This file was created by scanning the printed publication. Errors identified by the software have been corrected; however, some errors may remain.Abstract



### Concepts of stream dynamics are demonstrated through discussion of processes andprocess indicators; theory isincluded only where helpful to explain concepts. Present knowledge allows only qualitative prediction of stream behavior. However, such predictions show how management actions will affect the stream and its environment.

### USDA Forest Service GeneralTechnicalReportRM-72



# Stream Dynamics: An Overview for 

# Land Managers

Burchard H. 

### Heede, Principal Hydraulic Engineer Rocky Mountain Forest and Range Experiment Station1 

### April 1980

'Headquarters at Fort Collins, in cooperation with Colorado State University. Research reported here was conducted at the Station's Research Work Unit at Tempe, in cooperation withArizona State University.Contents



## ..................................................................... Introduction



## ............................................................. Scope and Purpose



## ...................................................... Characteristics of Streams



## ......................................................... The Basic Fluvial Process



## ............................................ SubcriticalVersus SupercriticalFlow



## .............................................................. Froude Number



## .......................................... Laminar Versus Turbulent Flow ;

## .......



## ............................................................ Reynolds Number Sediment Transport



## ............................................................

.......................................... Interdependency of Hydraulic Variables Equilibrium Condition andAdjustment Processes



## .................................... Dynamic Equilibrium



## ......................................... 

## :



## .................

...................................................... Complex Channel Response



## ...................................................... Major Adjustment Processes



## ................................... Processes Affecting ChannelPattern andShape Bar Formations



## ..............................................................

............................................................. Channel Patterns



## .............................................................. Channel Shapes



## .........................................................

Width-Depth Ratio



## .............................................................. Shape Factor AvoidingPitfalls of "In-Stream Flow" Investigations



## ...........................

............................................................... ChannelBanks Processes Affecting Longitudinal Profile



## ..........................................

............................................. Longitudinal Profile Relationships



## ................................................................. Aggradation Degradation



## ................................................................. Armoring



## ....................................................................



## .................. ........................ TheNeed to Monitor StreamBehavior



# .,,.

...................................................................... Conclusions



## ................................................................... Literature Cited



## ......................................................................... Notation

# Stream Dynamics: An Overview 

# for Land Managers

Burchard H. Heede

INTRODUCTION

Scope and Purpose

Alandmanager shouldunderstand general concepts of stream behavior to be aware of how management actions affect streams, since such actions caninfluence
streams drastically. For example, vegetation cover manipulations on a watershed canincrease water yield (Hibbert 1971),or streamside forest removal can activate bedload transport (Heede 1977). Streams are dynamic systemsthatareprone to changeevenwithout human interference (Heede 1975);change inthe system itself may bring about adjustment once a geomorphic thresholdhasbeen reached (Schurnrn 1974).Thus,land management-stream interactions are complex. Other professionals who need a general understanding of fluvial processes are hydrologists, civil engineers, fishery biologists, andplant biologists. Plant biologists might be concerned with riparian vegetation interactions with the stream,while the fisherybiologist works in the streamitself. The hydrologist, on the other hand, is concerned with precipitation input into a watershed, its concentration in channels, and the mode, quantity,andquality of flow discharge.The civil engineer is more likely to be concerned about scour at bridge piers (degradation),or loss of discharge capacity by deposition (aggradation). Knowledge of streamdynamics will help to point out what information is needed to characterize stream conditions, and what indicators suggest about present and future stream behavior. With this knowledge, professionals engaged in land management will be able
to estimate what, where, and when effects of their actions will take place. General understanding of fluvial concepts should also help managers recognize if a particular situation demands attention from an expert in river science (a potamologist). Unfortunately in many situations,
stream data are either nonexistent or cover only flow rates andyields, but do not characterizepresent conditions or make well founded projections possible (Heede 19 79). High-andlow-flowconditionshave different requirements for conveyance of the water. If flow changes drastically, the channel often does not meet the new requirements, and adjustments must be made through stream-erosion processes. Well known examples are channel bed degradation or channel meandering.

This report presents a general outline of water flow and sediment transport as basic to all channel changes. It describes streamequilibrium condition and the required adjustment processes if equilibrium is lost. These processes lead to alignment, shape, or profile changes. The user should be acquainted with the basics of flow and sediment transport and should recognize the strong interdependency between practically all hydraulic variables. Arrangement of this text permits the reader to consider only those processes of interest. The Literature Cited section will suffice or provide a starting point for in-depth study of specific processes

or theories.

Characteristics of Streams

We usually think of a stream as one entity with a specific characteristic, such asthe mightyMississippi, theunpredictable PlatteRiver, a smallarteryof a large
stream system,or a bubbling mountainbrook. But these

same streams are very different at different times. At high-flow stage, for instance, mountain brooks are anything but bubbling waters. At low-flow regime, they meander sluggishly between channel banks, often filling not more than a fraction of the total bed. But at high-flow regime or flood stage, the channel may be totally filled or even too small, flood plains become
water covered, and meanders straighten to convey the rushing waters most quickly. If we would analyze the hydraulic variables of these
two types of flow, we would have to conclude the character assigned to the stream is based on a single aspect andnot on its complexity, because two different
streams may be represented if low- and high-flow regimes are considered. Although the argument may appear merely semantic, in reality it is deep seated, since different processes are operative in both
streams. Even to the casual observer, stream systems

are dynamic.

THE BASIC FLUVIAL PROCESS

Subcritical Versus Supercritical Flow

Natural streams convey their water in different modes. At times, or in certain channel reaches, the flow is tranquil (subcritical) exerting low energies

on banks and bed; at others, shooting (supercritical) flows occur which energies may damage an unprotected channel. Human activities can cause undesirable high-energy (supercritical) flows. For example, encroachments into the channelby diversion structures

or bank revetments can narrow the channel. As 

### aconsequence, the area of flow may decrease to the point where shooting flows occur. Knowledge of flow regimes, describing the flow characteristics in terms of available energies, therefore is required to recognize problems in channels or proposed channel improvements. Fortunately, subcritical flow is the more common type of flow (fig. 1).Available energy of such flows is less than that of supercritical flows of the same discharge. The total energy of a flow (total head of flow) can therefore be better conserved in subcritical flow (Koloseus1971).Maintenance of total head isimportant for channel stability as well as for structures such as water diversions. In contrast, supercriticalflow is undesirable because of its great erosive power due to high velocities (fig. 2). Also, higher stagnation pressures of supercritical flows can develop uplift forces of such magnitude that canal linings and concrete diversion structures have been removed (fig. 3) (Koloseus 1971). Stagnation
pressure is the sum of the pressure intensity in a zone of uniform motion andthe riseinpressure intensity due
to channel obstruction or other changes. Supercritical flows can also cause standing waves, ~roduced when two equal waves travel in opposing directions. Standing waves may reach magnitudes requiring prohibitively high canal walls or diversion ditchbanks. Standing waves must also be considered where narrowing of channels by human works is planned. As a general rule, stream reacheswith supercritical (shooting)flow shouldbe avoided for structural installations, and this type of flow shouldnot be created by channel manipulations (narrowing).

Froude Number where V is the averagevelocity in the cross section of measurement, g if the acceleration due to gravity, and 

### d is the average water depth. If inertia is smaller than the gravitational force, Fr<l, and flow will be subcritical (fig.I), the flowwillbe supercriticalif the ratio

reverses and Fr>l. Critical flow, required for many artificial stream-gagingstations,has a Froude number of 1, but seldom will occur in natural channels. This regime is very unstable and generally occurs only for
very short periods of time as a transitional stage between tranquil and shooting flows. While subcritical flows will show a relatively smooth water surface except for waves created by winds or some protrusions, supercritical flows exhibit surface waves that travel upstream (fig. 2).

Laminar Versus Turbulent Flow

Flows canalsobe characterizedby themovementsof individual fluid elements with respect to each other, which result in either laminar or turbulent flow. The major distinctionis that, in turbulent flows, a complex secondary motion is superimposed on the primary (laminar)motion of the fluid elements (Rouse 1950).

In laminar flow, each fluid element moves in a straight line with uniform velocity. There is no diffusion between the layers or elements of flow, and thus no turbulence. In contrast, turbulent flow has a complicated pattern of eddies, producing random velocity fluctuations in alldirections. These arecaused by continuous interchange of finite masses of fluid between neighboring zones of flow. The phenomenon results in a disruption of the entire flow pattern; a current meter immersed in a turbulent stream shows continual deviations from the mean value. Obviously, constant changes of flow lines lead to surges of flow againstbanks and structures,increasing flow impacts. Turbulent flow is the normal condition in streams. The Froude number (Fr),a dimensionlessparameter, offers a quantitative measure to determine if subcritical or supercritical flow will occur. This number represents the ratio of inertial to the gravitational forces and is given by:

ReynoldsNumber

Movements of the fluid elements depend on the inertial andviscous forces.The latter,ina loose sense, couldbe envisioned asanexpression of internalfriction of the flow.TheReynoldsnumber (Re)is a dimensionless

measure of these forces:

Vd inertialforce Re=-=
v viscous force

where v is the kinematic viscosity represented by the ratiopl~; ,u is the absolute viscosityand Q the fluid density. For natural channels, the critical value dividing laminar fromturbulent flowis near a Reynolds number Figure 1.-Downstream view of the Verde River north of Phoenix, of 2,000; values less than 2,000 generally indicate
Ariz. The flow is subcritical (tranquil). laminar and those over 2,000 indicate turbulent flow.Figure 2.-Shooting flow in a constricted segment of the Salmon River, Idaho. The view is downstream. Notewaves are traveling upstream(toward the viewer).

In summary, most natural streams have subcritical flow (Fr=<I). Also, turbulent flow (Re=>2,000) prevails over laminar flow (Re =<2,000).

