suspended-sediment loads for East Fork White 

River at Seymour

Survey period Sediment-load 

period

Sediment 

load 

(tons)

4-20-66 to 4- 5-67 

4- 6-67 to 4-24-68 

4-25-68 to 4- 8-69

7- 1-66 to 4- 5-67 

4- 6-67 to 4-24-68 

4-25-68 to 4- 8-69

220,705

312,146

971,099

Estimated annual sediment load .................................................. 721,000
CHANNEL MOVEMENT OF MEANDERING INDIANA STREAMS A15

which was used to illustrate methods in the section 

on data analysis.

GENERAL CONCLUSIONS

Data indicate that for each of the three sites for 

which analysis was possible a well-defined relationship could be developed between time and path 

length as well as between discharge and path length. 

The relation between time and path length is not 

as sharply defined as that between discharge and 

path length, but for all practical purposes they are 

equivalent. The explanation for this is indicated in 

figure 17 where there is a lack of large deviations 

between the mass curve and the dashed line. This 

indicates that annual discharge volumes for days 

above average discharge are relatively constant. 

Therefore, an increase in path length would be 

relatively constant from year to year. This condition is more likely to occur in a subhumid climate, 

such as that in Indiana, than in a semiarid climate, 

such as that in the Great Plains, where yearly 

changes in discharge volume for days above average 

discharge are relatively much greater. Therefore, 

while a yearly path-increase rate for the sites in 

Indiana is sufficient for use, the same method probably could not be used for meander loops developing 

from different climatological conditions. For streams 

in different climates, the path-length versus discharge-volume relation should yield better results.

Through the study of the annual path-length increase, some insight can be gained into the effect 

of grain size. In figure 18 the rate of path-length 

increase has been transformed to a per-square-mile 

basis and plotted versus the silt-clay percentage. 

Not shown is the point defined by the Muscatatuck 

site (no expansion; 87 percent silt and clay), but it 

was considered in shaping the curve. Again, while 

not enough data are available for "proof" of a hypothesis, the points do indicate that the expansion 

rate would have a nonlinear relation to the silt-clay 

percentage. It seems reasonable that this relation 

would be asymptotic to the silt-clay axis, indicating 

that no bank would completely resist erosion. The 

extension of the curve toward zero silt and clay may 

be asymptotic to the rate axis also, but it probably

30

15

10 -

/

y

7

A

/

1937 1942 1947 1952 1957 

WATER YEAR

1962 1967

FIGURE 17. Accumulated flow volume versus water year 

for White River near Worthington site.

0.020

LJ o:

LL <

Z. >

-a: 0.015

tr j

la: i- <

0.010

0.005 -

-Martinsville 

-Worthington

Vallonia

2468 

WEIGHTED SILT-CLAY PERCENTAGE

10

FIGURE 18. Probable relation of path-length increase and 

silt-clay percentage.

would be discontinuous at some point close to that 

axis. This would indicate that as the path length 

increased at an extremely rapid rate the radius of 

curvature of the channel would become infinite, 

thereby resulting in a straight reach with little or no
A16 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS

change in path length. In other words, at some 

extremely small silt-clay percentage, the path length 

would not increase. The channel could still move, 

but the path length would not change except for 

short periods of time.

In order that comparison with meander migration in other regions can be made in the future, 

the data have been put into dimensionless form as 

shown in figure 19. The scatter of the points with 

regard to silt-clay percentage indicates a lack of

250

oi 200

150

100

- Worthington

Martinsville

Vallonia

246

WEIGHTED SILT-CLAY PERCENTAGE

10

FIGURE 19. Dimensionless relation of path-length increases 

and flow data to silt-clay percentage.

orderly progression. However, when width-depth 

ratio is used as the dimensionless parameter for 

the abscissa, as in figure 20, a logical sequence of 

points is obtained.

The apparent discrepancy between these two 

treatments can best be explained by sampling error. 

Schumm (1960) related width-depth ratio to siltclay percentage of the bed and banks. His data 

were derived from cross sections and indicate a 

definite correlation between the two parameters. 

