River Cha ne1 Pattern nderin and Str
By LUNA €3. LEOPOLD and M. GORDON WOLMAN
PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS
GEOLOGICAL SURVEY PROFESSIONAL PAPER 252--14
UNITED STATES GOVI'RNM15N'T PRINTING OFFICE, WASHINGTON : 1957 UNITED STATES DEPARTMENT OF THE INTERIOR
STEWART L. UDALL, Secretary
GEOLOGICAL SURVEY
Thomas B. Nolan, Director
REPRINTED 1963
For sale by the Superintendent of Documents, U.S. Government Printing Office Washington 25, D.C. - Price 50 cents (paper cover) CONTENTS
Page Page Symbols IV The nature of channel adjustment to independcii t, con- Abstract _____.-_____----.~~-~~--.-----....------~--39 trols-Con tinued Introduction and acknowledgmeiits- -.-...... _. ------. 39 Observations of adjustments in natural channels.. .. 70 The braided river__-. -. __ .. __ -~ - - - - -.. . -. __ .__ - ___. 40 Summary and interpretatioii--- ___- __ ------.-. . 71
Introduct,ion .._._____ ._ - ~ ~..- - - __ -.-. ___ - - - __ - 40 Application of observatioiis on channel adjustment to thc Horse Creek: t,ype locality of the braided stream-.-_ 40 problem of channel pattern _....- ______-.- -.. __ -. 72
Stages in the development of a braid __.___.______43 References cited _...___ __.___~ ______.__..___~___. 73 Changes associated with channel divisiou.. .. . - - - - 44 Appendix______.______-----..--.75 Flume experiments .___- ______~- - - __ -.. 44 A. Analyses of sand sizes used in flume experiments Divided and undivided reaches in the flume and and fed into flume-river .____.______75 in natural rivers ._.._._____._____.______4 8 B. Data on size characteristics of sand on channel
Summary: the braided river-.- ~ - -.- -.. . . _. __ -.__ 53 bed and on bars in flume-river.______~- ~ -. -. - 75 Straight channels ...... -~ .___ - - __..- - -. . - ~... - - ~- -. 53 C. Summary of data on flume experiments at Cali-
The wandering thalweg-_ ~.-. . - - -.. ~. -.. -~ - ~ - -.-. 53 fornia Institute of Technology .__._-- - - ~ ~. .-. - 76
Pools and riffles.. .._ ~ ~ ~ ~ ~ -.-. -..~ ~ - - - ~ 53 D. Comparison of hydraulic characteristics of uii-
Summary: straight chanuels .... .-~ ~ ~ __._..-. . -. 59 divided and divided reaches of braided streams. 77 The continuum of channels of differerit patterns.. .. -~ - 59 E. Data on wavelength of meanders, bankfull dis- Summary: cont,inuum of channel patterns. ._------63 charge, and bankfull width ..______.. 78 The nature of channel adjustment to independent controls. 63 F. Data on estimated bankfull discharge at various Development3of river width_._- -.- - __.______- 63 stream cross sections.. ------79 Channel roughness and resistance-_ - -.-. . - - - - -. 65 G. Distribution of bed-particle size in various stream
Resistance coritrollcd by size of bed material -... 65 cross sections..._____.______~ _____..._._._80 Resistancc rclated to bed configuration. _.__. 66 H. Values of hydraulic factors at various stream cross
Sediment transport, shear, and resistance.. ..___66 sections.. .. ~ ~ ~ -.- -.- - ~..~ -. - - - - -.. . . . -. . . - 81 Response of slope to changes of load in the flume- 69 Index..__.-..- __._____..______.--..-.-~~~~----85
ILLUSTRATIONS
Page Pane FIGURE28. Maps of Horse Creek and the Green River FIGURE 43. Plan and profile of the Pop0 Agie River near near Daniel, Wyo., showing dividing and Hudson, Wyo._---______56 rejoining of channels in 1877 and 1942 ...- 41 44. Profiles of three rivers of different channel 29. Plan and profile of Horse Creek near Daniel, patterns____-______57 WYO.__~______.______42 45. Wavelength of meanders and of riffles in rela- 30. Central gravel bar in Horse Creek ....-_._43 tion to bankfull discharge and channel 31. View of downst,ream end of central gravel width______-______58
bar in Horse Creek___-._-___._.__.___ ~ 43 46. Relation of channel slope to bankfull dis- 32. Cross sections of braided reach, Horse Creek. 43 charge in distinguishing braided, meander- 33. View of initial channel in flume .______._45 ing, and straight channels ______-.- ___ - 59 34. Sketches and cross sections showing develop- 47. Plan and profile of Cottonwood Creek near merit of braid in flume-river ..._..__._..46 Daniel, Wyo.______... - - 61 35. Braided channel in flume (runs 6-8) - - - - - 47 45. View of braided reach of Cottonwood Creek- 62 36. Island formed in braided channcl in flume 49. Relation of relative smoothness to resistance, (run 30)_.._.__.~~______~~______47 Brandywine Creek, Pa ______.___~___ 65 37. Progressive development of baa in flume- 50. Relation of relative smoothness to resistance, river 49 all data______------__------.^^.- 66 38. Measured and diagrammatic. profiles of 51. View of dunes in flume-river ______._67 flume-river. -.------.------50 52. Vertical profiles of velocity in flume-river. - 67 39. Map of braided reach in the Green River 53. View of initial channel in flume (run 29) - -.- 68 54. View of bed of flume-river with no load after near Daniel, Wyo- - ______- ___ - 51 l)/s hours.______.______-_------68 40. Plan and profile of the New Fork River 55. View of bed of flume-river with no load after near Pinedale, Wyo- _____ -..___. - - -.__ 52 21 hours- .______--__ 68 41. Plan and profile of Valley Creek near Down- 56. View of bed of flume-river with load being ington, Pa ______._...______54 introduced at r6te of 24 grams per minute- 69 42. Plan and profile of bhe Middle River near 57. View of bed of flume-river with load being Staunton, Va--_-_-.______,55 introduced at rate of 55 grams per minute- 69 111 IV CONTENTS TABLES
Page TABLEI. Comparison of divided and undivided reaches of Page I TABLE5. Effect of change in load on stream slope, other braided streams, in natural rivers and flume- I conditions being constant ______-____ - ______70 river .______50 6. Examples from river data of adjustments in 2. Comparison of channel factors in two runs of I depth, velocity, and slope to changes in flume for which discharge was equal_------64 suspended load at constant discharge and
3. Comparison of reaches of channel before and width-..- ._____....__. ~ ______._____ 7Q afler passage of sediment front.___-______67 4. Relation of width of moving band of sediment to rate of load introduced ______68
SYMBOLS
area of cross section of flowing water E sediment load, in units of weight per unit of tho drainage area M exponent in relation of velocity to discharge when exponent in relation of width to discharge when 2) cx &" WKQb P wetted perimeter, in feet sediment concentralion, in pounds of sediment Q water discharge, in cubic feet per second (cfs) per pound of clear water R hydraulic radius, in feet mean depth, defined as ratio of cross-sectional S slope of water surface area to width 80 sorting coefficient of a granular mixture size of sediment particle T temperature, in degrees Fahrenheit median size of sediment particle; subscripts 25, V* shear velocity 75, or 84 refer to percent of sample finer than 2) mean velocity defined as quotient of discharge specified size divided by cross-sectional area exponent in relation of depth to discharge when width dcx:QJ W Darcy-W eisbach resis tance factor Y specific weight of water, or 62.4 pounds per cubic acceleration due to gravity foot numerical coefficient having a specific but un- P mass density of water
determined value i-0 intensity of boundary shear PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS
RIVER CHANNEL PATTERNS: B AIDED, MEANDERING, AND S’I’fPAIGHT
By LUNAB. LEOPQLDand M. GORDONW-OLMAN
ABSTRACT
Channel pattern is used to describe the plan view of a reach of Channel roughness, to the extent that it is determined by river as seen from an airplane, and includes meandering, braiding, particle size, is an independent factor related to the drainage or relatively straight channels. basin rather than to the channel. Roughness in streams carrying Natural channels characteristically exhibit alternating pools or fine material, however, is also a function of the dunes or ot,her deep reaches and riffles or shallow reaches, regardless of the type characteristics of bed configuration. Where roughness is of pattern. The length of the pool or distance between riffles in independently determined as well as discharge and load, these a straight channel equals the straight line distance between studies indicate that a particular slope is associated with the successive points of inflection in the wave pattern of a meander- roughness. At the width determined by the discharge, velocity ing river of the same width. The points of inflection are also and depth must be adjusted to satisfy quasi-equilibrium in shallow points and correspond to riffles in the straight channel. accord with the particular slope. But if roughness also is variable, This distance, which is half the wavelength of the meander, depending on the transitory configuration of the bed, then a varies approximately as a linear function of channel width. In number of combinations of velocity, depth, and slope will satisfy the data we analysed the meander wavelength, or twice the equilibrium. distance between successive riffles, is from 7 to 12 times the An increase in load at constant discharge, width, and caliber channel width. It is concluded that the mechanics which may of load tends to be associated with an increasing slope if the lead to meandering operate in straight channels. roughness (dune or bed configuration) changes with the load. River braiding is characterized by channel division around In the laboratory river an increase of load at constant discharge, alluvial islands. The growth of an island begins as the deposition width, and caliber resulted in progressive aggradation of long of a central bar which results from sorting and deposition of the reaches of channel at constant slope. coarser fractions of the load which locally cannot be transported. The adjustments of several variables tending toward the The bar grows downstream and in height by continued deposition establishment of quasi-equilibrium in river channels lead to the on its surface, forcing the water into the flanking channels, which, different channel patternp observed in nature. For example, to carry the flow, deepen and cut laterally into the original banks. the data indicate that at a gi‘ven discharge, meanders occur at Such deepening locally lowers the water surface and the central smaller values of slope than do’ braids. Further, at the same bar emerges as an island which becomes stabilized by vegetation. slope braided channels are associated with higher bankfull dis- Braiding was observed in a small river in a laboratory. charges than are meanders. An additional evample is provided Measurements of the adjustments of velocity, depth, width, and by the division of discharge ar?pnd islands in braided rivers slope associated with island development lead to the conclusion which produces numerous small channels. The changes in slope, that braiding is one of the many patterns which can maintain roughness, and channel shape which accompany this division quasi-equilibrium among discharge, load, and transporting are in accord with quasi-equilibrium adjustments observed in ability. Braiding does not necessarily indicate an excess of total the comparison of large and small rivers. load. Channel cross section and pattern are ultimately controlled INTRODUCTION AND ACKNOWLEDGMENTS by the discharge and load provided by the drainage basin. It is important, therefore, to develop a picture of how the several From the consistency with which rivers of all sizes variables involved in channel shape interact to result in observed increase in size downstream, it can be inferred that the channel characteristics. Such a rationale is summarized as physical laws governing ‘the‘formation of the channel ’ follows: of a great river are the same as those operating in a Channel width appears to be primarily a function of near- small one. One step toward understanding the mech- , bankfull discharge, in conjunction with the inherent resistance of bed and bank to scour. Excessive width increases the shear on anisms by which these laws operate in a river is to the bed at the expense of that on the bank and the reverse is true describe many rivers of various kinds. for very narrow widths. Because at high stages width adjust- This study is primarily concerned with channel ment can take place rapidly and with the evacuation or deposi- pattern; that is, with the plan view of a channel as tion of relatively small volumes of debris, achievement of a seen from an airplane. In such a discussion some ,relatively stable width at high flow is a primary adjustment to which the further interadjustments between depth, velocity, consideration must also be given to channel shape. slope, and roughness tend to accommodate. Shape, as we shall use it, refers to the shape of the river 39 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS cross section and the changes in shape which are Wyoming, Peale (1879) was impressed by the manner in observed as one proceeds along the stream, both which tributaries joined the upper Green River. In headward to the ultimate rills and downstream to the streams which do not exhibit a braided pattern, a master