Sediment Transport

Sediment transport is very complex. At least 30 variables arelocked into the sedimentation processes, and the degree of interdependency between these variables is not fully understood. It is not surprising, therefore, that a reliable numerical method for determining bedload transport in alluvial streams is not yet available (Bogardi 1974,p. 17).Available methods are

Figure 3.-High stagnation pressures from shooting flows of the

unusual January 1979 flood inthe Verde River, central Arizona, created uplift forces that aided in upsetting thiswater-diversion structureanda 2-foot-diameter concrete pipeline. based on empirical relationships between a selected number of variables or require prerequisites based on assumptions not necessarily valid for the conditions.

For stable channels,Lane (1955a)demonstrated the qualitative relationships between sediment discharge (Q,) and water discharge (Q,) as a balance (fig.4)

where 

### D is the sedimentparticle size and Srepresents the slope. Lane's balance illustrates the intricate
streamadjustment processes. If one side of thebalance changes,the other must adjustto maintain equilibrium. Thus alterations in sediment or water discharge require changes in grain size andlor slope. For example, if the slope is increased, the stream will attempt to transport larger particles, or if stream discharge decreases, sediment load must decrease also to maintain balance. Otherwise, degradation or aggradation of the streambed will occur,respectively, asindicated by the figure. For his balance, Lane selected as sediment discharge (Q,) the coarser part of the sediment load, or

more exactly the bed material load. He defined bed material load as the sediment in transport of sizes readily available in considerable quantities in the streambed. It is the coarser material largely molding the bed formation. He argued, "in most cases, the quantity of the fine load of silt and clay sizes can change almost indefinitely without materially affecting the river profile." We know now there are exceptions
to this rule, such aswhen extremely large loads of fine material (washload) are available. Heavy concentrations of fines cause a higher apparent viscosity of the fluid, which in turn results in increased transportFigure 4.-Stable channel balance. (Sediment loads times sediment size) varies as (stream slope times stream discharge). (Courtesy of the American Society of Civil Engineers; from Lane, E. W. 1955. The importance of fluvial morphology in hydraulic engineering. American Society of Civil Engineers Proceedings, Hydraulic Division81:745-1to 745-17.)

capacity for sediment. More and larger particles can be transported,which in turn affect the streamprofile. An extreme condition, illustrating the viscosity influence (Bull 1968) in addition to the relatively high specific gravity of the flow mixture (Crandell 1968), is a mudflow carrying room-size boulders like soap bubbles. Johnson (1970, p. 461) suggested that lift forces may also be involved. Flume experiments by Simons et al. (1963)demonstrated that clay in suspension affects viscosity, bed form, and flow resistance. With clay suspension, the total sediment load increased, which in turn affected the bed form. Since bed forms influenceflow resistance (Simons 

### aria Richardson 1966),they enter directly into the hydraulics ofthe flow. Again, the interdependency of the processes illustrates the difficulty, if not impossibility, of quantitatively predicting the stream environment.

Water temperature also influences sediment transport capacity more than many investigators recognize. As temperature decreases, viscosity increases, and carrying capacity increases [Colby 1964). For example, when Colby dropped water temperature from 80° to 40° 

### F, the sediment discharge for sand sizes ranging fram 0.125 to 0.250 

### mm increased by 254%. The size class is common for riverbed sand.

Field investigations confirmed the temperaturesediment transport relations and their vital influence

on streambehavior. In the Lower Colorado River for a given discharge, the sediment loads were 2.5 times greater in winter than in summer (Lane et al. 1949). Fahnestock and Maddock (1964)reported a change in water temperature of about 35O F from March to August significantly affected the hydraulics of flow andbed formintheRio GrandeRivernear ElPaso, Tex. At some similar discharges. mean velocity was greater in March and the bed was plane, whereas mean velocitywaslessin August andlargedunes developed onthe bed (flow resistance increased with dune formation). Management implicationsbased on the temperaturesediment relations are many. Where data on annual sediment loads are required, best results will beobtained by sampling during summer and winter. Winter data of one stream should not be related to

summer data of another. Most land management actions result in increased water temperatures and, therefore, decreased sediment loads. Under extreme conditions, this could lead to aggradation.

From many observations it has been found the sediment load in natural streams varies roughly as the
square of the discharge (Laneet al. 1949).This approximation is expressed by the equation

where Q, is the sediment load in tons per day, Q, represents the water discharge in cubic feet per second, and 

### K, is a coefficient that normally changes from stream to stream and with the season. The 

### K, coefficient could be helpful for approximating future sediment loads if used with flow frequency curves (differentiated between winter and summer flows), because some probabilistic aspects of sedimentation would be taken care of. Because the variation in the original data will generally be large, long periods of record are required to obtain meaningful averages. The length of record required depends on the degree of uniformity in the particular stream system. Differences between sediment transport capacity and actual sediment load lead to deposition or scour (Lane 1955b). In other words, sediment is stored or depleted in a given reach, resulting in nonuniform flow of sediment. Uniform sediment flow represents equilibrium condition and satisfies the continuity principle of sediment (Vanoni et al. 1961). If actual sediment discharge differs from the equilibrium sediment discharge, the stream will try to adjust the actual to the equilibrium discharge. Both the actual rate of transport and the equilibrium rate will change, but they will tend to approach each other. Uniformity of sediment discharge must be considered over time, because sediment often moves in a wave-like mode, especially if movable bed forms such as dunes are present. In many instances, works of humans distort uniform sediment flow. Best known examples are river dams causing a decrease of equilibrium transport rate upstream from the reservoir (backwater zone), and a decrease of actual transport rate below the dam. While aggradation takes place in the backwater zone, the "starved" stream picks up material from the bed downstream from the dam to satisfy the equilibrium requirement. Vanoni et al. (1961) roughly categorized river engineering problems caused by nonuniform sediment transport. When the actual transport rate is larger than the equilibrium rate (deposition), the following

occur:

1. Aggradationupstream froma reservoir. 2. Sedimentationin reservoirs andlakes. 3. Tributary channels bring heavy sediment loads to

the main channel, causing local aggradation (examples arefanformation andtributarybar)(fig. 5). 4. Canyon streams discharge on alluvial fans,

causing widespread deposition (as in Los Angeles area). 5. Desiltinn works at water intakes that return all

sedimentload to the main channel,in which flow of
water is depleted, lead to aggradation (e.g., ImFigure 5.-A tributary contributed heavy sediment loads to Sycamore Creek, northeast of

Phoenix, Ariz. These loads could not be carried by the main stream, and an alluvial fan developed, pushing the flow into the opposite bank. Sycamore Creek flows from right to left.perial Dam). Remaining flow magnitudes provided

a small equilibrium transport rate compared with the original flow. 6. Where river regulation eliminates floods that

formerly cleared the channel of accumulated sediment and vegetation periodically, aggradation results in the clogged channel (e.g.,Colorado River
atNeedles).

When the actual transport rate is smaller than the equilibrium rate (scour),the following occur:

1. Degradation downstream from dams that trap sediment and thus decrease the actual transport
rate. 2. Canals receiving clear water will scour if the bed

material is fine enough that it can be picked up readily by the flow. Under such conditions, the equilibrium transport rate is large, while the actual transport rate of the flow entering the canalis essentially zero. 3. Channel realignments that increase the slope also

increase the equilibrium transport ratebecause of increased flowvelocities. parameters in the equations. Attempts to reduce the complex stream situation by empirical relationships between a few variables are stillpursued [Osterkamp 1977).Obviously, such relationships will be valid only for the area of their origin.

The complexityof the fluvial system suggests stream analysis is a probabilistic problem. Because of the interaction between channel bed, banks, and flow, the

core of the problem appears to be the random distribution of the flow energy (mVZ/2),where 

### rn is the mass of water. The velocity must be recognized as a vector force (i.e., it has direction). Because of turbulent flow inmostnatural streams,this direction occurs randomly.Thus the energy,itself of stochastic nature, acts

on randomly distributed sediment particles. Incipient particle motion is therefore a very complicated event and no satisfactory way of determining it has been found. Sedimenttransport is a fundamentalvariable in
stream dynamics.

EQUILIBRIUM CONDITIONAND ADJUSTMENT PROCESSES

Dynamic Equilibrium Interdependency of Hydraulic Variables

The complexity of hydraulic variables is immense. Lane (1957) singled out eight variables of this complex which he called most important: (1)stream discharge, (2)longitudinal slope, (3)sediment load, (4)resistance of banks andbed to movement of flowingwater, (5)vegetation, (6) temperature, (7)geology, and (8)works of humans. The interrelationships among longitudinal profile, sediment load, and resistance of the banks and bed to movement are particularly close and complex. Interdependency between many variables often precludes the establishment of one-value relationships. For example, Brooks (1958)found neither the velocity

nor the sediment discharge concentration could be expressed asa single-valued function of the bed shear stress, or any combination or" depth and slope, or hydraulic radius and slope. He showed experimentally that flow with a given depth and slope can occur with
at least two velocities. This is due to changeable bed configuration which causes large variations in the channel roughness. Thus if one or a combination of the interdependent factors change under the impact of externalor internalforces, adjustment of one, some, or all of the components will follow. It is important to recognize that established relationships between most interdependent variables, except for basic factors such as the shear, are empirical and thus notnecessarily applicable for a wide range of conditions. Examples are Blench's (1966)equations based

on the concept of the regime theory, originally developed by Lindley (1919) and Lacey (1932) for Indian canals. This theory assumes there exists only one type of cross section for a given stream with a given load. Thus width and depth of the channel are the main The concept of dynamic equilibrium is very useful in evaluating stream systems and their stage of development. This concept does not imply absolute equilibrium conditions, but that the stream can adjust to a new hydraulic situation within a relatively short time, perhapswithin a fewyears. Obviously,if considered in geologic time spans,dynamic equilibriumhas no place, because land denudation is the long-term process. Although dynamic equilibrium cannot be well defined, the investigator canuse indicators, some of which are readily recognizable in the channel, to analyze stream stability in terms of equilibrium condition.