For this investigation several points within each 

reach were sampled for silt-clay percentage, and 

the results were averaged for the reach. The scatter 

of data in figure 19 indicates that enough samples 

to establish a statistically significant average may 

not have been obtained. Apparently, then, the average width-depth ratio is a more integrated, and 

hence better, measure of the average silt-clay percentage than the bed and bank samples themselves.

tg 25°

200

150

100

LLJ 

^0 M

SS5 50 

2<2j

oil 

o

O an 

 O u- n

5-° °o

ce

Worthington -

Martinsville

Austin^

Vallonia

10 20 

WIDTH-DEPTH RATIO

30

FIGURE 20. Dimensionless relation of path-length increase 

and flow data to width-depth ratio.

The interpretation of figure 20 is similar to that 

of figure 18. The higher the width-depth ratio, the 

lower is the silt-clay percentage and the faster is 

the path-length increase. Conversely, the lower the 

width-depth ratio, the higher is the silt-clay percentage and the slower is the path-length increase. 

Again, as in the interpretation of figure 18, one 

would expect that no channel would completely resist erosion so that any curve should pass through 

the origin. However, because of the few points 

available, an extension of the curve to the origin 

has not been shown.

The inclusion of the drainage area in the ordinate 

may or may not tend to restrict the validity of 

figure 20 to climatic or geologic conditions similar 

to those for which it was developed. If it does and 

if the concept is correct, one would expect to find 

a family of curves, each representing a particular 

environment. To test this relation by studying 

meanders in other areas would seem to be a logical 

"next step" to this investigation.

The foregoing interpretation of figure 20 tends 

to invalidate the relation shown in figure 18. Because of this and because of its more usable dimensionless form, the author feels that figure 20 represents the best treatment of the available data. It 

could be used to estimate path-length increase of 

alluvial streams in Indiana having width-depth 

ratios within the approximate range of 8 to 28 and 

for most flow volumes. Time intervals for pathlength increases can be related to flow volume by 

doing flood-volume frequency analyses for short
CHANNEL MOVEMENT OF MEANDERING INDIANA STREAMS A17

time intervals or by considering only long intervals 

(several years) and using average discharge. It 

must be remembered, however, that path-length increase is only part of the movement mechanism.

The mechanisms of translation and rotation have 

been described earlier in this paper (figs. 2 and 3) 

but not enough data are available for a quantitative 

analysis of the total process. If the end points of a 

loop are likely to be stable, such as at the Vallonia 

site, then rotation and translation cease to have an 

appreciable effect. A useful estimate of movement 

might then be made with figure 20. Because this 

condition seldom exists, further investigation of 

rotation and translation is also a next step to this 

investigation.

It has also been impossible to evaluate the effects 

of vegetation on loop expansion. Qualitative descriptions of vegetative cover proposed by Dansereau 

(1957) and listed by Strahler (1965) have been 

given on the site illustrations. The percentage of 

path length supporting dense vegetation is nearly 

equal for each of the three sites used to develop 

the relation shown in figure 18. It seems logical 

that vegetation would slow down expansion. However, unless vegetation covers 100 percent of the 

path, the experience at the Martinsville site indicates that the effect may be overcome by expansion 

in that part of the loop which is not protected. The 

effect of dense vegetation can be likened to the effect 

of very different material composition; for example, 

abandoned clay-filled meanders are often the inhibiting factors that control channel movement on the 

lower Mississippi River (C. R. Kolb, written commun., 1969). Because similar problems in analyzing 

movement result from either cause, much more data 

are needed before any quantitative effect of vegetation or very different material zones can be assigned.

SUMMARY

The attempt has been made in this report to 

review some established principles of channel geomorphology and to use those principles to give some 

insight to the process and prediction of meander 

movement.

Meander loop movement has been investigated by 

using a sine-generated curve to determine the end 

points of a loop from which the actual path length 

can be measured. Using the simple physical model 

of impulse momentum, a relationship of discharge 

to loop expansion has been deduced and related to 

grain size of the bank material.

Consideration of traveltime data and the regression analyses of many other investigators has led

to the conclusion that channel-forming discharge 

begins very near, but just higher than, average 

discharge and continues throughout all higher discharges. Channel movement is then a function of the 

time distribution of the higher discharges.

A division of the channel material into fine and 

coarse fractions has been used in order to relate 

the rate of expansion to the cohesiveness of the 

banks. Suspended-sediment discharge records were 

collected for one site but are not of sufficient length 

for rigorous analysis.