rivers. Because the shape of the cross section tributary usually discharges all of its flow through a of flowing water varies, depending upon whether the single channel into the channel of the master stream. river is in flood or flowing at low flow, shape must take Peale observed that, in contrast, Horse Creek “flows into consideration the characteristics of river action out into a broad valley in which it is side by side with at various stages of flow. the Green, and finally, to use an anatomical term which The channel pattern refers to limited reaches of the exactly describes it, joins the latter by anastomosis. river that can be defined as straight, sinuous, meander- There are at least five islands formed by the two streams ing, or braided. Channel patterns do not fall easily in the lower end of the broad valley” (p. 528). into well-defined categories for, as will be discussed, The term “anastomosis” was apparently first applied there is a gradual merging of one pattern into another. to streams by Jackson (1834). Because it has occasion- The difference between a sinuous course and a meander- ally been misapplied in the geomorphic literature, it is ing one is a matter of degree and a question of how desirable here to recall its definition-the union of one symmetrical are the successive bends. Similarly, vessel with another-or the rejoining of different there is a gradation between the occurrence of scattered branches which have arisen from a common trunk, so as islands and a truly braided pattern. to form a network. Successive division and rejoining The interrelationship between channels of different with accompanying islands is the important charrtcter- patterns is the subject of this study. Because neither istic denoted by the synonymous terms, braided or braided channels nor straight channels have received anastomosing stream. the attention in the literature that meanders have, our A braided pattern probably brings to the minds of observations of these patterns precede the discussion many the concept of an aggrading stream. Not until of the interrelations between channels of different the work of Rubey (1952) was the problem of channel patterns. division and island formation discussed as one of the The flume experiments described were conducted in possible equilibrium conditions of a channel. The the Sedimentation Laboratory of the California Insti- examples which are discussed here allow some elabora- tute of Technology during the time when the senior tion of Rubey’s idea and perhaps a somewhat more author was a visiting professor in the Division of Geo- complete picture of the manner in which the channel logical Sciences. For this opportunity, as well as for division around islands proceeds. advice and encouragement, thanks are extended to Dr. Robert P. Sharp. The Division of Geological Sciences HORSE CREEK: TYPE LOCfUJTY OF THE BRAIDED also financed the laboratory phase. STREAM Dr. Vito A. Vanoni of the institute not only allowed It is appropriate to use as the first example of a typical the use of his laboratory for the work but generously braided river the same stream to which the term offered his counsel. Assembly of the laboratory equip- “anastomosing’, was early applied. There has been ment would not have been possible without the expert but little change in the stream pattern between 1877 craftsmanship of Elton F. Daly of the Hydrodynamics and 1942 when the modern topographic map was Laboratory of the institute. published. Figure 28 shows the area near Daniel, An early draft of the manuscript was rend by a num- Wyo., as depicted by Peale and as shown on a modern ber of friends in and out of the Geological Survey. For map. The islands shown by Peale still exist with but help at various stages of the work particular thanks are minor changes in form. extended to Norman H. Brooks, Ronald Shreve, and Within a few miles of the point where Peale viewed John P. Miller. the anastomosing reach of Horse Creek, 5 miles north- For her careful work in compiling and computing west of Daniel, Wyo., we mapped a reach of the river data for this, as well as previous studies, we gratefully which includes a gaging station of the Geological Survey acknowledge the assistance of Ethel W. Coffay of the (fig. 29). At this place Horse Creek has a drainage Geological Survey. area of 124 square miles and a mean discharge of about 65 cfs derived primarily from the headwater mountain THE BRAIDED RIVER area in the Wyoming Range. Though not so well INTRODUCTION developed here as downstream, the braided pattern is apparent. The reach near the gaging station was In 1877 when field parties of the Hayden Survey were chosen for study because the channel pattern is typical making the geologic reconnaissance of west-central and because the discharge data obtained at the station RIVER CHANNEL PATTERNS 41 can be used to analyse the flow characteristics of the character to the gravel island now smarating the two braided channel. active channels. In figure 29 it can be seen that the reach at the gaging The linear bar in the left channel is nearly bare of station has only a single channel, but withih a few vegetation except at its most headwater tip where hundred feet downstream the flow divides and then again young willows have become established. This can be joins into a single channel. The division begins as a low seen in figure 30, which looks downstream along the gravel bar (marked C) near the left bank which grades central gravel bar. The man stands by the young downstream into a central ridge meeting the tip of a willow at the headwater tip of the linear bar. Two gravel island (marked D) supporting a willow thicket. other bits of now growth on the bar can be seen 20 feet In the left channel about 200 feet downstream from the and 70 feet farther downstream. upper tip of the island, a linear gravel bar (marked The upstream end of the bar is gently rounded in E in fig. 29 and pictured in fig. 30) extends for nearly cross section and lobate in form like a beaver tail. 250 feet down the center of the channel. The bar ends Downstream the bar becomes pointed, flat on tog, and near the junction of the main channels. trapezoidal in cross section (figure 31). The two channels divided by the willow-covered When we first studied this linear bar there was no island are about equal in width, 30 to 40 feet. The vegetation on the lower end. One year later some
11 30'
BIG PINEY OUAORANGLE 30.MINUTE SERIES
I 11O"lY 1942 1
FIGURE28. Maps of lower Horse Creek and the Green River near Daniel, Wyo.. comparing a sketch made by Peale (1879, pl. L) in 1877 and a Geological Survey map of 1942. The islands (marked A) shown by Peale existed in 1942 with but minor changes in form. Note the successive dividing and rejoining of river channels.
sum of these widths is 20 to 30 percent greater than vegetation had sprouted on the formerly bare gravel the 50-foot width of the undivided reach. In the surface as can be seen in figure 31. On 425 square feet downstream part of the left channel where the central of area there were 80 individual plants, or one on every bar of gravel has been deposited, the width is only 5 square feet approximately. The plants were: slightly greater than in the rest of the left channel Number where there is no central bar. Species of plants Opposite the gravel island, and on the right side of Red top (Agrostis sp.) ------20 the little there is a slough which is alined with Sweet Clover (Melilotus Sp.) ______c__-_____17 Bluestem (Agropyron Smithii) ______-_ ._____-_------12 a grassed depression. During flood flow this slough Foxtail (Hordeum sp.) ------___ - - - - __ - __ - __ - - __ lo and the depression water* The con- Dandelion (Taraxacum sp.) - _ ------7 figuration of the slough and depression and their posi- Shepherd purse (Cruciferae)______4 tion in relation to the active right-hand channel indicate Carrot weed (Umbelliferae)------3 that they Once joined as a cont~uousactive Mint (Labiatae) ______2 2 which has subsequently been blocked by deposition. Timothy (Phleum sP.)------In its active stage this old channel was separated from Two cross sections of the braided reach on Horse the present right-hand channel by an island, similar in Creek are shown on figure 32. The valley bottom is 42 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS
c Uo
/ HLMON 3113NL3VW
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WnlWa AMWMllBMV :1334 NI ‘NOllVA313 43
.... "'" ...... -00. ___ .. __...... _ ...... ",",",it---- ...... _- __-- ...... _ 'b...... "_"_" -,, bounded by IW., low lo:tT'1«S, una 5 1..,\ ."d anothe. .ingle Or undi~idNl ~hann~l, a .h"rt, lubmerged ...,nl...:l 7 r.... t .1>0". low ..·.lCl' Aurfaco:o. Wilhin the <'(mlln;", bar iA d~poAiled during = high Oow_ The head of lh~ 1>&",,- of lhe 5-1001 t.c.....,. the gnI"el ",I."d ."d the !Ie"" 1P""'~1 bar iA romp<:HlC(i of the eo ...... fraction of the adj..,~nt gn.,·~1 fin conteining the ebandon...! chnn~l hed load ,,·hich iA mo,-,nll down the ~enter of Ihe d •• nne] lio e~ Ih ~ ...me ~le"uion. 'rhe new gruel b ... gcne..,ll,,· bed. n"".U5C of lOme local condition no~ all the COarse ;" IIOrno"'''e, lower th ... , the le,·c1 of tho adj&eent iol .. "d, particles Me traMpOlled IhrouKh thj~ particular re&<:h thougl, a~ a poi,,~ ebou~ hAl ! ,.... y dow" the l~ngth of ."d lOme &«umulale in llta ctn!eT of the .1I ... nnel. the bar the Hat UI'P'" auri...,.. of Lbe bat it a~ the...."., ),1011 of the "",.Jle' parlidOi mo .... O,tt. and pMt lhe elevatIOn ... the auriace 01 the island ,,,,,ip;tnl hv, but part of the lintr frac,ion iI t .... pped by the COOU'Wr mattri,l OUld 10 dt~tedt Though .TAoa [If TIIIt DKVELOPKIlI'T OP A .~ th" dtptb is gradually I'fdo.>efd, vtiocily o,'er I~ Th_ o~ntioruo auggeot " eequence of e~enU in P'O"';"( bar 1t",b 10 ...main un ...... ,_ero._ .. __ .. H .... ~ .... __ w ... , ...... __ ...... 1 44 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS bar near the center of the channel roll along the length D). At low flow the water which gets into the left of the new bar and are deposited beyond the !ower end channel pours over the downstream tip of the low bar where a marked increase in depth is associated with a in a direction nearly perpendicular to the general decrease in velocity. Thus the bar grows by successive stream course as indicated by the riffle symbols between addition at its downstream end, and presumably by the letters C and D in figure 29. some addition along the margins. The downstream At high discharge the flow impinges against the growth is suggested by the fact that willows became left bank and subsequently produces a sharp bend in established at the upstream tip while the downstream tha streamlines to the right as they become alined portions were still bare. A similar gradation in age of again with the left channel. Thus the low bar and vegetation exists in many other islands studied. the upper tip of the gravel island force the flow into a The growth of the gravel bar at first does not affect reverse curve or S-shaped path. As a consequence the width of the stream, but when the bar gets large the left bank would tend to erode where the flow enough, the channels along its sides are insufficient impinged against it, while the inside of this curve in width to remain stable. Widening then occurs would be a zone of deposition which would blunt or by trimming the edges of the central bar and by cutting widen the upstream tip of the gravel island. It is laterally against the original sides of the channel reasoned that the widening of an initial linear bar is until a stable width has been attained. At the same probably due mostly to the deposition on the inside time, some deepening of the flanking channels may of bends that results from obstruction by the bar. occnr and the bar emerges as an island. The bar The gravel island is interpreted as a stabilized and gradually becomes stabilized by vegetation. At some enlarged bar which had its origin in a manner typified stage lateral cutting against the bar to provide in- by the new bar. The gravel in the bar and island are creased channel width becomes just as difficult as similar. The island has a thin layer of silt covering the against the banks of the original channel, and so the surface of the underlying gravel; it is believed that bar is not eliminated. The hydraulic properties of the during overbank flow, vegetation stopped the fine channel during this process of island formation will be material and caused it to be deposited. Coarse material discussed in a later section. would ordinarily not be carried over the surface of the After the island has been formed, the new channels vegetated island for such material moves primarily in in the divided reach may become subdivided in the the swifter water of the established channels. same manner. As successive division occurs, the The initial vegetation which sprouts on a new gravel amount of water carried by an individual channel bar begins the screening process and the consequent tends to diminish so that in some of these, vegetation deposition of thin patches of silt or fine sand promotes prevents further