Heede (1975) listed several factors indicative of small mountain streams not in dynamic equilibrium: channel headcuts,under-developed drainagenets such

asthose having channelized water courses only on onehalf or less of the watershed area,frequent bedscarps, and the absence of a concave longitudinal profile where watershed conditions are relatively constant. The last condition will depend mainly on geologic homogeneity, availability of bedrock outcrop, and tributaries. When surveying a channel, select a reach with sufficient length to avoid distortion of the overall shape of the longitudinal profile by localirregularities. This length willvary with sizeof stream.In smallmountain streams, lengths of at least 0.25 mile should be sampled in the headwater, middle, and lower reaches. Obviously,greater lengths will improvethe representativeness of the profile. Channel headcuts are local erosion sources because headcuts advance upstream. They indicate that stream length and gradients have not been developed to allow equilibrium condition.Bedscarps that develop atchannel nickpoints similarly indicate pronounced breaksin longitudinal gradients. These scarps proceed upstreamuntil a smoothtransition betweenupstream and downstream gradient is attained. Thus, headcuts and bedscarps substantially add lo the sediment load because erosion will be severe until natural channelization is achieved and the longitudinal profile "smoothened." Actual sediment production rates higher than the equilibrium transport rate require steepening of the slope, normally attained by bed aggradation. Since aggradation processes are slow, such a stream must be judged out of dynamic equilibrium because of the long time required for reestablishment of this condition. Streams in dynamic equilibrium have no headcuts. Their watercourse begins high up on the watershed with a smooth transition from the unchannelized area to the channel. Bedscarps, not developed at locations of rock outcrop or variations in bedrock, are absent or few. As a result, sedimentproduction is negligible. The longitudinal profile is concave. Generally, flow, depth, width, and velocity increase downstream while gradient and sediment particle size decrease if watershed conditions are relatively constant over long stream reaches.

Complex Channel Response

Streams respond to an upset of a given equilibrium condition by different adjustment processes. These
processes follow a sequence if considered in terms of relative time and energy expenditures. Channel adjustments, ordered from small to large energy requirements, involve changes in: bed form, bed armor,width, pattern (alignment),and longitudinal profile. Generally, bed form changes require the least
amount of energy and time. Examples of bed forms are dunes in sand bed or gravel bars in boulder-strewn
streams. Bed forms determine resistance to flow (bed roughness) (Simons and Richardson 1966).Thus their change (i.e.,from a dune to ananti-dune)may be sufficient to achieve adjustment. A dune is a sand wave of approximately triangular cross section in the direction of flow. It has a gentle upstream slope and a steep downstream slope. The dune travels downstream by the upward movement of the sediment on the upstream slope andthe deposition of it on the downstream slope.

An antidune is a sand wave, indicated by a regular undulating water-surface wave. Usually, antidunes and accompanying surface waves occur in trains of 3
to 20 or more. If the antidunes move at all, it is upstream. The surface waves become gradually steeper

on their upstream sidesuntil they break like a surf and disappear. Often they reform after disappearing.

Where a change in form roughness is not sufficient

or is impossible, additional or different processes will be required to attain a new equilibrium condition. An additional process may be armor plating of the bed. It will require more time than bed form change. If armoring is not possible because of grain size distribution or insufficient amounts of large material, channel width changes generally wouldbe the next adjustment process. Width increases signify increases in the wetted perimeter of the flow, leading to larger roughness of flow and smaller flowvelocities.As a consequence, available energies are decreased.

Even width changes may not bring about the required adjustment. The next most energy- and timeconsuming process would be channel pattern change
to meander or braid.ing.If topographic and hydraulic conditionsdo not allow this change, aswillbe discussed in a later section, bed profile alterations will begin. Generally, these demand the greatest energy expenditures as well as the longest time of all adjustment
processes. Geology, soils, and vegetation also enter into the selective adjustment processes because of their influence on bank and bed stability and hence on sediment transport. Thus they add to the complexity of stream response. One must realize, therefore, an orderly succession of processes, as outlined, may not operate in
streams seeking new equilibrium conditions; the most energy-intensive process could be operating by itself. In short,the purpose of the above discussion isto show relative energy and time expenditures between different adjustment responses.

MAJOR ADJUSTMENTPROCESSES

Management activities may trigger or change channel adjustment processes. It is important, therefore,
to recognize the adjustment criteria and factors which must be addressedwhen evaluatingmanagement activities in terms of impact on streams. Five major channel adjustments were outlined in
terms of required energy expenditures in thepreceding section. The processes responsible for those adjustments are sometimes grouped into two categories: one affecting channel pattern and shape, the other affecting the longitudinal profile. Channelpattern refers
to the plan view of a stream and its alignment, while channel shape relates to the cross-sectional view

across the channel. Some processes are reponsible for more than one type of adjustment,however. Thus,bar formation processes may bring about three types of adjustment: in pattern, shape, and longitudinal profile. In a straight reach, for example, alternate bars force the thalweg (line of maximum depth)into a meander pattern. This, in turn, leads to increased streamlength andlongitudinalprofile changes,aswell asto changes of the channel

cross section. It is also obvious that aggradation or degradation processes change not only the stream's longitudinal profile but also its cross sections.The division of the processes into two categories is therefore a shortcoming of most of our classification systems, but it is accepted for convenience. The relationship between

one process andmultiple formsdemonstrates againthe complexity of stream systems.

### Four processes affecting channel pattern and shape

are recognized. They lead lo bar formation, channel patterns, cross-sectional channel shapes, and types of banks. Different types of bars develop in natural streams. All areintegrated into the stream hydraulics and are therefore not necessarily stationary, since most streams change their flows with season and individual events. Each type occurs in a given situation, and hence is an indicator of prevailing flow and channel conditions, aswill be discussed in the followingsection. Channel patterns are very diversified, as are most products of nature. Three dominant patterns will be described-straight, meandering, and braided-and,

as much asknown, their causative processes. Straight channels generally offer least problems for land management, but unfortunately, they are the exception. The rule is themeandering channel. Channel alignment changes offer relatively quick and drastic adjustments
to a new situation and are easily recognizable indicators of past, present, and possibly future channel developments. Generally, channel shapes respond quickly to changes in the fluvial systembecause shapeinfluences
water as well as sediment transport. Thus, channels closest to a semicircular shape are most efficient for conveyance of water and fine sediment. Coarse sediment requires relatively wide, shallow channels (Leopold and Maddock 1953). Unstable channels may therefore be recognized by channel shape changes. Parameters have been developed whichpermit quantitative determination of these changes. Consistency of bank material and availability of bank vegetation exert a strong influence on channel shape. Besides these factors, water movement within

or over banks may play animportantrole in the attainment of bank stability and shape. But bank characteristics also influence channel patterns. For example, banks of cohesivematerial (clay and silt,mainly)usually preclude braided stream patterns, but noncohesive materials favor them. Bank characteristics may change due to lateral stream movements. Recognition of these changes is important because they may indicate future bank stability conditions and channel shape.Banks aretherefore considered separatelyfrom shape.

Older geologic literature overemphasizedthe importance of theprofile in channeladjustment. As shownby the preceding section and stated by Wolman (19551, slope is not necessarily the primary mechanism by which equilibrium is maintained. Three major processes lead directlyto adjustment of the longitudinal profile: (1) 

### aggradation, (2) 

### degradation, and (3)armoring. These processes act on the topography andthe material inbed andbanks. General relationships between profile, topography, and geology

canbe utilized to human advantage. An example is the

use of a bedrock outcrop for gradient stabilization instead of a check dam. Generally, aggradation and degradation processes

are undesirable, but necessary, adjustments where there are drastic differences between the sedimentcarrying capacity of a flow and the sediment load coming into a channel reach. Aggradation may lead to channel widening and flooding; degradation to bank cavingandlowering of the water table in areascloseto the channel. Armoring can stop the degradation process if sufficiently large bed material is available. In this sense, armoring is a beneficial byproduct of degradation. Amount and depth of the armor material below channel bottom determine the depth of degradation before an effective armor is established.

Processes Affecting Channel Pattern and Shape

Bar Formations



### Bars are defined as bed forms having lengths of the

same order as the channel width or greater, and heights comparable to the mean depth of the generating flow (American Society of Civil Engineers 1966).Bars

are deposits that may be visible or submerged, and of grain sizes ranging from clay to boulders. Most are built predominantly from sand or gravel or both. In longitudinal section,bars areapproximatelytriangular. The upstream slopes are very long and gentle, while the downstream slopes are short and approximately the angle ofrepose of the bed material. Since bars are

an active part of the geometry of flow, they change in size, height, or location with flow conditions.

Generally, bar surfaces rise and fall with the magnitude of flow. Bars generated by high flows frequently appear as small islands during low flows. On sandbars, portions of the upstream slopes are often covered with ripples or dunes.

Bars may be classified as point, alternating, transverse, middle, or tributary bars. The most obvious one may 

### be the point bar, which develops near the convex (inside) bank of channel bends (fig. 6). 

### Its shape may vary with changing flow conditions, but it does not

move relative to thebend. Theprocesses leadingto this bar formation demonstrate the strong relationship between flow and bed forms. Rzhanitsyn (1960) describing the processes in bends, stresses not only the longitudinal currents but also the cross currents that influence the channel-forming processes. The actions of both lead toward the development of a deep pool at the concave (outside) bank and a bar at the convex bank (fig. 7). 