Several simple models of channel movement by 

rotation, translation, and expansion have been illustrated on the basis of the experience gained 

from this investigation. No general relation has 

been found with which the first two processes could 

be analyzed. Therefore, the goal of movement prediction has not been achieved. However, if reasonable relationships can be found to relate rotation 

and translation to common factors, those relationships, along with the expansion relation which has 

been defined, will give scientists a tool with which 

it may be possible to predict the movement of 

meanders.

SELECTED REFERENCES

Bagnold, R. A., 1960, Some aspects of the shape of river 

meanders: U.S. Geol. Survey Prof. Paper 282-E, p. 

135-144.

Carlston, C. W., 1965, The relation of free meander geometry to stream discharge and its geomorphic implications: Am. Jour. Sci., v. 263, p. 864-885.

Dansereau, Pierre, 1957, Biogeography, an ecological perspective: New York, The Ronald Press Co., 394 p.

Friedkin, J. F., 1945, A laboratory study of the meandering 

of alluvial rivers: Vicksburg, Miss., U.S. Waterways 

Expt. Sta., 40 p.

Guy, H. P., Rathburn, R. E., and Richardson, E. V., 1967, 

Recirculation and sand-feed type flume experiments: 

Am. Soc. Civil Eng. Trans., v. 93, p. 97-114.

Langbein, W. B., and Leopold, L. B., 1966, River meanders 

theory of minimum variance: U.S. Geol. Survey Prof. 

Paper 422-H, 15 p.

Leopold, L. B., Bagnold, R. A., Wolman, M. G., and Brush, 

L. M., 1960, Flow resistance in sinuous or irregular 

channels: U.S. Geol. Survey Prof. Paper 282-D, p. HI134.

Leopold, L. B., and Langbein, W. B., 1962, The concept of 

entropy in landscape evolution: U.S. Geol. Survey 

Prof. Paper 500-A, 20 p.

Leopold, L. B., and Haddock, Thomas, Jr., 1953, The hydraulic geometry of stream channels and some physiographic implications: U.S. Geol. Survey Prof. Paper 

252, 27 p.

Leopold, L. B., Wolman, M. G., and Miller, J. P., 1964, 

Fluvial processes in geomorphology: San Francisco, 

W. H. Freeman & Co., 522 p.
A18 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS

Popov, I. V., 1965, The use of hydrologic-morphological analysis in water intake planning: Soviet Hydrology, Selected Papers, no. 5, 1965, p. 437-450 (1966).

Scheidegger, A. E., and Langbein, W. B., 1966, Probability 

concepts in geomorphology: U.S. Geol. Survey Prof. 

Paper 500-C, 14 p.

Schumm, S. A., 1960, The shape of alluvial channels in relation to sediment type: U.S. Geol. Survey Prof. Paper 

352-B, p. 17-31.

 1968, River adjustment to altered hydrolcgic regimen Murrumbidgee River and paleochannels, Australia: U.S. Geol. Survey Prof. Paper 598, 65 p.

1969, River metamorphosis: Am. Soc. Civil Eng.

Trans., v. 95, p. 255-273. 

Stall, J. B., and Fok, Yu-si, 1968, Hydraulic geometry of

Illinois streams: Illinois Univ. Water Resources Center

Research Rept. 15, 47 p. 

Strahler, A. N., 1965, Introduction to physical geography:

New York, John Wiley & Sons, Inc., 455 p.

Thornbury, W. D., 1950, Glacial sluiceways and lacustrine 

plains of southern Indiana: Indiana Dept. Conserv., 

Div. Geol. Bull. 4, 21 p.

Toebes, G. H., and Sooky, A. A., 1966, Hydraulics of meandering rivers with flood plains: Am. Soc. Civil Engineers Water Resources Eng. Conf., Denver 1966, Preprint 351, 38 p.

Twidale, C. R., 1964, Erosion of an alluvial bank at Birdwood, South Australia: Zeitschr. Geomorphologie, 

New Ser. v. 8, no. 2, p. 189-209.

Wayne, W. J., 1958, Glacial geology of Indiana: Indiana 

Dept. Conserv., Geol. Survey Atlas Min. Resources Map 

10.

Wolman, M. G., and Leopold, L. B., 1957, River flood plains: 

some observations on their formation: U.S. Geol. Survey 

Prof. Paper 282-C, p. 87-109.

Woodyer, K. D., 1968, Bankfull frequency in rivers: Jour. 

Hydrology, v. 6, p. 114-142.

U. S. GOVERNMENT PRINTING OFFICE : 1971 O - 443-512