erosion and, by screening action, the stand of vegetation. Screening of fine material and promotes deposition. the improvement of the stand of vegetation by altering The Horse Creek example demonstrates all of these the texture of the surface layer are reciprocal and features. The new gravel bar deposited in the left perpetuating. channel occupies the center of a channel not yet widened by stream action. The sequence of age of CHANGES ASSOCIATED WITH CHANNEL DIVISION vegetation shows that the bar was extended down- FLUME EXPERIMENTS stream with time, and presumably was built in 2 or Experimental work in a flume at California Institute 3 years, for at the time the lower part of the bar was of Technology allowed us to test the hypothesis of bar bare, the willows at the upstream tip were not more than deposition just outlined. The observations made in the 2 years old. laboratory provide some insight into not only the The gravel island separating the two main channels sequence of events leading to braiding but also into the is considerably wider than the new gravel bar. The hydraulic relations between the divided and undivided right channel is separated from the abandoned channel reaches of channel. First, the progressive development by a former island which also was wider than the new of braid? in the flume will be discussed and compared bar. When a central linear gravel bar is deposited, with field examples. Second, the interrelations of the bar may continue to increase in width, forcing the hydraulic facLors in both the laboratory and natural channels farther apart. One reason for this lateral rivers will be analyzed. cutting into the original banks can be seen by the The 60-foot flume had a width of about 3 feet and direction of the flow at the tip of the gravel island. was filled to a dcpth of about 5 inches with a poorly The low bar (marked C in fig. 29) just below the sorted medium sand (identical to run 1, app. A). cable has built downstream until it actually joins the Initial channels of various shapes and sizes were upstream tip of the much older gravel island (marked molded by means of a template mounted on a moving IU\"ER CHASS"!. PATT'ERSS s...li",~nl ... 11 f..r illlo ,h. "l",'~m i" Ih~ {o"n 01 dry .. nd. From an ov.rhud hopP/'r.1 .he UPp<'l" enrl of Ih~ tlume, Ihe M"d wu rarri"!l OUI on • l!Jl}all en , ..... -, __.. _ ..... _ ... "... _.~r ... _ .~dll">n or degradalion could be "",u",'~ly ",P" urtd dunn[\" Iht pTOgT?M of. run of reuon.ble durol,on, Til.... ,,"p,.,. the elr<:11"'"tanr..- for m",,1 runl, bulo morr r.rr'Aj(C', 0,," of lire "'-II,il,.! ,·Ira",,"I~ ig pi,·lu ...... r in ,.,.finM mr,hod of detrmlin,ng "Iuilibrium would bto hKUr(' la, The l ...v~lil\jl r.m.1{<' .111<1 ...rriffi • f'Oim dl"'il'llble. jl:ll«' for mtlUurU'jI: ~Ie",'ion 10 .11 ..... u ...... of 0.001 II it important 10 .mphuin .be fart th.t Ih~ .hann~1 1001 ,· .... ,ic.n.,· .•nd O.OO~ foot horizon,.U.", Th~ 1Ikr~ de,'''op<' EXPLANATION houts STATION I I .":*. ::. 7' 22 18 7' 1c Deposit more coarse than original sand *- m Deposit finer than original sand - - /.-..-.- Path of principal- bed transport >hours Riffle, or water flowing in steep, thin, sheet "~llllllllilll~~ Island or area nearly out of water I Well-defined edge of bar ----____ 111.defined edge of bar 7 hoc-r Island -/---- , SUCCESSIVE CROSS SECTIONS AT STATION 14 Incipient bar Initial Water surface 9 hours 0.25 0w Water surface 0 25 -7 10 hwm 0.25 1 0 1 2 Feet I-. -.- PROGRESS IN DEVELOPMEN1 OF BRAID IN FLIJML c1ANia:i FIGURE34.-Sketches and moss sectlons showing prowess in development of braid in flume-river (February 1642,1954, runs S-a.) (Profiles shown in fig. 38.) Rl\"~R CIIANNI:L 'A'lTF.RNS in I amlU areulte I'ftfItranl in the formerly .. nipl bank. The hud of Ihe ...bm~~ bu had limillrly ","uoef principoal bed t.n.nllport liel "" lOp oj ".. m ... "., ctnlnd 6<1.. The grain mO"em""t in th e deeper p"rLl of the channel adja.,.,nt 10 the centnl bar ...·u ulu.lly negligible in Ihe t&rIy lla&<' of Wind de"eLopmenl The CO'IIIrIl bar ""nlIDued 10 build ru.tr 10 tl,e .... ter lunlOll yet the pnneipal ..,ne of movement rem.ined fo •• lime .Iong the lOp of the build"'g bar. [t "·U there th.t .orne of the luger P*"liclei llOppM. tr.ppinr omallc. part ..]eI in tM building bar Th_ ..nalle. ,...... C(luld hove been mO"ed by the UIAtina; Ho .. had they Dol h«ome pro_ted or bloek...! by lorge. ","in•. Th,,«nt... l bar in thellum... ri,·or wu «used by 10011 ..."" ... - ...... _ ,,,...... _" ...... __, f ...... ,_ .orting, tilar .Ii~kin~ OUI of Ihe ..·.Itr as A ....1 illlnd. Sueh ltOu ...... ved in mUly of \l.e runo IUId Ihe iIIln.do . ·hkh Ire indir.ttd in 1108 lItekhei io fi"' .... 34 ""'errro ..... '""It of Ih;" p ~. This ~ondi l ;on i, .. 110 tho"." in figure 36, • photograph of, de"clopin&, ill.nd. The arto d ..ig".ttd II "incipient b.r" in figure 34 .t bou.7 had enl .. rged Ind emerged ....n w.nd by hour 9. - ....___ .. _~ ... _.-...... oa..l Fu.tbenno ... , .ft.... hour 9 of flo ..' • lin .... bor hld """ _ ... H .... """". _ .. ... ~,·tloped in Ihe ~hllnel.te* loCI "'""" Ihe 1.'0 iol.ndo, 48 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS bisecting the flow into two parts, marked A and B. This is shown on the sketch of the plan view in tho By hour 13, continued bar building in channel A and ower right part of figure 37 and on the cross sections subsequent lowwing of the chmnel B diverted most ‘or that timv arranged vertically on the figure. of the water out of the old channel A and the primary The growth and subsequent erosion of a central bar zone of transport over the bar arw was restricted to s also illustrated tit station 10 (fig. 37). On the left- charinel B. land diagram of station 10 the shape of the initial Similar sequeiices continued to change the configura- :hannel molded by template is shown as a dashed line. tion of the braided reach, moving the principal zones 4ftcf 1:: hours this shape had been altered by the of transport from one place to another, and at hour 22 milding of a central bar and by slight degradation of there were three island areas. It should be unclcrstood he channrls bcsidc the bar. By the crid of 4 hours thc that in the flume-river the constant discharge did not :ombination of lateral building and deposition on the permit the islands to receive any increment of deposition Jar surface had widended the bar arid made a double after emergence so that an “is1arid~’actually represented :rest. Bar building resulted in a clivcrsion of most of merely the highest knob of a bar most of which remains [tie watcr into tlic right clianncl tit station 10 which submerged. 7‘11~cross section of station 14 at hour 18 :auscd loc.al scouring. (bottom diagram, right side, fig. 34) illustrates this feature. DIVIL)EI> AND tJNl>IVIDlH> REACIIEH IN TIIF, FLUME AND IN NA’L’IJHAL RIVERS The succession of events observed in the flume are analogous to those postulated to account for the charac- In both natural strrtims and thc flume-river the slope teristics of thc rcach studied on Horse C‘reck. The Df the divided reach provcd to be greater than that of central bar built closer to the water surface and c~xtendcd the undivided reach. Tlie stecpening of thc divided itself downstream with time, channels were successively rcach in tht. flumr is vcry marlied. Figure 38 sliows formed and abandoned, and the bars were macle up of the watcr surfacc profile data associated with runs the coarser fractions of tlic introduced load but mixed 6a and b arid 8, Fc~brunry16-22, 1954. The measure- with considrrable fine material which hat1 become rncnts presented in tlic left part of the figure are inter- trapped. ‘l’hc similarities hetwrcn the field example preted diagrammatically on tlie right half of the figure. and tlie flume can be scm by comparing the photo- When considering the nieasurrments it must be recalled graphs in figures 30 and 35. that tlic elevation of the watcr surface WRS nicasured Nearly all observers who have recorded notes on tlie relative to a sloping datum. Thus, water surface action of a braided stream have reinarlied on thc shifting profilcs which rise downstream relative to the datum of bars and the caving of banks. Once a bar is deposited mean that the water surface became adjusted to a slope it does not ncccssarily remain fixed in form, contour, less than that of the flume rails. This can be seen by or position. Tliis can be seen in the successive cross reference to thc diagrammatic profiles on the right of sections of four stations made during the run pictured in figure 38 where the initial profile, shown as a heavy line, figure 37. Tim(. changes at a particular position arc reprcscnts the slope of the water surface when the run arranged sidc by side and the downstream variation at a began and the water started to flow down a channel particular time can be seen in tlie vertical groups. A parallel to the sloping rails. By tlic end of 9 hours, reference lrrel is givtm for c~iicti scction so tliat tlic aggradation had tnltcn place in the reach between station changes of watrr surface elevation can be compared. 6 and station 12, and also downstream from station 35. The sections grouped on tlie uppermost horizontal line Degradation of the initial channel liad occurred between are at station F. Comparing the sections from left to stations 15 and 3.5 with the establishment of a steep right it can be seen tliat station 6 underwcnt continued reach in tlic divided or braided section. aggradation and t Ii11 shape of the cross section ctianged Betwrrn hours 9 and 20 of flow, continued aggradn- radically, murh more than did the area of the cross tion took place in tlie divided reach but, in general, thc section. steep slope was maintained approximately parallcl to The horizontally arranged group of sketctics at that which cxistcd at tlic cnd of hour 9. Similarly, station IO illustrate tlie varying cltvation of wntrr tbe aggrading reach downstream from station 20 main- surface which rose twtwcen hours 1): ant1 4, fcll from tained nearly the same average slope as that which hours 4 to 6, and rosc again from hours 6 to 11. The fall existed at hour 9, this slope being much flatter than that of water surface elevation is clearly duc to the scour of of the divided or braided reach. A similar sequence the right-hand chiinnel between liours 4 and 6. can be observed in thr profiles presented in tlie lower The initial linear nature of the central bilr is hcst Irft-hand part of figure 37 (associated with run 17, illustratcd at 6 hours where a central ridge is present March 11-12). In figure 37 it can be seen that bc- through an 11-foot reach between stations 6 and 17. tween hours 1ji and 4, the reach from station 10 to 830 P M 11 hours 1050 A.M 140PM 4'30 P M Ik hours 4 hours 6 hourr Water surface we+ STATION 6 O.'.-3 47a STATION 8 OZ5.: OZ5.: 1.0 Feet O-LuxLLL VERTICAL SCALE I I I I I 025 1 I E-- --I- \ Initial channel ==STATION 14 STATION 6 VI PROFILES OF WATER SURFACE , -11 hours zb 026 8W--XT--X 30 40 50 DISTANCE ALONG FLUME IN FEET DIAGRAMMATIC PLAN VIEW OF BAR AFTER 6 HOURS I FIC~RE3i.-Cross sections showing the progressive development of harp in a braided reach of the flume-river, profiles of water surface, and diegrammatic plan view of bar (March 11-12, 19! ) 50 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS 0.3 r vi- 2 2 0.2 3 LL c -w I-4 0.2 w a 2 0 Q s 0.2 w 10 20 30 40 50 10 20 30 STATIONING ALONG FLUME, IN FEET HORIZONTAL DISTANCE, IN FEET e 1030 Feb 16 20min Slope of rails 0 0114 0 2 10 4 hr DIAGRAMMATIC PROFILES INTERPRETING MEASUREMENT DATA ---X 1140 Feb 18 9hr 0 0 085 cts V 330 19 17 hr L 120 grams per minute V 11 05 22 20% hr ACTUAL MEASUREMENTS lM~ine38.-Measured and diagrammatic profiles of flume-river during run of February 1&22,1954. (Plan view and cross sections for these runs are shown h fig. 34.) station 22 steepened markedly, but from hours 4 to 1 : TABLE1.-Ratio of hydraulic factors of divided to undivided reaches of braided streams (natural rivers and jlume-river) aggradation occurred at approximately the same sl~pe which existed in this downstream reach at hour 4. In New Fork River/ Flume at California Institute of Technology the braided reach upstream from station 10, however, _____ continued aggradation was accompanied by continued Wyo. Reach 1 Reach 2 Feb. 15 Feb. 16 Feb. 18 Mar. 5 steepening between hours 4 and 11. (1953) (1954) Sta. 10 Sta. 14 Sta. 10 Sta. 12 ! and 14 1 and 22 I and 14 1 and 38 It is important to notc in these runs that aggradation 1 1 could take place at a constant slope without braiding even Area...-...... ~~... 1.3 1.03 1.6 0.94 1.08 0.78 1.07 Width --...... ~ ....-.. 1.513 1.83 2.0 1.05 1.34 1.48 1.70 when the total load exceeded the capacity of the channel Depth. __...... ~... .. ,88 .56 .79 .%I.80 -52 .63 Velocity...... -. .. .77 .97 .. . ~. .~~ 1.06 .93 1.27 .93 for transport. Braiding is developed by sorting as the Slope ...-...~~.~~.~ .... 5.7 2.3 1.4 1.3 1.4 1.9 1.7 Uarcy-Weisbach resis- stream leaves behind those sizes of the load which it is tancehctor .... ~ ..... 