### Two causes were thought to be responsible for the
transverse circulation: the centrifugal force acting on the particles passing the curve and the difference in the longitudinal component resulting in a general spiral-like motion. The secondary circulation, sometimes also called helical, helicoidal, or spiralflow

or current, continually sweeps sediment from the pool depression toward the convex bank, bringing clearer
water from the upper layersto the bottom andthus increasing the erosional activity. Most of the material eroded from the pool is deposited on the point bar. These processes leadto asymmetrical cross sections inbends. Upstream and downstream ends of the bar are pointed. Intensity of erosion increaseswith increasing secondary circulation. Sincethis circulation increases with decreasing radius of curvature, the depth of the pool is inversely related to the radius of curvature of the bend. Therefore, gentle bends will have shallower pools than sharp bends (fig. 7). The maximum depth at the concave bank is greater than that of the straight reach. With the deepening of the channel at the concave bank and the reduction of depth atthe convexbank, the principal flowgradually

moves closer to the concave bank. There the longiludinalvelocityofflowincreases dueto greater depth. In contrast, the longitudinal velocity atthe convexbank is reduced with decrease of depth. High flowstend to shortenthe thalweg (i.e.,the flow selects the shortest route as it cuts across the point bar). This process leads to erosion at that part of the point bar located toward the center of the channel. The bar becomes narrower (fig. 6) until other flows may build it up again. Point bars can also be fully submerged resulting in loss of bar height, or a high-flow channel may be cut through the point bar (fig. 8).

Althoughhelical flow apparently plays animportant role in the process of erosion anddeposition in a bend, the mechanics of bend formation are not known. Meanders areknownto form on the surface of glaciers where they are cut by meltwater carryingno sediment load, and point bars do not form. Meanders are also known to exist in ocean currents such as the Gulf Stream where boundaries and loads are absent. Leopold andWolman (1960)argued, therefore, thatthe shapes of curves in streams are primarily determined by the dynamics of flow rather than by the sediment 

# /

# /'

, Point Bar

Figure 7.-Schematic presentation of channel shapes in gentle

(A-A') and sharp bends B-B'). The line in the channelof the plan view represents the thalweg. Note in the section view the increase of pool depth with decreasing radius of curvature and the higher water surface elevation at the outside as compared with the inside bank. This is due to the gravitational force and is called superelevation. they carry.These authorscompiled evidencethatwhen other conditions, as yet unknown, cause a stream of
any size flowing in a deformable channel to develop a meander pattern, the radius of curvature will be between two and three times the mean channel width. In contrast to point bars, alternating bars are not stationary. While point bars form in channel bends,

Figure 6.-Point bar in Salt River north of Phoenix,Ariz. Flow is from left to right inthe fore. ground. Note the pointed downstream bar end.

9Figure 8.-In Black Canyon Creek, northern Arizona, high flows cut a channel behind this point barto speed upwater conveyance through this stream reach. Flow isfrom leftto right.

alternating bars develop in straight channel reaches, and arethe reason why natural streams rarely remain straight. They "tend to be distributed periodically along a channel, with alternate bars near opposite channelbanks. Their lateralextent is significantly less than the channel width. Alternating bars move slowly downstream" (American Society of Civil Engineers 1966). The thalweg meanders between these bars, creating an undulating profile by forming pools and riffles (figs. 9 and 10). Alternating barsmay not be visiblebecause they are often partially submerged.Pools and riffles are spaced

more or less regularly at a repeating distance equal to five to seven widths of the channel (Leopold et al. 1964).Because the spacingis similar to that of bends in

Figure9.-(a) Schematic planview of alternating bars (A) and thalweg (B) in a straight channel reach, and section view of the associated longitudinal profile (b) showing pool (C) and riffle formations (D). Riffles form at crossings of the thalweg between bends. meandering streams, these authors suggest the pooland-riffle mechanism in straight channels is the same

as that creating meandering channels, possibly associated with somewave phenomenon.Normally,the bed material on the riffles tends to be somewhatlarger than in the pools, but at high flows, the reverse may exist.

Alternating pools and riffles were not found in high mountain streams of the Sangre de Christos, New Mexico (Miller 1958),nor the Rocky Mountains, Colorado, or the White Mountains, Arizona (Heede 1975). Miller argued the coarse material, left by Pleistocene glaciers or depositedby steep cliffs,etc.,is too largeto be effectively transported by the present-day flow regime. In Heede's streams, gravel bars were not spaced
at a repeating distance, but distance decreased with increasing channel gradient (fig. 11). Heede's gravel bars could adjust their height with flow while remaining stationary; transverse bars of rivers move slowly downstream and occur both as isolated and asperiodic forms along a channel. Generally, they occupy nearly full channel width (fig. 12).Transverse bars result from slope adjustment processes. Their main effect on the flow is increased bed roughness, as shown by strong relationships between bed form and resistance to flow (Simons and Richardson 1966).

Where the width-depth ratio is very large and the
stream divides itself into two or several branches to adjust for lost depth, middle bars will be created. At times, they appear as submerged islands. Some are sufficiently long to bear willows (fig. 13). Middle bars

are a typical bed form for braiding streams, characterizedby extremelywide and shallow channels andflowspassing through a number of small, interlaced channels separated by bars (Friedkin 1945).

Tributary bars often form immediately downstream from tributary junctions (fig. 14).They indicate large sediment discharge from the tributary stream. At times, this discharge may outweigh the capability of the main stream to transport the additional load. A sediment fan may be built at the tributary mouth into the main stream(fig. 5). During a subsequentlargeflow ofthemain-stemriver, the sedimentfanmaybe fullyor partially removed, and only a tributary bar may remain. Bars are anintegral part of the hydraulic geometry of a stream.With the diminutionor exhaustion of flood plains and river terraces by gravel quarrying, the
streams themselves become increasingly attractive gravel sources (fig. 15). If bars are destroyed by natural adjustment processes, they will not form again unless the hydraulic geometry changes back to the original condition.In contrast,bars obliterated by man will be reestablished if a sufficient sediment supply is available. If not, or if reestablishment is very slow, adjustments such as degradation may take place. Degradation is generally detrimental to the environFigure 11.-Looking upstreamonatransverse gravel bar(between arrows) in a small mountain stream (North Fork of Thomas Creek, Arizona White Mountains). Notethe steep slope gradient (average 17%)that required adjustmentof slope. Consequently, several transverse bars developedabove the indicated bar.

ment. Where transverse bars (bed forms created for slope adjustment) are removed, bedscarps will soon signify degradation is taking place. Removal of sediment will invariably destroy the bed armor, and a new

armor can only be established by lowering the bed, which often leads to bank instability. Gravel operations may not be harmful where large sediment loads are available to replace bars quickly, thus avoidingdrastic upsets of the stream system. The Eel River in California, one of the largest known sediment carriers in the United States, may be such a stream. But even in this case, we would not know the long-term environmental effects (redwood trees have lived for more than a thousand years on the periodically aggrading Eel River flood plain, as shown by multilayered root systems (Stone et al. 1972)).



### Channel Patterns

Figure 10.-Alternating bars (arrows)in Black Canyon Creek. High

flows cut small channels through the bars. Flow istoward back. In light of the interdependency of many hydraulic ground. variables, it is not surprisingto find a large variety ofFigure 12.-Downstream view of atransverse bar (between arrows) intheVerde River, Arizona. The bar isnotfully exposed across thechannel. Darknessof thewater surface inthetwobar openings (A and B) suggests submergence of the bar at these locations. Sediment accumulations above this bar, a natural slope adjustment structure, are indicated by shallow flow depth intheforeground.

Figure 13.-Middle bars (arrows) in the Salt River near Roosevelt Reservoir bear vegetation

such as willow and saltcedar. Flow is from left to right. At highwater stages, the bars are submerged, while at lowerstages, shown infigure, stream braidingdevelops.Figure 14.-Where the Salt River(a) isjoined by tributary Verde River(b), a tributary bar (c) has formed. Size of tributary bars changes readily if sediment loads delivered by the tributary fluctuate strongly. The submerged outline of the bar at (c) suggests exposed bar size was reduced considerably by recession flows after the heavy load-carrying floods of 1978 and January 1979.

Figure 15.-Many rivers havea substantial supply of aggregates, demonstrated by a large middle bar inthe Verde River, central Arizona, that may be sought by industry. In many situations, however, removalof such materialwould detrimentally affect streamequilibrium.

### channel patterns because pattern changes are one possibility for adjustment ofthe hydraulic geometry to

a new situation. This is especially trueif the slope must change. Thelarge variety ofpatterns canbe reduced to three basic types: straight, meandering, and braiding. There are, of course, intermediate forms. Long reaches of straight channels arehard to find in
nature. Evenin straightchannels, the thalweg wanders back andforthbetween the banks (fig.

## lo),and only the high flow may fill the straight reach. One could thus conclude that meandering and braiding channels offer better and easierways for attaining equilibrium conditions than straight channels. Meandering andbraiding increase the length of the thalweg and thus decrease slope. Ameasure of meander intensity is sinuosity, expressed asthe coefficient of thalweg length divided by valley length. Large coefficients, therefore, express strong sinuosity (meandering).A 

### straight reach would have a coefficient of 1. 

### In braided streams, the flow is relatively shallow and the width-depth ratio large, larger than in meandering streams.The streamflows aroundmany islands (fig. 16). If this process increases, branching of the main channel may occur,the flow running in different channels more or less parallel to each other, joining and anabranching (diverging) in succession. Brice (1975)called these "anabranching streams."

Why channel patterns change cannot be precisely answered yet. Certainly, localized channel width increasesmay leadto meandering because of introduced flow deflections. A 

### large boulder or other obstruction, for example, may cause a local channelwidth increase that results in a meander. But on glaciers meanders also appear without visible flow deflections. Profile is one of the major causes for pattern changes. Braided streams are steeper than meandering streams. Steeperstreamshavehigher velocities, attack banks more strongly, and carry larger sediment loads. For bank erosion to occur, erodible bank material
must be available. For example, braiding does not usually take place where banks are densely vegetated, but may where this cover is sparse. Although cause and effect are suggestive, they arenotproven (Leopold
et a]. 1964). In alluvial streams,whose bed andbanks areformed by sediment transported by them, amount and character of the particles composing the sediment load also

seemto have animportant effecton channelpattern.It
appears available load is one of the factors separating meandering from braided streams. Lane (1957) concluded not only overloadingby sediment but also steep slopes areprerequisite for braiding. Overloadingleads
to aggradation, causing wide channels where banks

aresoft and, thus, the developmentofbars andislands. The width-depth ratio is larger than in meandering
streams. But Leopold et al. (1964) pointed out that braiding is not necessarily associated with aggradation, since it can represent the equilibrium pattern (sediment inflow equals sediment outflow). Yet it can be arguedthat for braiding to occur depositions (aggradation) are required to initiate drastic channel width increases; with braiding, a new equilibrium condition
may be established. In flumeexperiments, ShenandVedula [1969)showed depth of flow may become so shallow due to sediment overloading that flow could not occur in a single channel. It had to divide into several narrow channels to increase depth of flow and sediment-carrying capacity.