10.5 1.3 ~ ...... ~ 1.1 1.3 .63 1.25 incompetent to handle. If such sorting results in pro- gressive coarsening of the bed material then the slope island is the width of flowing water. The width of the increases progressively If the stream is competent to undivided reach is the width of the water surface up- move all sizes comprising the load but is unable to move stream or downstream from the island or where thera is the total quantity provided to it, then aggradation may but a single channel. take place without braiding. Hence, contrary to the All examples show that channd division is associated assumption often made, the action in thc flume rivcr with increased width of water surface, increased slope, suggests that braiding is not a consequence of aggrada- and with decreased depth. In the three comparisons tion alone. This is brought out in flume runs 30a to 35 from our measurements of natural rivers the sum of the which are discussed later in relation to the adjustment of widths of the divided channels ranges from 1.6 to 2.0 slope in natural channels. times t,hat of the undivided one. In the four compari- Although thn, steepening of slope in i8h: divided reach sons made in the flume tlie ratios vary from 1.05 to 1.70. is one of the more obvious of tlie observed changes in Tlii.; increase in water surface width caused by the channel associatcd with division around an island, development of a bar or an island is accompanied by a nearly all other hydraulic parameters arc also affectcd. decrease in mean depth. The mean depth of the divided D&iled comparisons of an undivid-d channel and a reach was computed by dividing the cross-sectional area channel divided around an island, or a potential island, of flowing water by the total width of water surface in are availabl- for thee river reaches and four runs in thc the two channels. 'I'he ratio of dcpths in the divided flume-river. These comparisons are presented in reach to dcpth in the undivided reach varied from 0.6 table 1. (Complete data are tabulated in app. D) to 0.9 in natural rivers and from 0.5 to 0.9 in thc Comparisons are shown as ratios of the measurements flume-river . in the divided reach to similar measurements in the With regard to changes in slope, the profiles of Horse undivided one. The width io R reach containing an Creek in figure 29 show tirat the left channel is more RIVER CHANNEL PATTERNS 51 conspicuously divided in to pools and rimes thnn the unable to show from the maps available to liim any right ow, but, tbe slope of each of these divided channels significant increase in slope in the divided reach, but is unquestionably greater-in fact, it is three times as the maps suggested that “on the average, the slope large-as the slope of the undivided part of the stream. opposite islands is steeper by something like 5 to 10 The increased slope of the divided reach is wen more percent.” marked on the profile of the Green River neai Daniel, As table 1 shows, there is more variation in the ratios Wyo., where there is nearly a six-fold increase in slope in slopes than there is in the ratios of widths and of after the river divides (fig. 39). In the example of the depths in divided and undivided reaches. This is due New Fork River (fig. 40), the steepening is less obvious primarily to one example in a natural river, the Green primarily because there is a steep riffle between stations River near Daniel, for which the slope of the divided 200 and 500 which tends to increase the average slope channel was nearly six times that of the undivided one. of the upper 1,000 feet of the mapped reach. If, how- With the exception of this one large ratio, however, tbca ever, the divided reach between stations 1700 and 2400 natural rivers have ratios of 1.4 and 2.3, and the is compared with the undivided reach from stations ratios in the flume ranged from 1.3 to 1.9 1500 to 1700, steepening of the slope in the undivided The changes in width, depth, and slope caused by part is again apparent (table 1). island development in the flume-river are of the same In Rubey’s analysis (1952, p. 126) of the division of order of magnitude as comparable changes in the the channel of the Illinois River by islands he was natural rivers studied. From plmctabla map by Leopold and Wmm. Aup. 12,1953 FIGIJRE39.-Mop of Green River near Dnniel, Ryo., showing a reach in which the chnnnel divides around nil island nnd is, therclore, braidrd; the indiviciunl divided chnnnels meandcr. 52 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS EXPLANATION /---- Riffle The change of cross-sectional area depends upon the that conditions in channel division could be approxi- relative amounts of change of width and depth. The mated by assuming that the width-to-depth ratio, division by an island caused the cross-sectional area to slope, and roughncss are identical in divided and increase in all three reaches of the natural rivers studied undivided channels. Such assumptions would apply but in the flume there was an increase in cross-sectional only in certain cases but could not be assumed generally area in two instances and a decrease in two instanccs. applicable. Chien (1955) computcd the charactcristics The velocity in the divided channels was sompwhat loss of divided channels, using the Einstein bedload equation in the two natural rivers for which data are available, (1950) and assuming that 110 change of grain size accom- but in the flume division caused the velocity to increase panied channel division. ‘This assumption is more liltcly in two rcachcs and to decreasc in two others. Non- to be fulfilled in natural clianiicls than those of Franzius, uniform changes caused by island growtli can also be but both the flume data and the streams studied by US seen in the Darcy-Weisbach resistance factor f (table 1). in the ficld indicate that selective deposition of coarsc’ These data indicate that changes in neaily all the fractions of tlie load in the braiding process tends to hydraulic parameters occur when a channel divides. In result in coarser material in the beds of the separate discussing this matter Franzius (1936, p. 38) assumcd channels than in tlie undivided channel. RIVER CHANNEL PATTERNS 53 The adjustment of various hydraulic factors to any STRAIGHT CHANNELS change in the indepcridcnt factors may take the form In the field it is relatively easy to find illustrations of of any one of inany possibilities. The adjustments are zither meandering or braided channels. The same intrrdependen t and it is difficult to specify in advance :annot be said of straight channcls. In our experience up how an alteratioii of caonditions will be taken by the truly straight channels ara so rare among natural deprndrn t f ac tors. rivers as to bt> almost nonexistent. Extremdy short New islands form and channels often change too segments or reaches of the channel may be straight, rapidly for complete adjustment to cqiiilibrium condi- but it can be stated as a generalization thaf, reaches tiom, but some reac1ic.s of braided rivcrs are very which are straight for distances exceeding ten timss stable indeed, as judged by the size and age distribution the channel width are rare. of vegetation. The island shown on Peak’s map of the Green River near Daniel still exists 70 pears later, THE WANDERINQ THALWEG) as can bc seen in figure 28. Presumably, in such instances, a closer approach to equilibrium is possible Figure 41 shows in plan arid profile a reach of Vall~y than in transitory channel division. Nevertli eless Creek near Downingtown, Pa. For 500 feet this we interpret our obswvat ions presented above as rhannel is straight in a reach where the alluvium c,f indicative that a braiclcd pattern as well as other the valley is 30 feet thick. Its sinuosity (ratio of patterns can indeed be one of the possible conditions thalweg length to valley length) is practically 1 .O. of quasi-equilibrium. The thalweg, or line of maximum depth, is indicated by a dashed line in the upper portion of figure 41. SUMMARY: THE BRAIDED RIVER ‘I’hough the channel itself is straight, the thalwcg wanders back and forth from positions near one bank A braided river is onc whicli flows in two or more adthen the other. This is typical of a number of anastomosing channels around alluvial islands. This nearly straight, reaches which we tiavo studied. The study indicates that, braided reaches taken as a whole wandering thalweg is easier to see in the sketch shown are steeper, wider, and shallower than undivided in the lower part of figure 41 in which the position of reaches carrying the same flow. A mode of formation thc thalweg relative to a channel of uniform width of a braided channel was demonstrated by a small is plotted. stream in the laboratory. ‘I’lie braided pattern d3vel- Along with the wandering thalweg it is not uncommon oped after deposition of an initial central bar. The to find deposits of mud adjacent to the banks of straight bar consisted of coarse particles, wnich could not be channels. These commonly occur in alternating (as transported untlcr local conditions existing in that opposed to “opposite”) positions. A similar obsrrva- reach, arid of finer material trapped among these tion has been made by Schaffernak (1950, p. 45). The coarser particls. This coarse fraction bxame the alternating mud “bars” are related to a thalweg which nucleus of the bar which subsequently grew into an also moves alternately from bank to bank. In an island. Both in the laboratory-river and in its natural idealized sense, this plan view of straightr cIianne1s counterpart, Horse Creek near Daniel, Wyo., gradual appears to bear a remarkable resemblance to a mcander. formation of a central bar deflected the main current In a straight flume Quraishy (1944) observrd that a against tlie channel banks causing them to erode. series of alternating shoals formed in the channel. The braided pattern is one among many possible These lie referred to as “skew shoals” (p. 36). Sim conditions which a river might establish for itself as a ilarly, Brooks (1955, p. 668-8) called the condition in result of the adjustment of a number of variables to a which low channel bars formed alternately adjacent to set of indapendent controls. The requirements of the left and right walls of his straight flume a “meandthr” channel adjustment may be met by a variety of possible condition. combinations of velocity, cross-seccional area, and POOLS AND RIFFLES roughness. Braiding represents a pardcular combina- tion, albeit a striking combination, of a set of variables Another characteristic of natural streams even in in the continuum of river shapes and patterns. straight reaches is the occurrence of pools and riffles. Braiding is not necessarily an indication of excesFJive This has been noted by Pettis (1927), Dittbrenner total load. A braided pattern once established, may (1954), and Wolman (1955). Figures 40, 42, and 43, be maintained with only slow modifications. The respectively, the New Fork River near Pinedale, Wyo., stability of tlie features in the braided reaches of Horse the Middle River near Staunton, Va., and the Pop0 Creek suggests that rivers with braided patterns may Agie near Hudson, Wyo., present plans and profiles for be as close to quasi-equilibrium as are rivers possessing a braided reach, a straight reach, and a meandering meandering or other patterns. reach. Profiles of these three examples are compared 54 PHYSIOGRAPHIC ANI) HYDRAULIC STUDIES OF RIVERS I -/ 1 / \ I I i \ \ \ / / I I '\ \ \ / I / / / / \ '\ \ \ \ / / / / I I \ \ \ \ \ \ / / / / 4 '.\ 0 m RIVER CHANNEL PATTERNS 55 iw 0 300 Feel P EXPLANATION _jc Rlnle Bedrock in channel through this reach From planetable map by Lmpola ana woln m AUBW ?w- STATIONING ALONG RIVER CHANNEL IN FEET FIG1 RE 42 --Plan and profilr of d icach of tho Middlo River lirar Stnunton, Vn in figure 44 which reveals a similarity in tlie profiles tcst of this hypothesis, bankfull discharge wliai I) u of streams possessed of very dissimilar patterns. Thus, consider equivalent to “dominant dischargc” nf 111 a straight channel implies neither a uniform stream bed Indian literature, has been plotted in figur 3 45A ncn~n~+ nor a straight thalweg. wavelength of meanders. The figure Includrs dtil As demonstrated first by Inglis (1949, p. 147), the from straight reaches for which “wavchngtti ’ :\ twicv wavelength of a meander is proportional to the square the distance between successive riffles. root of the “dominant discharge.” One wavelength (a The data in figure 45, tabulated in appendix E, eomplcte sine curve or 2a radians) encompasses twice include measurements of rivers in India from lnglis the distance between succcssive points of inflection of (1949), our own ficld measurements, and some fiumc. the meander wave. It is well known that meandering data from Friedkin (1945) and Brooks (1955 and pcrsonal channels characteristically are deep at the bcnd and communication). The wavelengths In Brooks’ dtll a shallow at the crossover or point of inflection. Thus, obtained in a fixed-wall flume (no. 259, appendix E> twice the distance between successive rimes in a straight represent, as in the nonrneandering natural channels, reach appears analogous to the wavelength of a meander twice the distance between the “riffles,” or low bars, and should also be proportional to Qo5. As an initial which he observed. 56 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS 9 t: zI 0 0m z 0 a oz 3 WnlVO AWtlllEllV :1334 NI NOllVh313 57 5000 6000 7000 I 1 80 2000 3000 4000 5000 DISTANCE ALONG STREAM, IN FEET 1 I I DISTANCE ALONG STREAM, IN FEET FIGURE44.-Profiles of three rivers including straight, meandering, and braided reaches. 58 PHYSIOGRAPHIC AND HTDRAULIC STUDIES OF RIVERS EANKFULL DISCHARGE. IN CUBIC FEET PER SECOND EXPLANATION MLANDERS --1 0 1 Rivers and flumes from Leapold and Wolrnan - (lhlr repon) Friadkin(1945). Quraishy(1944). 7 and Inglis (1949) D Rivers in Oriru India lrom lnglli (193940 p 111) POOLS AND RIFFLES 0 In straight channels fmm Leo Id and Wolman (this report). and Broor(1955) BANKFULL WlDTU OF CHANNEL, IN FEET IWL'RE45.--\\ia! drngth of incandcrs and of riffles as functions of b;tiikfull discharge and channel width. Figure 45A drmonstratcs that, with considerable cmsistent though it includes straight channels as well scatter, a relation between wavelength and discharge as mcanders, and the widths range from less than 1 foot exists through a IO8 variation in Q. Thr data for in the flume to 1 mile in the Mississippi River. The straight channels do not vary from the average relation line drawn through the plotted points in figure 45R any more than those for meanders. indicates that in general, the ratio of wavelength to Inglis (1949, p. 144) had called attcntion to the fact bankfull width varies from about 7 for small streams that since width is also proportional to the square root having widths of 1 to 10 feet, up to 15 for large rivers of discharge, wavclcngth is a linear function of stream having widths in excess of 1,000 feet. width. Inglis did not mention the fact, illustrated in Dr. T. &I. Prus-Chacinski has told us that European figure 45B, that the sctltter of points in the width-wave- 1 engineers have a rule-of-thumb that the meander wave- length relation is Icss than that in thc. discliargc length is lt5 times the channel width. That our ratio wavelength relation. The relation in figurc 45B is quitc is 1 :15 only for large rivers may possiblybe influencjd by RIVER CHANNEL PATTERNS 59 the fact that our data show bankfull width rather than and thus indirectly a function of dischargt. Third, width at some lower stage. Our data indicate that the even straight channels cxhibit somc t cdency for the relation is not a constant ratio but a power function flow to follow a sinuous path within thc confincs of their having an exponent slightly larger than 1.O, specifically straight banks. X=6. 5w1.’. THE CONTINUUM OF CHANNELS OF DIFFERENT Comparison of figures 45A and 45B leads us to PATTERNS postulate that in terms of the mechanical principles governing meander formation and the formation of pools The physical characteristics of the three specific and riffles, the wavelength is more directly dependent channel patterns discussed in thc preceding section on width than on discharge. It is argued later in this suggest that all natural channel pattrrns intcrgradc. paper that in general, at a constant slope, channel width Braids and meanders arc strikingly tlitferent but thy follows from discharge as a dependent variable. We actually represent extrcmes in an uninterrupted range suggest, therefore, that wavelength is dependent on of channel pattern. If we assume that the pattern of ti width and thus depends only indirectly on discharge. stream is controlled by thc mutual intewwtion of a That this relation describes both the distance between number of variables, arid the rarigc of thcsc variables riffles in straight channels and the wavelength of in nature is continuous, then we should cxpcct to find n meanders leads us to conclude that the processes which complete range of clianncl patterns. A givcn reach of may lead to meanders are operative in straight channds. river may exhibit both braiding arid mrandering. In fact, Russell (1954) points out that the hleander River SUMMARY: STRAIGHT CHANNELS in Turkey, which gave us the term “menridering,” has The observations discdssed lead us to three tentative both braided and straight reaches. conclusions. First, pools and rimes are a fundamental This conception of transition in pattern or interrela- characteristic of nearly all natural channels and are not tion of channels of diverse pattern is supported by the confined to meanders. Second, river curves all tend to data in figure 46 in which the average channel slope is have a wavelength that is a function of stream width plotted as a function of bankfull discharge (data tabu- EXPLANATION e Braided 227 X x ;z9 S t r a ig h t X 233 X V 232 Meandering 128 -X ‘125 .1: hi;!_e434 vx\ 24 30’ 3: 240x ’42 24 BANKFULL DISCHARGE, IN CUBIC FEET PER SECOND FIGURE 46.-Values ofslope and bankfull discharge lor various natural channels and a llne defining critical values which distinguish braided from meandering channels. 60 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS h lated iri app. F). Meandering, braidrd, and straight dcscribe ti sr.t of conditions which arc to be expected channels are designated by diffcrrnt symbols. ‘I’hc in many natural channels. reaches which have been called meanclrrs are those in Two ideas that will be explored more fully are inherent which the sinuosity, the ratio of thalweg length to in figure 46. First, at a given discharge various slopes valley length, is equal to or greater than 1.5. This are associated with varying channel shapes and pat- value is an arbitrary one but in our experience where the terns. Second, in considering an individual bifurcating sinuosity is 1.5 or greater, one would readily agree that channel, we are concerned with a division of discharge the stream is a true meander. Many channels which comparable to the comparison of n downstream point appear to the eye to be very tortuous actually have with an upstream point in a river channel system. rather low sinuosity ratings. The reader may be Cottonwood Creek near Daniel, Wyo., is a striking helped in visualizing these values by inspecting the map illustration of a11 abrupt change from one stream pattern of the Pop0 Agie River near Hudson, Wyo. (fig. 43). to another (fig. 47). Above the gaging station, Cotton- Tliis meander on the Pop0 Agie, the most symmetrical wood Creek is a very sinuous meander. Immediately that we have seen in the field, has a sinuosity of 1.73. bclow the gagc it becomes a braid. The character of The term “braid” is applied here to those reaches in thca channel where braiding begins is shown by thc which there are relatively stable alluvial islands, and photograph in figure 48. As the profile in figure 47 hence two or more separate channels. shows, tlie meander reach has a slope of 0.0011, while The data in figure 46 indicate that in the rivers the braided section occurs on a slope of 0.004. ‘I’hc studied the braided channels are separated from the difference in slope is accompanied by a change in thc mcanders by a line described by the equation median grain size from 0.049 foot in the meander to 0.060 foot in the braidctl reach. Data for this reach arc plotted in figure 46. At n discharge of 800 cfs points 12a and 12b rcpreseiit, For a given tlisc.hargc, mcanders, us one would expect, respectively, the meandering arid the braided parts of dloccur on the smaller slopes. At the sanie slope a the reach of Cottonwood Creek pictured in figure 47 braitlcd cliaiinel will havc a higher discharge than a In changing from a meander to a braid at a constnnt inc~nnderingone. ‘I‘lic figure shows, moreover, that discharge we should expect the two conditions on straight clianiicls, those with sinuosities less thnn 1.5, Cottonwood Creek to bc represented by points OII occur tliroughout the range of slopes. This supports different sides of the line of figure 46, and indced this the view that the scpnration of a true meander from a expectation is fulfilled. straight channel is arbitrary. Study of the sinuosities It is clear that through the short reach of Cottonwood of these channels does not reveal an increasing sinuosity Creek discharge is the same in both mcantlering arid with dvcrcasing slope; that is, greater tortuosity is not braided parts, for no tributaries entw The load tiec~esst~ril,yussocmtccl with decreasing slope. A diagram curried is the same in both meandering arid braided similar to tlie one in figure 43 has been plotted by parts. ‘I‘here is no indication of rapid aggradation or Nuguid.’ His clcsigrintioii of meanders was not based degrnclation, and to the extent that this is true, if the upon a particular sinuosity but was apparently an nicandrring reach is assumed to be in quasi-ccluilihriurn, arbitrary designation based upon the plan or map of then the braided reach is also. The braided pattern the c~hannel. Nuguid indicated that what he ,:ails here is not due to excessive load but appears to be a normal, or straight, ciiannels have a smaller value of channel adjustincnt causecl by the fortuitous occurrencc slope than meanders for any given discharge. The Df a patch of coarser gravel deposited locally in thc present data do not demonstrate such a distinction. valley alluvium, the bulk of which was probably laid In considering figure 46 it is important to keep in lowii in late Pleistocene time. mind thaL these data tiescrihe certain natural channels. A reach of the Green River near Daoicl, Wyo., is In natural charincls spccific variablcs often occur in shown on tlic map in figure 39. Here thr traiisition association. For example, steep slopes are associated from undivided to divided channel irivolvcs ti change of with coarse material. In a system which contains, as dope, and by reason of the individual channels, 11 we have pointed out, a minimum of seven variables, u hngc in discharge. The river at this point has cliagram sucbh as figure 46 which treats only two of these i drainngch urea of 600 square miles and a barikfull cannot be expected to describe either the mechanism of lischnrge of about 2,000 cfs. It flows in a broad adjustment or all theoretically possible conditions. illuvial plain about 2 miles wide. Tlierc are myriad Because it IS drawn from nature, however, it does Joughs mid marshes with a dense growth of sedges and _.__- villows. In the r~achmapped in figure 39 the main I Nuguid, C P 1050, A .Judy of stream meanders Iowa State Univ , runstel’s theqls. ~Iiannrldivicles into two channels about one-quarter RIVER CHANNEL PATTERNS 61 I WnlVO AWtlllEW '1334 NI 'NOllVA313 PlIl'SIOOIlAPUlC A~D HYDRAt;LIC 6TU1H~S OF RIVEIIl! Ii.. t • S milM .fter it I... ,· ... the mount.in fro"t .nd thi' b ..iditljl ;. _iated with dtporoition of Ihe ..,... e r I ..ChOu. of itl dehri. load. j .... t .. in the Hume upe.-; n,,,nt.l d""";M do. llelo'" Ihe div;,,;on tlte lelt channel h..,] & _ell (poinl 171k) plotllOme"'hat .bo.... IILe ltntative Tlic relation of clianriel pattern to slope and discliargc the details of how this control is exercised, pnrtirularly is of particular iritcrwt in conncction with the rcron- with respect to thc. Iiydraulic mcchanisrns, litilvc not bcc~n struction of the alluvial landscape from profiles of fully described. terrace remnants and from alluvial fiIls. Changes of It is thc purpose of this final section of the prescnt climate such as occiirrcd in tlic Plcistocenr might be report to illiistratc, from our field and laboratory accompanied by changes in precipitation md runoff. obswvations, somc parts of the process by which tlic Such variations in streamflow might produce changes river channel is ultimately controlled by geology and in the stream pattern without any accompanying changc climate tlirougli the effect of these factors on discliargc in tlic quantity or caliber of tlie load. An increase of and bad. flow could result in a meander becoming IL braid; a The shapc and pattwn of tlic river cliannel are detcr- decrease in discliargc could nialw a braidtd channel mined by the simultaneous adjustment of discharge, a meandering one. Yet, a change in tlic character of load, width, depth, velocity, slope, and roughness. In tlie load, such as an increase in caliber which the order to study the behavior of any of the variables presence of ti vallcy glacier might provide, could result separately, the remaining ones must be kept constant. in an incrcasc in slope and a change from meandering Obviously, this seldom occurs in nature. Nevcrthclcss, to braiding without any changc in the precipitation or it has been possible to makt. som~observations in discliarge. The presence, then, of material of different natural ehnnels in the field and in the flume under sizes in successivc vallcy fills suggclsts that at diff eren t conditions in which several of the variables do remain periods in its history the river which occupied the constant. These observations of isolated parts of the valley may have had several distinctive patterns. As mechanism of adjustment in river channels are pre- the pattern of major rivers in an area is a significant sented in the following section. Each example is a feature of the landscape, the application of such simplification of the general case involving simultaneous principles to historical geology may prove of somc help adjustment of all of the variables. Segregated into a in reconstructing the past sequence of actions and responses, the process of adjustment is somewhat easier to visualize. SUMMARY: THE CONTINUUM OF CHANNEL PATTERNS DEVELOPMENT .OF RIVER WIDTH The observations descrihrd above demonstrate tlie During a flood the process of bank caving and cutting hnsitional nature of stream patterns. A braided takes place with relative rapidity. One high flow can stream can change into a meandering one in a relatively make more change in channel shape in the direction of short reach. Individual channels of a braided stream increasing width than many succeeding days of lower may meander. A tributary may meander to its junction flows can alter. It is reasonable to suppose, however, with a braided master stream. that the quasi-equilibrium width of the channel is When streams of diff (>rentpat terns arc considered in determined not by those floods which occupy the entire terms of hydraulic variables, braided patterns seem to valley, but rather by discharges wliich attain or just be diffrrentiatrd from meandering ones by certain com- overtop the banks of the channel (Wolman and Leopold, binations of slope, discliarge, and width-to-depth ratio. 