Figure 16.-Looking downstream on Delta River, a braided glacial stream draining the north

face of theAlaska Range incentral Alaska. Glacial streams tendtodevelopvery pronounced braided patterns. (CourtesyTroy L. ~6~6, Arizona State University)

14Figure 17.-Heavy sediment loads inthis Salt River reachabove Roosevelt Reservoir, Arizona, created a wide bed with shallow flow depth. Thus, stream competence (sediment-carrying capacity) was drastically reduced. To increase flow depth (and competence), the flow split intoseveral channels (arrows). Flow inthe foreground isfrom leftto right.



### That this process takes place also in rivers was demonstrated during a recent recession stage of the Salt River, Arizona (fig. 17).



### In a glacial stream on Mount Rainier, Washington, Fahnestock (1963)observed braiding at much greater magnitude when anabundant bedload was introduced than when the material was derived just from bank erosion. Fluctuating flow discharges also favored braiding. In some situations suchasmountain streamsflowing in V-shaped valley bottoms, lateral stream movements

arenot possible. A straight channel reach may therefore remain straight. Slope adjustment is possible only within the given channel. In smallstreams,this adjustment may be achieved by the formation of transverse gravel bars (fig. 11)

### and incorporation of fallen trees and logs (Heede 1975). Apparently, slope is seldom adjusted by severe degradation because of the presence of large bed material sizes.

The limitations set by the topography, such as V-shaped valleys, help to explain why braids tend to develop in channels having certain variable combinations, while meanders occur in different conditions; the straight pattern can occur in either. Although causes for pattern changes cannot be precisely delineated (Morisawa 1968), channel changes obviously take place in response to changed
streamconditions.For the land manager, meander and braiding processes areusually costlybecausevaluable land may erode or other investments, such asroads or buildings,maybe destroyed.It istherefore desirable to control lateral stream movement, but vertical bed adjustment processes may be initiated if the lateral process is stopped. Unless durable bed armor prevents channel depth changes or these changes are acceptable, additionalbed controlmeasures willbe required. If depth changes are permissible, it should be recognized bed adjustment will also take place in the tributary streams.Thus a streamcontrolmeasure may have adverse effects far beyond the immediate region of the stream.

As a generalrule, the landmanager shouldlive with the present natural adjustment processes and, if possible, offset losses with land improvements elsewhere.

Channel Shapes

Channel shape is of management interest because shapeispredominantly influencedby the (1) 

### quantityof water; (2) 

### the type of sediment load (suspended load, the material moving in suspension; or bedload, the coarse material moving on or near the bed);and (3)the type of bank material. Any change in one or more of these factors will therefore introduce a shape change

aswell. Recognition of shape changes is a first step in the determination of their cause, but recognitionis not always easybecause of turbidity of thewater, or transitional shape changes that are not easily seen (for instance, from slightly parabolic to rectangular). For these cases, thewidth-depthratio andthe shapefactor

can be calculated from field survey notes on channel

cross sections. Both will be described in succeeding sections.

Land management measures can influence water and sediment discharge. Costly stream training

measures such asriprap or gabions changebanks andtheir materialmakeup. Such changes maybebeneficial

or detrimental to management goals. For example, a semicircular cross section, not existing in natural streams, would convey the largest quantity of water with the least resistance (erosion or deposition). The

more channels deviate from this idealistic shape, the less water will be conveyed, and flow resistance increases. Thus a wide flat channelwill showtendencies for aggradation by sediment, possibly leading to a braided channel pattern. Obviously, granting permission for additional water conveyance through such a channel would add to the problem.

Relations between shape and sediment load show channelwidth increases with increasing coarseness of the sediment particles. Thus, causes for channel widening may be tracedback to new sediment sources

on the watershed caused by events such aslandslides or rockfalls from talus (cliff debris) slopes, or channel deepening in an upstream reach may make available

coarser material. Of course,the basic question of what caused slides or deep cutting must still be answered before correctivemanagement actionscanbe initiated.
Also, the particle sizes in the channel banks determine channel shape. While banks with a high silt-clay percentage lead to narrow and deep channels, those with a predominance of sand and coarser material develop into wide, flat channels. Thus, lateral stream movements may leadto shape changes by exposingdifferent bank materials.

Lateral stream movement may not be caused by management but may result from natural adjustment
processes where dynamic equilibrium was lost due to unusual events such as earthquakes or land flows (unusuallylarge land slides).If bank material changes

aredetected atanearly stage and futureproblems are expected,protective actionscouldbe taken intime. For such a decision, projections must be made as to other types of adjustment the stream may undergo if lateral
movement is stopped. Down cuttingmay take place, for example, requiring additional bed control structures under expected severe conditions.

Width-depth ratio.-The width-depth ratio relates the top width (W)of the channel to the mean depth 

### (d). Mean depth is defined as the cross sectional area at bank-full stage divided by the top width. Where bankfull stagewould not be a meaningfulcriterion, channel width and flow depth should be taken at high water mark. In cross sections with nongeometric forms, a planimeter or similar instrument is best suited for determining cross-sectional area. In cross sections with pure geometric shapes, the following relationships hold: in a triangular channel, the width-depth ratio remains constant with changing discharge; the width-depth ratio decreases in trapezoidal and elliptical cross sections when discharge increases;andwidth-depth ratio decreases much more rapidly with increasing discharge in rectangular channels. Width-depth ratio changes with discharge can be graphically shown if the ratio is expressed asa simple power function of discharge:



### wld =rQs

where Q is the discharge, and 

### r and s are numerical coefficients. The value of s, the slope of the line resulting from a log-log plot of the equation, expresses the relative rate of decrease of theratio with increasing discharge (i.e.,it constitutes a measure of how readily

a stream adjusts width and depth to discharge changes).An example from three stations is plotted in figure 18. In general, cross sections in straight reaches have a large width-depth ratio. In bends, this ratio is small. The sharper the bend, the deeper the pool, and the smaller the ratio (fig. 7). This relationship is so strong the cross-sectional shape of the pool could be used to determine the approximate degree of curvature of the bend if empirical data on bends and bank material are available. Schumm (1960)found that in western channels the type of material in banks and bottoms controls the cross-sectional channel shape. When the mechanical analysis of the soils was related to the width-depth ratio, linear regression indicated that increases in the ratio conformed with the increases of the average percent sand in the measured load: wide, shallow channels form in sandy soils, while clayey soils lead to narrow, deep channels. An extremely large width-depth ratio for a given river would indicate braiding must be expected because of large availableloads andunstable banks or very large width of channel. The decreased flow will
concentrate into smaller branches to obtain some depth and velocity for the transport of the material. Values for the ratio should be evaluated relative to prevailing values within the stream system.The range of the ratio can be large. Fahnestock (1963) found values ranging from 10 to 71 for glacial streams of Mount Rainier in Washington, while those for small
streams in the southernRocky Mountains of Colorado ranged between 3 and 27 (Heede 1972).

Shape factor.-The shape factor is the quotient of maximum depth divided by mean depth. Because the value may be the same for a variety of unusual cross sections, the factor must be interpreted cautiously. Only in exceptional cases, however, do channels in alluvial material have unusual sections. If considered

asgeometric figures, a triangular channelhas a shape factor of 2, a parabolic section 1.5, and a rectangular section 1.0.
As stated before, the semicircular channel would have the most efficient cross section, because for a given cross-sectional area it has the smallest wetted perimeter. If slope and roughness are constant, the velocity increases with the hydraulic radius, which is the coefficient of area of flow over wetted perimeter. Hence,the semicircular channelwould dischargemore

### water than any other'channel shape.The most efficient naturally occurring cross section is a parabolic channel with a shape factor of 1.5. Thus, the discharge efficiency of a channel can be quantitatively judged. This may be of importance for projects which require additional conveyance of water. Where cross sections
appear to be obscure,plottingthe sectionwill revealif the factor truly expresses the shape. In the streams mentioned above, Fahnestock's (1963) shape factors ranged from 1.1

### to 2.7 andHeede's (1972)ranged from
1.1

### to 2.3.

Avoidingpitfalls in "in-streamflow"investigations.- 

### Surveys of channel cross sections are anintegralpart of theland manager's "in-stream flow" investigations. Thepresent type of flow shouldbe definedbecause, as shownin a previous section,with flow the thalweg may



## Discharge (cubicfeet/second)

Figure 18.-Relationship of width-depth ratio to discharge for

three stream stations of Fool Creek, central Rocky Mountains in Colorado. Station A adjusted most quickly to discharge changes (sediment carrying capacity is better maintained in A than inB or C). Figure 19.-Schematic diagram of a channel cross section in an anabranchingriver.The overallappearance suggests several independent parallel streams.


### change its position and in turn channel shape. At low flow, for example, the stream may create a pool at a bank due to increased flow sinuosity; while at high flow, water fills the channel and a low occurs in the section center.