1957). If tlie u idth is larger than necessary for quasi- Straight channels, liowcv(x, have less diagnostic com- equilibrium, the unused parts of tlic wide channel are binations of these variables. The regular spacing and taken over by vegetation which not only tends to alternation of shallows and dccps is characteristic, stabilize the places where the roots are present, but tlic however, of all three patterns. vegetation itself induces deposition. Tlic cstablisli- This continuum of channel typt.s emphasizes the ment of vegetation in unused parts of a natural clianncl similarity in physical principles which determine the provides a slow but effective way of reducing a width nature of an individual cliannel. Thc next section which has been made excessive during high flows. The discusses some aspects of these principles. #Itliough deposition of root-bound mud lumps seen on the bars our understanding of them is far from complete, the of braided streams in Wyoming is one way vegetation analysis does indicate the complex nature of the tends to become established. It is well known that, mechanisms con trolling diverse natural cliannels. plant seeds are frequently included in flood debris deposited along high-water marks. As described by THE NATURE OF CHANNEL ADJUSTMENT TO INDE- Dietz (1952), lines of even-age vegetation can often be PENDENT CONTROLS observed marking the zone of deposition of seeds on Many geologists accept tlie idea that geology, cli sloping river banks. mate, and interrela tcd hydrologic factors are thc ulti- We have noted in natiiral cliannels and in the flume mate determinants of river morphology. Nevcrthclcss, that the wandering thalweg of a straight reach provides 64 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS an additional mechanism for decreasing the width of The close relation between channel width and dis- the channel. Deposition of makrial on the insides of charge is also shown by several runs in the flume (table these thalweg bends tends to reduce the channel width. 2). Runs 23b and 30d each had a discharge of 0.033 These areas of deposition may also be associated with cfs. Despite the fact that the bed material in run 30d the loci of vegetation mentioned above. was 6 times as coarse as that in run 23,b, and the slope The width of a river is subject to constant readjust- about 10 times as steep, each run developed the same ment if the banks are not well stabilized by vegetation. width. The magnitude of the readjustment depends on the TABLEZ.-Comparison of channel factors in two Jume-runs at nature of the banks and the amount and type of vegeta- equal discharge tion they support. In the eastern United States river [California Institute of Technology flume, 19541 banks generally tend to be composed of fine-grained material having considerable cohesiveness, and large I Run trees typically grow out from the bank and lean over the stream. Their roots are powerful binding agents, ~ 23b 30d and under these conditions width adjustments are small and slow. Only the large floods are capable of 0. 033 .0036 tearing out the banks. In the semiarid West width .00202 adjustments appear to be greater owing to generally . 67 . 0320 more friable materials making up the banks and to less, 1. 36 dense vegetation. Though examples for which ade- .0117 quate data are available are not numerous, a few may be . 0523 mentioned. The Verde River in Arizona has experienced in the The rapidity with which the width of the channel in last half century several floods of considerable magni- the flume adjusted to the discharge indicates the close tude, The flood of 1891 widened the channel greatly association of the two. When the water was first but in subsequent years vegetation became established turned on, if the initial channel shape molded by the and the width gradually became restricted. The Gila template was not in equilibrium with the discharge, River in Arizona has not experienced a great flood since the adjustment of shape took place very rapidly 1916 and vegetation and deposition have tended to indeed. More than 20 runs were made in which the narrow thc channel in the subsequent years initial channel shape was not wide enough for quasi- After construction of Hoover Dam the channel of equilibrium with the discharge, and in all of these runs the lower Colorado River changed considerably. Data the adjustment of the channel width by bank erosion on changes of width at Yuma, Ariz., were analysed by and the consequent change of mean depth took place, Leopold and Maddock (1953) who showed that the on the average, in less than 5 minutes. The runs new width is much smaller than existed before the lasted not less than 5 hours and often as long as 30 higher flows were eliminated. hours. After the initial adjustment in channel width If these lines of reasoning are correct, it might be within the first 5 minutes, no Subsequent change in supposed that if rivers from a great, diversity of geo- width took place during the rest of the run. In inter- graphic areas were considered, flood discharge would preting this flume observation, it should be noted that correlate more closely with river width than it would the channel within the flume was composed of com- with any of the other channel factors such as depth, pletely uncemented sand without any clay for binding velocity, slope, or grain size, because the latter are the channel banks. An inspection of the cross sections apparently less directly controlled by discharge. Data of figure 37 shows that the sand banks above the water from such diverse rivers as the arroyos in New Mexico, line stood nearly vertical for the duration of a run Brandywine Creek, Pa., the Yellowstone and Bighorn without any tendency for caving or progressive Rivers, and tho upper Green River indicate that such is widening. is the case. There is, of course, considerable variation When a template was used which established a in width of streams having equal discharges of a similar channel wider than that which the water would have frequency. Nevertheless, the variation between streams rut-that is, widcr than necessary for quasi-equilib- at a particular dischargc is small relative to the change rium-thcrc was little or no adjustment of the channel in width with increasing discharge in the downstream di- to a narrower widLh except gradually in conncction rection. Tliedifference in width between streams having with teridencies for general aggradation or degradation. equal dischargr appears to be related to sediment concen- From the cvidencc presented we tentatively concludc tration and to the composition of the bed and banks. that the width is primarily a function of discharge. RIVER CHANNEL PATTERNS 65 The magnitude of the effective discharge to which the size Ds4. The 84 percent figure is one standard devia- width is adjusted is considered in another paper tion larger than the median size, a choice guided by our (Wolman and Leopold, 1957) where we argue that it experience that this size gave the best corrzlation with occurs about once a year. resistance. Figure 49 shows an empirical relation between a CHANNEL ROUQHNESS AND RESISTANCE 1 resistanc3 parameter - (wheref is the Darcy-Weisbach Onz of the ways by which the lithologic character of a $f basin affects river morphology is the size of the particles coefficient) and relative smoothn2ss (the ratio of meau contributed to the debris load To relate this effect to depbh of water, d, to grain siz3 Da4). The data in figure the hydrauli-, mechanisms by which the channel is ad- 49 are for a number of rsaches of Brandywine Creek, justed, it is nxessary to consider the interaction of Pa., (data from Wolman, 1955). The equation for the grain size with other hydraulic factors. straight line drawn through tho points is Engineers are familiar with the concepb (Rouse, 1950) that at high Reynolds numbers the Darcy-Weisbach resistance coefficient, sf= (d)O.BD,, (3) (2) The data from Brandywine Creek include measure- ments of the slope of the water surface which, in con- is a function of relative roughness. Where the rough- junction with the measurements of the bed material ness is controlled by the grain size, relative roughness size, are available for very few locations elsewhere. To may be defined as the ratio of grsin size to the depth of be correct, the slope used in the computation of f flow. should be the slope of the energy grade line. Our data For flow in pipes empirical relations between resist- indicate, however, that for tha purposes of this genera€- ance coefficient and relative roughness have been ob- ized analysis, the differznce between the water surface tained, and in thess relations the “grai? size” term has and energy slopes is not significant. usually been defined on the basis of a uniform sand size. For streams other than Brandywine Creek, our dah The size of roughness elements of pipes of various ma- do not include water surface slope but only the mean terials are often expressed in terms of “equivalent grain slope of the channel bed. The latter is usually a rough size,” that is, uniform grains which gave comparable approximation to water surface slope bub its use consti- resistance. tutes an additional source of variance. It is not astonishing, therefore, that when such data arz added RESISTANCE CONTROLLED BY SIZE OF BED MATERIAL to those for Brandywine Creek as has been done ill figure The beds of natural rivers are often characterized by a 50, the scatter is gre%terthan in figur3 49. Nsverthe- wide range of particle size, particularly where the bed less, the mass of points encompass the points for Brandy- matericll is gravel. Because of both organized and wine Creek alone and these two figures indicate in a random variation of grain size-distribution over the g2neral way how geology, through its effect on grain channel bed, the sampling problem is in itself important. size, may influcnce the river channel properties. Furthermore, even when an adequate sampling pro ccdure is adopted, one must choosz some representative size or some characteristic of the size distribution to typify the bed material. Thus far no completely satisfactory method has been developed for relating grain size in natural rivers to resistance. Our approach to the problem has been an empirical one. The size-distribution of grains making up the beds of several river reaches was measured, using a method described by Wolman (1954). Some of the size-distribution data are included in appendix G, and the values of median grain size determined by the same method are shown in appendix H for a more extcnsivc list of river locations. In our attempt to relate grain size to resistance, the Relative smoothness d 084 grain size parameter cbosen is DS4;that is, 84 percent FIGURE49.-Relation of relative smoothness and a resistance factor for data collected of the material on the cumulative curve is finer than the on Brandywino Creek, Pa. 66 PHYSIOGRAPHIC AND HYDRAULIC STUDIES C)F RIVERS 10 Im 5 X 0 Opq I X X. - X t X X .-M in X 8 1 0 0) C +-m .-in u) 0.5 8- E X X Wyoming streams V New Mexico arroyos o Brandywine Creek, Pa. 0’ Maryland and Virginia streams X - ‘x I 0.1 0.1 0.5 5 10 50 100 Onc reason the empirical rclation prcscntcd abovo is as largc 8s it was in run 23b. Figurc 57 shows the bctl defined only poorly is that the computed resistance is in riin 30d. When cadi was espcriencing tlic same probably not solely a function of thc size of thc brd discharge, howcver, the resistance factor in ru11 23b material. Although the data largely reprcscnt streams was approximately cqual to that in run 3Od. Thus, with coarse beds in which tlic ratio of width to dcptli is tlic ndjustmcnts in velocity, depth, and slopc which usually greater than 20 to 1, the resistance in somc of accompanied the changes in the configuration of thcb thcm may be affected by vegetation, channel alinemcnt, bcd of fine sand resultccl in a rwistancc in the bcd of or otlicr factors riot attributable to grain rouglincss. fiiic material cquivaleiit to thaL in the much coarser In the event that grain sizc is not tlic dominant factor channel. Where bed configurntion is important, the controlling the rcsistancc, thc relation sfiowri in figiircs chaiinel roughness can no longer be considcred cven 49 and 50 would not apply. partially inclepcndcnt. Roughness is controlled by changes which take plaw in velocit.y, depth, and sloptl RESISTANCE RELATED TO BED CONB’IGURATION in rcsporise to changes in discharge and load. Dctailctl In many natural channels with beds of fine material st,udics of sediment transport by Rgopks (1955) support tho roughness of the channel is rclated to the dunes this conclusion. and ripples which form on thc bcd rather than to the size of the djscretc particles themselves. This relation SEDIMENT TRANSPORT, SHEAR, AND ItEHlHTANC’K is illustratcd by an csamplc from tlic flume. ‘l’lir cbomplcsity of the problem indimtcd hy thr brkf The photoginph (fig. 51) of the bed of thc c~liann~lobservations on bcd cw~figurationarid resistancc lcads in run 23b shows the size and spacing of dunes. Thcse directly to a consideration of somc illustrations of t lie dunes were characteristic of all runs in which tlic bcd intcrrclation of rcsistancc, shear, ni\d sediment trans- was composed of fine sand, D,,equal to .00059 foot. I,ort. As tnblc 3 shows, in run 30d t,hc grain sizc was 6 timcs 111 sonic of tlic ruiis rnude in tlic Numc~,a dccp HI,' EH CJ'A"".:L PATT~H"S 67 T .. e. ~. - Co .. ,..ri.. " '" ,,~.. ; .. ,,' ,.\a•• <1 "",... ..d o.fl" 1""_ oj ,.d,,.,., I'• •, 1,·. , ~::'.. .. . tT~~ ,, ~ '""'__ _ ---,--""''-r--:::- ~ ~ - ~~...... ". ,. ".... , . ."" ..... ""' ...... _.... -,...... ,-_ ...... ~ ...... "' ...... """ .. " ,_'-'.. ,_- ...... - . •N•._• - - -, ,...... ,...... ~ ,.-"... . ':,... . H._"_... ..- ~ - •,.• ...... ' ...... ,... ,"". ,. ~ " .. • • ,-,...... - . , . •• - -...... _-_.~-~~ .- ' by a (Iecr ~.... , in hy,l .... uli ~ r.d;u.. The "Ion. (rom_ I'ul~d ... .,.110) a~ 8lat.ion 26 i" which no "",lim ~nt wu "",..;ng. !'''''',wcr, "ory nearly equabl lhe 81o".r a~ s!.aLio" 13 Ihrough .... hid, "",limenL ...... ,,"o,·illl:. Th~ movement of sedimcnt. how~'·"r. Rt >tation 1:\ ...... M80Ciated will, a much lower ' C$ i ", a.n ~ . At tho oU lsd 01 run 17 no oedimcnt ...... bei"g removoo from th e bed of the cI,a,.nd until ..nd inlro d,,~.,.) at lhr. hea,l of the flume moved down the channel. As tho run progr-oo the oedi",,,nt loatl i"tro<.j uced i"to Ihe flow Ino,'",) progr_ive!y uo .... ".tr"a,n .... thin gl, •.,. of ",aterial along the 1H.~1. Alter I'~e 01 th" sheel., mO"CmN,t on the bed wu ronti""ou•. Verlical "elocity profil .. ("ken at OIalio ", 36.8 belo,"" and after 1'_1:" of Lhe ah.,.,t nrC .hown in figuro 52. TIo" grain . i.e re"'ained c<"'SIRnt ."d Ih e ruo of d""'go of ,'elocil }" wilh d"pth wu greater when sediment was not moving on tI, e be,1. A. Ihe rate of chang , ...",,',...... _.... _'-,---" . ,.... ~,.-__...... , a",1 I~Jnpl&I~ .,U-. T .... ",i\;..1 clwlntl ..... molded "'jtb • u·"I"'KOidal....,'ior> lining" lOP width or 9 jt>Cb .. Mild" d~plh of ~I; I,,~h... K~p"ri~"tf! 1.. 01 1Iho.'" that " diN'hllrg.. of o,oaa d. "''lul.l "'..,u,"" no r ..;Jj".tm.1ll or th" ... idth, Th .. i"itial rhannol ill Ill)O"" in filfUrc! J;3. TIlt' nu,,", <10".. ,,'11''''1 U O.GLOJ. In th~ fin! run in lilt otfteo no load ..... intrOd...... J 11,orf .... IIl!T"dU1I1 .';"no"';,,!!' of lilt bNJ dunnl whi.b Illtn' .... aclin mo.-rllle"t o,'rr lilt tent .. l as i".h... Clf Ih. un,t hed "',dtl! or 7 ind,,,". T il .....nl ..J hoi".! of Nnd tnO'·~m."L III 1111 ion :!O afltr I hour ."d :!O millUl"," """ I ... -.. in liplnt M ..\f'tr IS boW'll of no ... wllh no le."l bem,: mtrodLll:f 1''' .. ,.- .r.) li"""')-" .". ~ 21. " ""' '"lT~ .", Another """<'0 of runs in the nume w"" d""igued to t""tlhe ....,Ialion bet""~n _Iimen~ load .. nd .Iope at a con.t"n~ dischorg<'. T he or""" section remained p .... c lically OOU6tal)t during Ihe ""i.... The following data (table 5) were obtained under oonstant initial conditions except rat" of introduction of load. All material co a ~ r thon 3.32 mm had been screened lrom the introduced load, ."d "" a ..... ul~ no island or bar appeB,ed. Whell the load w ... introduced a~ various rat.. at the .... me discharge (runs 32 to 35) the . Iope beeamc adjusted to nearly tho ...me valuo whelher th reach w .... stahle or aggrading. Aggradation w...... , ...... - ... " ...... characterized by a gnldual and uniform rise of Ihe bed ...... _ ----" -- all along the lIume. 70 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS TABLE5.--E$ecl of changing load on stream slope, all other condi- OBSERVATIONS OF ADJUSTMENTS IN NATURAL tions being kept constant CHANNELB [California Institute of Technology flume, 19541 Measurements in the flume are complemented by Load in- Discharqe troduced examples drawn from larger rivers illustrating the same (cubic feet (grams per principles of adjustment. Table 6 indicates the nature Rim per second) minute) Slope Condition of channel of the adjustments which accompgny changes in sedi- 32 0. 033 56 0. 0105 Nearly stable. 33 .033 115 .0105 Slow aggradation ment load at constant discharge. Unfortunately, 34 . 033 175 . 0109 Aggradation. there are few rivers for which data on the flow param- 35 . 033 212 . 0110 Rapid aggradation. eters, including slope, are available and the data for Despite a .fourfold increase in load, slope remained these few suffer because suspended load but not bed essentially constant. Although this appears to conflict load was measured. with Gilbert’s conclusion (1914), analysis of Gilbert’s In table 6 the flow characteristics of the Elkhorn data shows that the increase in slope which took place River, which are compared at a discharge of 6,000 cfs, with increasing load in his experiments was also ac- represent the rising and falling sides of a hydrograph. companied by an inc,rease in roughness. In our experi- The rising stago was typified by a lesser depth and lesser ment t>liercwas but a relatively small change in either slope, and a greater velocity and greater load than the slope or resistance. falling stage. The elevation of the bed remained the Though slope was little affected by changes of total srtme. The larger load of the rising stage was associated load in the flume experiments, there was some indication with lessar roughness. This lower resistance led to a that at constant grain size, relatively steep slope is greater velority and a lesser depbh despite the slightly associated with small discharge and flat slope with large lesser slop-,. The product of depth times slope, which is discharge. The data do not permit a definite statement directly proportional to the shear, was less in the rising on this relation. Considering the downstream rate of stage, and thus tlie larger load was associated with the change of velocity, depth, and width with discharge in lesser shear. It is presumed that the increase in veloc- an average river (Leopold and Maddock, 1953, p. 26) ity associated with the lesser roughness was of greater under tho assumption of constant roughness (f),slope importance than the relatively small diff erencc in shear must dec.rease with discharge as in promoting equilibrium with the large load. Also in table 6, the data on tlie Rio Grande at Berna- (x Q-na (4) lillo show another type of adjustment. The rising stage was characterized by a lesser depth, greater The part which changing cross-sectional area down- velocity, and greater load than the falling stage. In stream plays in this relation is unknown. Tenta- the falling stage, slope was somewhat less, and thus the tively, it is believed that at constant grain size, river smaller load was associated with the lesser shear. sections having diff crent effective discharges should Here, then, the greater shear was associated with the differ in slope, larger discharges being associated with larger load, but, as in the Elkhorn River, the total flatter slopes. resistance was less when the load was large. TABLE6.-Examples from river data of adjustments of depth, velocity, and slope to changes in suspended load at constant discharge and width Elkhorn River near Water- Section A-2, Rio Grande at loo, Nebr., March 26 to Bernalillo, N. Mex., April Stage April 9, 1952 to June, 1952 Rising Falling Rising Falling 6, 000 6,000 4,700 4,700 255 263 275 275 4. 90 4. 56 5. 5 5. 0 4. 8 5. 0 3. 1 3. 4 . 00038 . 00046 .00094 . 00084 06, 000 74,000 46,000 21,000 7. 8 7. 8 3. 2 3. 2 . 114 . 143 . 182 . 178 .o1n .028 . 025 .029 .04 13 . 13 __. 3 2 . 32 RIVER CHANNEL PATTERNS 71 SUMMARY AND INTERPRETATION Moreover, large volumes of runoff are associated with From these diverse observations on the nature of relatively large depths of flow both in rills and in over- channel adjustments to independent controls we draw land flow. These depths are accompanied by relstivsly several tentative conclusions: 1. Channel width is high flow-velocity and increased transport of debris to largely determined by discharge. The effective dis- the chsnnel system. For such reasons large flows are charge we believe to be that corresponding approxi- usually accompanied by large loads. mately to bankfull stage. 2. Where resistance is con- In a given period of time there are far fewer large trolled by the roughness provided by discrete particles AOUW than small or moderate ones. An intermediate on the bod of a channel, the resistance factor may be range of discharge includes flows that occur often correlated with the size of the particles. 3. Where the enough in time and possess sufficient vigor to constitute configuration of the bed enters into the determination the effective discharge (Wolman, 1956). During these of roughness, the resistance is a function of the discharge flows the river can move the material on its bed and in and load and represents a simultaneous adjustment of its banks and thus is capable of modifying its shape and velocity, depth, and slope. 4. The load transported at a pattern. given discharge is riot solely a function of shear and It is within the framework of these characteristics of grain size. At a constant shear decreased resistance runoff of water and sediment that channel systems appears to be associated with greater transport. The develop. The water and load, including their time and resistance is not necessarily governed by caliber of the space distribution as well as quantity, that are delivered load but may be determined principally by bed con- to the channel system are functions of the climate and figuration. 5. In the flume-river the width of th? band geology. The water and load carve the channels that of moving sediment was often less tlian the width of the transmit them downstream. To the water and debris, channel, and width of the band was related to the therefore, the channels ultimately owe their shape and quantity of load being transported. If such bands pattern, but processes within the channel itself effect exist in natural channels, errors might result from esti- specific modifications. mates of total load based on computations of load per Channel width is primarily, determined by discharge. foot of width multiplied by the total width. 6. Where Widening is rapid relative to other changes and the no change in roughness occurs at constant discharge, a channel generally tends to become adjusted at the large increase in load is not accompanied by an ap width provided by large flows near the bankfull stage. preciable increase in slope. Both aggradation and The roughness of any reach of a channel is governed, degradation may occur, therefore, without change in initially at least, by the geologic character of the bed slope. 