How flow types can influence channel shapes is determined not only by the thalweg position in the

cross section,but alsoby changes of the streampower. The cross sectional channelshapeis directlyrelated to the changes of the streampower 

### TVacross the stream, where T 

### is the tractive force yRS; y 

### represents the specific weight of water,

### R is the hydraulic radius Alp, A 

### represents the area of flow, p 

### is the wetted perimeter, and S 

### is the slope. The wetted perimeter is thatpart of the channel cross section submergedunder the water of a given flow. Simons and Richardson (1966)have shown

### TVisrelatedto mean sedimentgrain size, which determines bedform and, in turn, resistance to flow. Cross sections canbe influenced alsoby channelpatterns. Thus a straight reach tends to have a V-shaped

cross section; in bends, a pool exists at the outside bank (fig. 7);

### while inbraided streamsthe cross section has anundulating outline.Where anabranchingtakes place, a given streamlocationmayhave a successionof channel cross sections each separated from the next by unchannelized sections (fig. 19).The survey should therefore include information on the channel pattern and the location of the section relative to pattern features such as "at crossover between meanders." Thisinformation isimportant because thepatternitself
maybe responsiblefor a giventype offlow andchannel shape, and different processes induced by different patterns may form similar cross sectional shapes. Examples will illustrate this. In a straight reach, two circulation cells have been observed in the plane perpendicular to the flow (Leopold et al. 1964). The authors presented crosschannel water-surfaceprofiles showing a marked central hump and water surface elevations lower at the
two edges of the stream,resulting from the transverse
water circulations (fig. 20). This so-called secondary circulation moves from the edges to the stream center and then downward. There may alsobe several circulations above each other, but circulation seems to take place in an even number of cells (Koloseus 1971). The secondary circulation has been associated with

### turbulent flow in prismatic channels illustrating an influence of channel shape on flow characteristics. At a meander crossing (the point of inflection from

one meander to the next), the flow is often deflected towards onebank. Thisleadstothe formationof a pool there and a bar at the opposite bank. Appearance of such a section in a cross-sectional drawing may be similar to that of a meander. Onlythe planeviewwould show dissimilarity in appearance.

Ifinstabilityof flowincreases ata meander crossing,

a bar may form in the middle of the channel, practically dividing the flow into two branches. At low flow, this may appear like the cross section of a braiding
stream.Description of the section location is therefore required. Because of inherent instability, meander crossings shouldbe avoided for structuralinstallations such asbridges and culverts.

Channel Banks

With time, most natural channels form their bed and are therefore embedded in alluvial materials. Banks may offer serious soil mechanical and fluvial geomorphologic problems. Factors such as temperature, chemistry of clay, or vegetation influence bank stability. Bank material may range in size from clay to boulders, and the occurrence of this material may change with location or it maybe stratified.Generally, banks with high clay content are more stable than those without clay. Therefore, the bank material must be considered if bank stability is evaluated. Failures of banks arecustomarily classified into slip failure and scaling. Scalingis a type of exfoliationthat produces thin flakes, laminae, or scales. Slip failures

are induced by piping (development of pipe-like subterranean tunnels) or often indirectly by horizontal stratification of the bank materials. Scaling begins in smaller magnitudes at the bank toe, generally, and proceeds up the bank. Where piping takes place, material stratification
may add to the problem. This stratification should be considered relative to high and low flows and to the elevation of the water table in the bank. Piping is subFigure 20.-Idealized secondary circulation cells in a cross section ofastraight reach. Water surface elevation shown (Leopold et al. 1964). Note the water surface shows a hump in the channelcenter anda low at both banks.The central hump may be as much as 1foot above water surfaceat banks. 

### terranean erosion where soil is removed from root canals, cracks, burrows, or other voids in the solum. Normally, pipes have an inlet and outlet, the latter
at a lower elevation, and thus convey overland flow. Repeated flows increase tunnel size until it collapses. Heede (1971) described soil piping in gully banks with high-clay soils (>45% clay),andfound piping was related to high exchangeable sodium percentage, low
gypsum content, and fine-textured soils with montmorillonite clay. Vegetation as a bank stability factor must be evaluated in terms of plant vigor, density, and rooting depth. Obviously, the stronger, these characteristics, the greater the impact on bank stability. Research results arefewonthis subject,andthe designer canbe guided only by experience andjudgment.

Where theload of a streamconsists oflargeamounts of fine sediment, extensive berms may form along the banks by deposition of silts and clays. On the other hand, where channels widen continuously,theprocess mustbe suspected tobe a function of the bank material.

Processes Affecting Longitudinal Profile

LongitudinalProfile Relationships

The longitudinal profile of a stream is determined largely by thetopography.Ingeneral, streamgradients will decrease from the headwater downstream to the mouth, but gradient steepening or lowering may occur in any stream reach, especially if there arehuman or natural controls such as rock outcrops or rock type changes. When evaluating the overall shape of the longitudinal profile, one must be aware of the scale factor that may enhance local irregularities and thus misconstrue the overall shape. Profile shapes can be classed as concave, straight, or convex if local irregularities caused by bed features such asbars, pools, and riffles areignored.

The longitudinal profile is a function of the following variables: discharge, load, size of sediment particles, flowresistance,velocity,width,depth,and slope. Since there are more unknowns than equations, an exact solution incorporating all variables is not possible. Simplified equations of various forms have been devised, however, typified by two kinds. One is based on Sternberg's (1875)abrasionlaw, the other on Gilbert's (1880)law of declivities. Langbein (1964) suggested the concavity of river profiles with uniform discharge increases with length and decreases with rate of discharge. He proposed further that profile shape is independent of base level and is determined by length, fall, and discharge. Concavity can be expressed asthe ratio 2A'IH, whereA' is the difference in elevation between the profile atmiddistance and the straight line connecting the ends of the profile, and H is the total fall (fig. 21).

In small mountain watersheds with homogeneous geology, Heede (1977) found ephemeral streams with

convex profiles, while perennial streams showed con-cave profiles. He argued, considering homogeneous geology and other parameters of flow and channel geometry, concavity represents the equilibrium profile and convexityrepresents theprofile of streams outside of equilibrium.

Previous sections showed that the processes leading
to a given profile are interrelated with others. Together, the processes tend to either establish or maintain equilibrium conditions. Since the profile directly influences flow velocities, artificial changes of the equilibrium slope should be avoided.

Where a streammust share a narrow valley bottom with a road, the stream reach is often shortened, steepening the channel slope. Normally, a bedscarp developsatthedownstreamendof the shortenedreach andproceeds upstream with time, deepening the channel (fig. 22) and the tributaries. The deepening of the main channel lowers the local base level of tributaries
to which they must adjust. In many cases, available
space does not permit relocating the road in such a way that new channel length equals the original. Artificial armor plating or check dams would solve the problem, but are expensive. Where check dams are used, it is important that the last upstream structure will not create a pronounced break in gradient atthe upstream toe of the future dam deposits. A smooth transition from the lower to the upper gradient is required to avoid the development of a bedscarp at the deposition toe. An expected depositiongradient should be estimated from measurements of deposits above artificialbarriers within the stream system.

Aggradation

If the sediment inflow into a reach is in excess of the reach's carrying capacity, the excess material is deposited until a new slope is established that equals the upstream slope. This is the new equilibrium slope. Based on flume experiments, Suryanarayana (1969) reported on the mechanics of aggradation. The new equilibrium slopeestablishedby aggradation can carry all the incoming sediment, but downstream the slope has not adjusted yet and deposition occurs. This obstructs the flow, and deposition occurs above also. Thus, deposition takes place above and below this



### Distance

Figure 21.-Schematic illustration of Langbein's (1954) profile concavity ratio. location,raising the bed parallelto the new equilibrium slope. The rate of this movement decreases with time

or with downstream advance, and so does the rate of aggradation. The channel upstream and downstream from the aggrading front behave as two different reaches with different flow conditions. Aggradation

ceases once all slope segments allow equilibrium sediment discharge. Aggradation creates a slightly convex longitudinal profile (Suryanarayana 1969) resulting from interaction between transport and deposition. Since more power is required to move coarse material than fine material, the coarser sediment will be deposited first while the fines move farther downstream. Particle sizes of sediment therefore decrease downstream within the aggrading reach. Particle abrasionbecomes

an additional factor (Schurnrn and Stevens 1973).

Where aggradationtakes place, the streambedrises slowly and, with time, the tendency increases for the flow to spill over the banks. This will lead to rising of the banks. A good example is the Rio Grande at Albuquerque,N. Mex.,wherethe streambed aggraded to an elevation 4 to 6 feet above the river's flood plain. The banks rose, but not high enoughto contain exceptional floods and streamtraining measures were required to safeguard the city.

Theprocessleadingto naturallevee formation(raised banks) canbe explained by sedimentation.When floodwaters spill over banks, a sudden loss of transporting
power occurs at the brink of the banks due to decreasing flow depth and flow velocity. Most of the transported sediment isthus deposited atthebrink and much less material is available for deposition on the flood plain (fig. 23).Under extreme flooding or bed aggradation, the stream may divide itself by building another channel on the flood-plain side of the levee, and the levee keeps both channels apart. This process may continue during successive floods, and the end result is a "braided" river. This exampleillustrates an important fact in stream hydraulics: different types of
processes may lead to similar end results. Unfortunately, flume studies are not helpful in predicting the behavior of natural alluvial channels. The main reasons are flumes have rigid boundaries, and sediment characteristics such as shape and smoothness cannot be modeled. Knowledge of natural
streamsmust therefore be developedunder fieldconditions. Yet, due to the intricacy of different adjustment
processes in alluvial channels all of which may be acting at one time, we cannot precisely forecast what will happen at any one point. The problem is compounded by the fact individual processes require different time scales. Thus, bed forms may adjust quickly and width slowly or erratically, while the processes leading to longitudinal stream profile changes are slow.The aggradationprocess is somewhatfasterthan degradation; the two processes generally alternate along the length of the stream. In short, morphologic adjustment processes are stochastic in nature, and
streambehavior prediction is therefore a probabilistic problem.Figure 22.-(a) Inmountaincountry, highway construction often infringes on streams. A relatively large meander bend (A) of Sycamore Creek, centralArizona (flowing from leftto right),

was cut off and the streambed relocated to the opposite side of the road (B). Thus streamlength was shortened, slope gradient steepened, and a nickpoint introduced at (D) that led tothedevelopment of a bedscarp inthe volcanic bed rocks. This scarp advanced about 300feet uostream(C) withinaaoroximatelv 25 vears. At ID), the originalmeanderbend connected with short straight reach still usedbythe creek. (bjkloseupview of the &foot. deep bedscarp (arrow). Adjustment processes not only caused a bedscarp but also tried to reestablish the meander, endangering the road bed by undercutting. (c) Rock riprap bank protection was required between A and B to protect the road. Arrow signifies bedscarp location.Unless anunusual event occurs such as a flood, slow profile adjustments are difficult to observe. Normally,
many years of investigationwillbe required, therefore,
to test the effectiveness of a design. Observation reaches shouldbe aslongandasuniform aspossible so that the average bed conditions are insensitive to seasonal changes [Gessler 1971)that could distort the results.

Degradation

In general, degradation processes are extremely slow, especially where geologic processes such as uplift areinvolved.A classic exampleis the Grand Canyon in Arizona. Where equilibrium conditions have been violently disturbed (massiveland slides, earthquakes), degradation may be fastinitially,but willbecomeprogressively slower with time. An example isManti Creek, draining the Wasatch monocline in Utah. In 1974, the third largestmodern landflowin the United Stateslifted portions of the streambed by about 110feet. Within 2 to 3
years, degradation in the uplifted reach amounted to about 60 feet. Degradation is now so slow that downcutting rates cannotyet be established.' Manti Creek's behavior, typical for alluvial streams, illustrates that degradation processes are asymptotic in nature and, therefore, slow if considered over the full adjustment time. The profile of a degrading bed is concave (Suryanarayana 19693, and the associated channel cross sections tend to be V-shaped (Gessler 1971). As for aggradation, the processes shaping the profile of degrading reaches can be described in terms of sediment transport. Duringdegradation, materialis picked up from the bed until load limits (threshold values for the transport of particular grain size) are reached. While certain smaller sizes are still set in motion, the larger ones remain in place until even the small sizes cannot be picked up. With thelimitation in bed particle movement, the slope of the concave profile decreases downstream. The gentler bed gradient will have an equilibrium sediment transport rate less than that of the upstream degrading reach. The tendency for formation of V-shaped cross sections in degrading channels is a result of variations in resistance to flow across the channel.Normally, carrying capacity for sediment is lower near banks than in the channel center due to bank roughness. Pickup of bed material may therefore increase toward the
center. Other processes, however, such as spiral-like flowin bends (discussedinanearlier section)may have

an overriding influence on channel cross-sectional shape. Also, the profile may not be concave if only considered over short distances.

The processes of degradation aswell as aggradation

are thus correlated with flow and sediment transport. The aim of these processes is to adjustto some change

'Oral communication with Manti-LaSal National Forest personnel, and personal site observations. Figure 24.-Tractor excavation of sediment from this streambed

was unavoidable because of the road location. Since sediment loads are very high during high flows, as indicated by high frequency of large bars in the river, this branch channel will refill. In the long run, relocation of the road may be less costly than repeated excavations.

in the stream system; the end result is a new equilibrium condition. Except for adjustment processes that are detrimental to immediate management goals

or to important installations, the land manager therefore should not interfere. If possible, he should work with the stream processes, not against them. Such anapproach is less costly.For example, dredging the river bottom in aggrading reaches is not always unavoidable, but is nearly always of infinite duration and excessive cost (fig. 24).

Armoring

In many situations, the process of degradation is halted by the selectivetransport of the flow before the equilibrium slope is attained. This slope would have corresponded to the original bed material gradation. An example is Livesey's (1963)report on the Missouri Riverbelow Fort Randall, where 15 feet of degradation

was expected. But after the bed had lowered 3.5 feet, degradation ceased because anarmor was established

on the bed. Within 10 years, the Dss (65% of the material on the cumulative curve is finer than the size Dss) increasedfrom0.20mmtonearly 1m, representing

a coarsening of bed particles by 500%.

Duringthe armoring processes, smaller particles are carried awayby the flow, while the larger onesremain in place and create a stable bed. Two prerequisites
must be fulfilled before an armor can be established: bed material must include a gradation.from finer to larger grain sizes (which is true for most natural streams),and fluctuations in flow magnitude must be mild and flow velocities relatively low during time periods long enough for armor formation. The armor coat is determined by the largest flows of the establishment period because particles light enough and available for transport are moved out by these flows,but by no means areall smaller grain sizes removed, although the large components arepredomi-

### nant in the armor. The individuallarger grains exert a shingle effect by fully or partially covering smaller

ones thus keeping them in place (Lane and Carlson 1953). There is no distinct boundary, therefore, between the armor and the sublayer.The armorbecomes effective when it is one grain size thick (Lane and Carlson 1953). Future flows, larger than those experienced during the establishment of a given armor, may destroy the present coat and a new armor, consisting of a predominance of still larger particles,
may be created. In contrast to the aggradation and degradation processes, armoring does not cause bed slope changes;instead, the bed is lowered parallel to its original slope (Gessler 1970, 1971).

Although precise quantitative projections on armor development arenot possible (Littleand Mayer 1976), the investigator should attempt to determine the availability of large sediment particles in sufficient quantities which can resist the largestflowsin a given time period. Under conditions of degradation, this material
must be exposedby a flow before it can act as armor. The size distribution of the sedimentburied below the bed layer or in the banks is therefore important. If newly exposedbanks aresufficientlysoft for alignment changes to take place, degradation will not continue generally. Where high values are at stake, Gessler's (1967) method of prediction should be used. This requires data on flow and sediment transport, which in many

cases must be generated before analysis canproceed. Where the situation permits and data are not available, the expected depth of degradation and armor plating can be estimated by comparing present bed materials with those expected to be exposed by degradation.Drilling or other excavationswouldbe requiredto determine the size of thelower bedmaterials. Because the judgment requires experience, an expert shouldbe consulted.

THE NEED TO MONITOR STREAM BEHAVIOR



### We should not underestimate the benefits that can be derived from predicting stream behavior. If bridge piers willbe undermined by scour [degradation) or the bridge buried by sediments [aggradation), such knowledge ismost valuable formanagementactioneven if it is notprecise intime andvolume. Butdata arerequired to make soundpredictions.Many streamprojects have been completed, but post-project behavior is seldom monitored. Monitoring is also needed because most theoretical relationships were developed under controlled laboratory conditions, and verification or modification of the relationships by case histories is required. Observations spanninglong stream reaches and long time periods are expensive, but how else can

we increase our knowledge abdut the real world? Monitoring should be based on sampling at random

or predetermined stations to reduce expenditures. Generally, the latter approach is preferable because fewer stations will be required for representation. An example would be the establishment of one sediment sampling station each in the head water, middle, and lower stream reach, since stream gradients and sediment particle sizes generally decrease downstream while flow and velocity increase. Often, average gradients of the reaches can be determined from maps. But sampling of total sediment load, one of the most influential hydraulic variables, is difficult. Bedload

canbe sampledonlyin catchbasins orwhere turbulent flowplaces the total load in suspension. Thelatter condition may be found where channels are excessively constricted. Thus, usually only suspended load is monitored (by use of dip or pumping samples)to represent sediment load. Often, suspended load is 75% to 90% of the total.

Bed material particle sizes can be sampled at low flow. Agridpattern shouldbe used comprising an area

on thebed frombank to bank. Samplingtotalbed width will ensure the particle changes with changing flow lines across the channel will be representative. Wolman (1954)tested sucha pattern and found significant representation of the particle size distribution. Changes in particle sizes are indicative of changes in bedload transport.

Monitoring bed material at a stream-gaging station will not show true sediment productionin a watershed because of the lag time between production at a location and transport to the station. Especially in 

### ephemeral streams, many years may pass before a substantial part of the sediment production reaches the station; and some amount never will (Heede 1976). Also, channel storage by bar and other depositional features (bed aggradation, riffles) generally is many times larger than the bedload caught at the gaging station.

If any sediment transport equations are to be used, they should be thoroughly tested for applicability. Because streambehaviorinvolvesintricateprocesses as demonstrated in the preceding sections, the processes have different modes at different flow conditions. If stream-gagingstations arenot available,a current meter or velocity headrod should be used for flow determinations. Heede (1974)showed velocity measurements by the rod require less time. In boulder-strewn streams, results did not differ significantly from the
current meter readings.

Where channel cross sections must be sampled because of expected severe consequences from future channel shape changes, it is importantto select representative sections of a reach. These canbest be determined from aerial photographs, if low-flying images

are available, or by ocular selection on the ground.

To facilitate ground surveys, benchmarks shouldbe established at some distance from the brink of the
streambanks. Regularland surveytools suchasahand level or engineer's level will suffice. The intensity of stream sampling depends on the objective and on available funds. But if the user focuses on the basic stream processes as outlined in this report, the complexity of stream dynamics can be

### better understood and efforts limited to essential monitoring.

CONCLUSIONS



### Thisreport focuseson themajorprocesses of stream dynamics and shows how the complexity of stream behavior forces the user to consider the individual componentsof each case. The report should be helpful indelineating the individual characteristics.Above all, stream restraining measures must be applied with great caution so that treatment of one criticallocation will not simply lead to the formationof another, or that future treatment "side effects" will not be more detrimental to the attainment of a new equilibriumcondition than no treatment.

From the preceding sections, it follows that the science of fluvialhydraulics has not been developedto

a level that permits accurate prediction of stream behavior. Judgment is still required in addition to mathematical-statistical analyses.Yet somequalitative predictions arepossible since conceptual relationships have been developed formosthydraulic interactions. If streamflow records areavailable,the investigator can predict at least the trend of future stream behavior.

LITERATURE CITED



### American Societyof CivilEngineers,TaskForce onBed Forms in Alluvial Channels of the Committee on Sedimentation. 1966.Nomenclature for bed formsin alluvial channels. American Society of Civil EngineersProceedings, HydraulicDivisionHY3:61-64. Blench,T. 1966.Mobile-bedfluviology-A regimetheory
treatment of rivers for engineers and hydrologists. 300 p. T. Blench and Associates Limited, Edmonton, Alberta, Canada. Bogardi, Janos. 1974. Sediment transport in alluvial
streams. 826 p. Akademiai Kiado, Budapest, Hungary.
Brice, J. C. 1975. Airphoto interpretation of the form and behavior of alluvial rivers. Defense Documentation Center, Defense Logistics Agency, Cameron Station, Alexandria,Va. Brooks, Norman H. 1958. Mechanics of streams with movable beds of fine sand. Paper 2931. Transactions of the American Society of Civil Engineers 23:526-594. Bull, W. D. 1968. Deposition on alluvial fans. p. 7. 

### In Encyclopedia of geomorphology. Rhodes W. Fairbridge, editor. Dowden, Hutchinson, and Ross, Inc., Stroudsburg,Pa. Colby, Bruce R. 1964. Discharge of sands and mean velocity relationships in sand-bed streams.U.S. Geological Survey ProfessionalPaper462-A, 47p. Crandell, Dwight R. 1968. Mudflow. p. 763. 

### In Encyclopedia of geomorphology. Rhodes W. Fairbridge, editor. Dowden,Hutchinson,andRoss, Inc., StroudsburgPa. Fahnestock, Robert K. 1963.Morphologyandhydrology of a glacial stream-White River, Mount Rainier, Washington. U.S. Geological Survey Professional Paper422-A, 70 p. Washington,D.C. Fahnestock,

### R. K., 

### and ThomasMaddock,Jr. 1964.Preliminary report onbed formsandflowphenomenain the Rio Grandenear El Paso, Texas. U.S. Geological Survey Professional Paper 501-B:140-142. Washington,D.C. Friedkin, J. F. 1945. A laboratory study of the meandering of alluvial rivers. 40 p. U.S. Army Corps of Engineers, Waterways Experiment Station, Vicksburg,Miss. Gessler, Johannes. 1967. The beginning of bedload
movement of mixtures investigated as natural armoring in channels. 89 p. Translation T-5 by Edmund A. Prych,W. M. Keck Laboratory, Hydraulics and Water Resources, California Institute of Technology,Pasadena, Calif. Gessler, Johannes. 1970. Self-stabilizingtendencies of alluvial channels. American Society of Civil Engineers Proceedings, Waterways and Harbors DivisionWW2:235-249. Gessler, Johannes. 1971.Aggradation anddegradation.
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### In River mechanics I. Hsieh Wen Shen,editor.Fort Collins,Colo. Gilbert, G. 

### K. 1880. Report on the geology of the Henry Mountains. 170p. Secondedition. U.S. Geographical andGeologicalSurvey,RockyMountainRegion. Heede, Burchard H. 1971. Characteristics and processes of soil piping in gullies. USDA Forest Service Research Paper RM-68, 15 p. Rocky Mountain Forest and Range Experiment Station, Fort Collins, Colo. Heede, Burchard H. 1972. Flow and channel characteristics of two high mountain streams. USDA Forest Service Research Paper RM-96, 12 p. Rocky Mountain Forest and Range Experiment Station, FortCollins,Colo. Heede, Burchard H. 1974. Velocity-head rod and current meter use inboulder-strewn mountain streams. USDA Forest Service Research Note RM-211, 4 p. Rocky Mountain Forest and Range Experiment Station, Fort Collins,Colo. Heede, Burchard H. 1975. Mountain watersheds and dynamic equilibrium. p. 407-419. 

### In Watershed management symposium. American Society of Civil Engineers,Logan,Utah. Heede, Burchard H. 1976. Equilibrium condition and sediment transport in an ephemeral mountain
stream.6:97-102. InHydrologyand water resources in Arizona and the Southwest: Proceedings of the 1976 meeting of the Arizona Section, American Water Resources Association, and Hydrology Section, Arizona Academy of Sciences [Tucson, Ariz., April 29-May 1, 19761.

### Heede, Burchard H. 1977. Influence of forest density

on bedload movement in a small mountain stream. 7:103-107. In Hydrology and water resources in Arizona andthe Southwest: Proceedings ofthe 1977 Meeting of the Arizona Section, American Water Resources Association, and Hydrology Section, Arizona Academy of Sciences [Las Vegas, Nev., April 15-16,19771. Heede, BurchardH. 1979.Predicting impact of a restoration project on river dynamics-A case history. USDA Forest Service General Technical Report RM-62, 8 

### p. Rocky Mountain Forest and Range Experiment Station,Fort Collins,Colo. Hibbert, A. R. 1971.Increases in streamflow after converting chaparral to grass. Water Resources Research7(1):71-80. Johnson, Arvid M. 1970. Physical processes in geology. 577 p. Freeman, Cooper, and Co., San Francisco, Calif. Koloseus, H. J. 1971. Rigid boundary hydraulics for steady flow. p. 3-1 to 3-51. In River mechanics I. HsiehWen Shen, editor. Fort Collins Colo. Lacey, G. 1932. Regime diagrams for the design of canals of distributaries. Technical Paper 1. 

### Irrigation Branch, Upper Punjab Public Works Department, India. Lane, E. W. 1955a. The importance of fluvial morphology in hydraulic engineering. American Society of Civil Engineers Proceedings, Hydraulic Division 81:745-1 to745-17. Lane, Emory W. 195%. Design of stable channels. Transactions of the American Society of Civil Engineers 120:1234-1279. Lane, E. W. 1957. A study of the shape of channels formed by natural streams flowing in erodible material. Report 9, 106 p. U.S. Army Corps of Engineers, Omaha,Nebr. Lane, E. W., and E. J. Carlson. 1953. Some factors affecting the stability of canals constructed in coarse granular material. p. 37-38. In Minnesota international convention: Proceedings of the international association for hydraulic research, fifth general meeting [Minneapolis,Minn., Sept. 1-4, 19531. Lane, E. W., E. 

### J. Carlson, and 0. S. Hanson. 1949.Low temperature increases sediment transportation in ColoradoRiver. CivilEngineering l9:619-620. Langbein,W. B. 1964. Profiles or rivers of uniform discharge. U.S. Geological Survey Professional Paper 501-B:119-122.Washington,D.C. Leopold, Luna B., M. Gordon, andJohnP. Miller. 1964. Fluvial processes in geomorphology. 522 p. W. H. Freeman andCo., SanFrancisco, Calif., andLondon, England. Leopold, Luna B., andThomas Maddock, Jr. 1953. The hydraulic geometry of stream channels and some physiographic implications. U.S. Geological Survey ProfessionalPaper 252,57p. Leopold,Luna B., andGordon M. Wolman. 1960.River meanders. Geological Society of America Bulletin 71:769-793. LindIey, E. S. 1919. Regime channels. Proceedings of the seventhcongress of thePunjab engineers. Little, William C., andPaulG. Mayer. 1976. Stabilityof channel beds by armoring. American Societyof Civil Engineers Proceedings, Hydraulic Division HYll:1647-1661. Livesey, Robert H. 1963. Channel armoring below Fort Randall Dam. p. 461-470. In Proceedings of the federalinteragency sedimentation conference, 1963 [Jackson, Miss.] U.S. Department of Agriculture, Agricultural Research Service, Washington,D.C. Miller, JohnP. 1958. High mountain streams: Effect of geology on channel characteristics and bed material. New Mexico State Bureau of Mines and MineralResources Memoir 4, 51p. Socorro,N. Mex. Morisawa, Marie. 1968. Streams: Their dynamics and morphology. 175 p. McGraw-Hill, New York, N.Y., andLondon,England. Osterkamp,

### W. R. 1977.Effect of channel sediment on width-discharge relations with emphasis on streams in Kansas. Kansas Water Resources Board Bulletin 21, 25p. Rouse, Hunter 1950. Fundamental principles of flow.
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### 1-135. In Engineering hydraulics. Hunter Rouse, editor. John Wiley and Sons, Inc., New York, N.Y., andLondon,England. Rzhanitsyn, N. A. 1960. Morphological and hydrologicalregularities of the structure of the river net. 380
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### B. Krimgold,U. S.Departmentof Agriculture, Agricultural Research Service, Soiland Water Research Division, and U.S. Department of the Interior, Geological Survey, Water Resources Division. Schumrn, S. A. 1960.The shape of alluvial channels in relation to sediment type. U.S. Geological Survey ProfessionalPaper 352-B:16-30.Washington,D.C. Schumm, S. A. 1974. Geomorphic threshold and complex response of drainage systems. p. 299-310. In Fluvial geomorphology:Proceedings of the fourth annual geomorphology symposium. Marie Morisawa, editor. StateUniversity ofNew York, Binghamton. Schumm, S. A., and M. A. Stevens. 1973. Abrasion in place: Amechanism for rounding and size reduction of coarsesediment in rivers. Geology 1:37-40. Shen, H. W., and S. Vedula. 1969. A basic cause of a braided channel. 5(1):201-205.InProceedingsof the 13th congress of the international association for hydraulicresearch [Kyoto,Japan]. Simons, D. B., and E. V. Richardson. 1966. Resistance
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NOTATION

A =

### cross-sectional area of flow-square feet A' =

### difference in altitude between concave profile
at mid-distance and straight line connecting the ends of profile-feet 

### D =

### sediment particle size-millimeters d =

### depth of flow-feet Fr =

### Froude number

g =

### acceleration due to gravity-feet per second
per second H =total fall of stream-feet K, = 

### coefficient relating sediment load and water discharge

m =mass of water-pounds
p 

### =wetted perimeter-feet Q =

### stream discharge-cubic feet per second Q, =

### sediment discharge-pounds Q, 

### =water discharge-cubic feet per second Re =Reynolds number R =

### hydraulic radius-feet

r =

### numerical constant S =

### slope-feet rise or fall divided by feet horizontal distance

s =

### numerical constant V =

### average velocity-feet per second

w =

### top width of channel-feet

y 

### =specific weight of water-pounds per cubic foot
p =

### absolute (dynamic)viscosity-pound-seconds
per square foot

v 

### =kinematic viscosity-square feet per second

Q 

### =fluid density-pounds per cubic foot

T 

### =tractive force-pounds per square foot

Agriculture-CSU, Fort Collins