9 material supplied by the drainage basin. Although We shall now attempt to construct a general though abrasion and sorting may modify the material on the oversimplified picture of the way in which the shape and bed, the rock character partly determines the extent of pattern of a natural channel may be determined by the such modification. The roughness may be primarily river itself within the framework provided by the grain roughness. Alternatively, owing to the size climate, rocks, and physiography of the region in which distribution of the particles and their movement, the it lies. rugosity may be due to the configuration of the dunes. In a given region the magnitude and character of the ripples, or waves in which the particles on the bed runoff are determined by climate and lithologic factors arrange themselves. quite independent of the channel system. The amount The roughness of the boundary affects the stress and distribution of precipitation, and characteristics structure and the velocity distribution in the flowing which affect the runoff, are functions of the climate. water. In addition, turbulent eddies near the bed The topographic and lithologic character of the drainage produced by the roughness elements lift particles of basin helps to determine, in conjunction with vcgeta- debris off the bed. These alternately move forward in tion, not only the characteristics of the runoff, but of the current and ,settle back to the bed under the equal importance, it greatly helps to determine the load influence of gravity. Not only the resistance then, but of debris delivered to the channel systcm from the also the movement of debris through turbulence and interstream areas and from the stream margins. Both shear is related to roughness. quantity and nature of the load are greatly influenced At a given discharge, with width fixed thereby, and often are primarily governed by geologic factors. velocity, depth, and slope become mutually adjust'ed. Exceptional runoff is accompanied by conditions To visualize the nature of this adjustment, one may which increase the movement of soil and rock debris. assume temporarily a value of slope. With slope given; Of particular importance are datively large amouncs velocity and depth must mutually adjust to meet two of rainfall, often at high intensity, and saturated soils. requirements: The first is that the product of width, 72 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS depth, and velocity is equal to tlie valiie of discharge, or the bed are inextricably related. It is, of course, possible that the increase in capacity resulting from the Q=wda (1) increase in velocity is still inadequate to transport the Tlie second is the relation of resistance to depth, slope, total load, in which event both the bed and the water and velocity, which is expressed by the equation for tlie surface will rise. Darcy-Weisbach coefficient, If a stream can move only some of the sizes in tlie load provided to tlie reach, the process of adjustment is similar to the one described above save for the fact that by winnowing from the bed certain sized fractions only, Tlie resistance f can be assumed to be fixed by the the mean size of the bed material is increased. This materials in the bank and on the bed. increased size will be associated with an increased slope These two equations must be satisfied. They contain over the entire reach, thereby increasing the total six factors, but where four of the factors are fixed or capacity for transport of all movable sizes. temporarily assumed, these two equations fix the remaining two variables. APPLICATION OF OBSERVATIONS ON CHANNEL At a given discharge width is considered fixed. ADJUSTMENT TO THE PROBLEM OF CHANNEL Resistance is determined by the nature of the material PATTERN in bed and banks, channel configuration, and bed condition. Slope has been temporarily assumed. As explained, eight and possibly more variables enter Hence, velocity and depth become deternmined by thest. in a consideration of natural stream channels : discharge, two equations. amount of sediment load, caliber of load, width, depth, If this combination of depth, velocity, and slope con- velocity, slope, and roughness. Each of these factors a. stitute a channel that will transmit the given dischargc varies as a continuous function; that is, within the and load without erosion or deposition, the slope is not limits of observed values, any intermediate value is altered. If the hydraulic factors of the channel are not possible. The factor having the largest range of values in equilibrium with the imposed load, erosion or deposi- is discharge, for in natural channels it can vary from 0 tion will occur. By such action the slope of relatively to any amount less than 10,000,000 cfs. Load, ex- long reaches of the channel is altered and as the altera- pressed as concentration by weight, varies from nearly 0 tion occurs, the velocity and depth also are changed. to about 500,000 ppm. (:aliber of load, expressed as This explanation provides a perspective of how tlic median grain size, may vary from a value near 0 to 10- several variables interact to make the channels which foot boulders. Width of natural channels varies be- are observed in nature. These variables are inter- tween a few tenths of a foot to about 20,000 feet, mean dependent, but their relative order of importance is depth from 0 to an amount less than 80 feet, mean believed at this time to be generally as outlined above. velocity from near 0 to less than 25 feet prr second, If correct reasoning about the relations of geologic and slope from near 0 to 1.O, and resistance, expressed a? the other factors to fluvial processes is to be achieved, it is dimensionless Darcy-Weisbacli number, from about necessary to determine the relative independence of 0.001 to about 0.30. these variables. Combinations observed in nature are far more In further explanation we reason that if, for example, restricted than the permutations of the values of the a river is able to mova the size of material in the load but eight variables. To our knowledge, for example, rivers is unable to transport the total quantity of load brought capable of discharging more than 1,000,000 cfs do not into the reach, deposition may take place along the have slopes in excess of 0.0009 and usually less than reach with little or no change in slope. During a flood 0.0002. in an alluvial river if deposition occurs 00 the bed, this Channel patterns, braided, moandering, and straight, deposition at a constant width is customarily accom- each occurs in nature throughout the whole range of paiiied by a decrease in depth and consequent increase possible discharges. Some of the largest rivers in the in velocity through reduction in cross-sectional area. world are braided; for example, the lower Ganges and The increase in velocity at the expense of depth implies Amazon. More are meandering, of which the lower that deposition on th3 bed does not cause an equal rise hfississippi is the best known example. Meanders an in elevation of the water surface and of tlie bed. cornlnon in very small creeks, and braids are common Our studies indicate that an increase in load at a in many small ephemeral streams. Both meanders and constant discharge is usually accompanied by a decrease braids have been observed in the laboratory at dis- in bed roughness which serves to increase the velocity. charges less than 0.1 cfs. The straight pattern occurs The adjustment in depth then, and the smoothing of at all discharges. RIVER CHANNEL PATTERNS 73 Our observations iiitlicatc that brsicls terld to occur Eiiisteiii, H. A,, 1950, The bed-load friiictiou for scdirnent in c~liannclshaving certain combinations of values of the transportat,iori iri open chaniiel flows: U. S. Ilept. Agr. Tech. Bull. 1026, 71 p. flow factors, and tliat mpanders occur in diffcrcrit Fraiiziiis, Otto, I!G6, Waterway engineering: Canibridge, Mass. combinations. ’l’lie straight pattern can occur in Inst. Tcclinology Press, 527 p. either. Specifically, at a given discharga, braids seldom Friedkill, J. F., 1945, A laboratory study of thc inearidering of occi~rin clianiic~ls linvirig slopesa less i liaii t~ certain alluvial rivers: IT. S. Waterways I‘lxpt. Sta., Vicksl)lirg, value, wIiil(1 meantlers stxldom occur at slopes grcxatcr Miss., 40 p. Gilbert, 6. K., 1914, Tlic t,ramport,atiorl of debris runliilig same by than that valur. water: IJ. S. Gcol. Survey Prof. Paper 86. ’I’liesc considciatioris t ogetlier with thc tictails dis- Iiiglis, C. C., 1940, Cerihal Board Irrigat,ioii Aliliual Itept. cussctl carlier in this study lead to oiic of tlic principal 1939-40, I’uhl. 110. 24. points of tlic prtserit discussion : Tlic~rrIS a continuum 1949, The behavior and coiitrol of rivers a~itlcallals: of natural stream channels having diffrrcnt cliaracteris- Central Waterpower Irrigat,iori arid Navigat io11 I APPENDIXA -Analyses OJ stzes of sand used in flume experiments and fed into Jlume-river, 1954 [California Institute of Technology flume] - __ ~- - I fercrnt finer than given sile (millimetem) - Mcdiari bize (inm) I I 078 I 156 ,312 - ___- Medium sand: I Run I. February 12...... 0.90 ...... 7 IS 36 61 80 Rull10 Februxry2F ...... a2 ...... 3 15 37 64 83 Run 12: March 5...... 72 ...... 1 17 44 6iJ 8fi Riiri17,MurchIl ...... 65 ...... 7 17 48 73 89 Ruri18,March15...... 1.00 ...... 2 12 32 56 78 Run20,AtarchlE...... 73 ...... 3 17 44 68 85 Fine mud: Run 22, March 24...... 42 93 98.G ...... Medium sand screened of all particles >3.32 mm: Run34,AprilIB...... I .R1.I7! I...... 6 20 49 APPENDIXB.-Data on size characteristics of sand on channel bed and on bars in flume-river, 1954 [California Institute of Technology flume] 1 1 Percent flner than given size (millimeters)- I j Size in niillinieters Median ,156 ,312 .R2S 1.2s __ __ Bar or island in braided reach: Station 6. February 12...... 2.10 ...... 1.2 7 20 35 58 ...... Station 10, February 12...... 1.45 ...... 3 14 28 45 65 ...... Channel hed, unbraided: Station 16, February 12..~:...... 1.30 ...... S 19 35 49 G9 ...... RUN 12, MARCH 5 Braided reach: ...... 3.nn 4.20 1. 7s I. 55 ...... 1.75 3.60 2 74 ...... 48 1.30 2.21 ...... 75 2.2s .33 2. ti0 ...... 1.80 3.75 57 2. 56 ...... 1 1.251 3.20 3x ~ 2. 90 75 APPEN~IXD.-Comparison of hydraulic characteristics of undivided and divided reaches of braided streams i Green RivgFDaniel, New Fork River near Pinedale, Wyo. 1 Flume at California Inqtitute of Technology, 1954 -- .~______~- I Reach 1 (1953) I Reach 2 (1954) Feh. 15 i Feb. 16 Feb. 18 Mar. 5 Hydraulic factor 1 Braided reach - ______- Undivid. ed reach Braided reach Braided reach Sta. 10 Sta. 14 j Sta. 14 1 Sta. 22 Sta. 14 I Sta. IO Sta. 12 1 Sta. 38 .___ -I ~ Undivid. Undivid- i Right 1 ed reach ed reach Left Right Left Right Braided Jndivid- Braided Undivid Braided 1 Undivid Braided 1 Undivid- 1 reach !d reach reach ed reach reach i ed reach reach , ed reach -~___ ~~ Area ...... square feet .. 152 70 169 25 82 105 52 0.0619 0,0657 0,0684 0.0631 0.0748 0.0699 Discharge...... cubic feet per second.. 305 120 425 35 290 325 ,085 ,085 ,085 ,085 ,085 .085 ,093 ,093 Width...... -feet.. 65 .44 70 35 64 54 1.38 1.32 1.60 1. 19 1.90 1.28 2. 15 1.27 Mean depth ...... feet.. 2.4 .7 1.3 1.94 ,045 ,050 ,050 ,053 ,029 .055 .035 ,055 2.3 1.6 1.33 Velocity ...... feet per second.. 2.0 1. 7 2. 5 1.46 3.5 3.1 i.:aa2g4. ~ .:oozsl- - - .:ooii4- 1.37 1. 29 1.24 1.34 1.53 1.20 1. 24 Slope...... ,0029 ,00286 ,00125 .0104 ,0079 ,0133 .0095 ,0157 .00*1 ,0165 ,0095 ,0029 ,0005 ,00286 .OM7 Resistance factor ...... 04 .24 ...... ,065 ...... ,050 ,083 , ,064 ,044 .070 ,0865 .43 .41 ,' Shear velocity...... feet per second.. .46 .41 .49 .25 ...... ?!:.." ,102 ,126 ~ .119 ,129 ,123 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS APPENDIXE.-Data on wavelength of meanders, bankfull discharge, arid bankfull width [e estimated, pattern: M meander, S pool-and-riffle spacing in straight channcls] Estimated Serial hankfull Wavelength Bankfull No. Location discharee 1 (feet) width (feet) Pattern Source of data (cubic fert per second) ~~ _____ 21 Duck Creek near Cora Wyo...... 110 8 nt Authors 23 Buffalo For& near Jae&on Wyo. (Flybox reach)--...... I, 200 I, : RIVERS IN ORISSA, INDIA I1 Mahanadi, helow Jobra--...... 610. om 21.600 ...... Inglis, (1940, p. 111) I2 Berupa. below weir...... in,no0 7. ,500 ...... Do. I3 Mahanadi, below Chitertola.- ...... 237, oon lfi, 200 ...... Do. ' I4 338. 000 16,800 ...... Do. I5 Pyka ...... 112,000 8,000 ...... Do. I6 Nuna ...... 155 0 0 10,500 ...... Do. I7 Chitertola, below Nuna...... 111: 080 8,400 ...... DO. I8 Katiuri. helow Surua head-...... 159,000 10,800 ...... Do. I9 14,400 ...... DO. I 10 Bhargovi ...... 7,200 ...... Do. I11 Daya-...... 47,500 7. 500 ...... Do. I12 Bhargovi. below Achhutpur ...... 29,000 5,700 ...... Do. I 13 Dnya. below Belmora escape- ...... 34, ooo 4, KJo ...... Do. I 14 Brahmini..- ...... 650, OOo 21,600 ...... Do. I 15 Kharsua ...... 162, OOO 8,000 Do. I 16 Bnitarani ...... 260,000 10,800 DO. I For method of estimating bankfull discharge see footnote to corresponding serial number in appendix F. 2 At gage height, M It. w RIVER CHANNEL PATTERNS 79 APITXDIX F.-Data on estimated bankfull discharge at various stream sections [Pattern: €3 hraidcd. M meander. S straight] ~- . Estimated Serial Drainage area bankfull No . Stream and location (squarc miles) Pattern Slope discharge per(cubic second) feet . 6 Little Pom.. Aeie R . niw Lander.... . Wvo ...... ~~ ...... -.I 108 S 0.0049 7 New Fork R., Jenkins Ranch nehr Cka. Wyo ...... 45 B .0047 8 Green R., at Warren Bridge neiir Daniel, Wyo ...... 46M S .0034 9 Reaver Creek, near Ihniel. Wyo ...... 141 B .0066 in New Fork R .. below New Fork Lake ncar Cora . Wyo...... 36 S .0051 llh Horsecrock. ncar Daniel. Wyo ...... 124 B .0073 im Cottonwood Creek.near Daniel ... Wvo ...... 204 M .no1 1 12b ... do.-.----- ...... ~ ~ ~~~~~~ 204 B .0041 14a OroenR ..atI)anirl,Wy o.(undivided)...... I 660 S .on05 14h - (rixht cliannel).-.--~...... M .nom 14c - (lrftchanncl) ...... R .nom 18h New Fork R., at American Gothic Iteacli nwar Pincdale, Wyo ...... 372 B .0029 21 Dock Creek, ncar Cora . Wyo ...... 5 M .wnig n Snake R . below mouth of Hohack R.,.ncar Jackson, Wyo ...... 3, 440 B .no21 23 Buffalo F&k Flyhox rearh nwtr Jackson, Wyo ...... 345 M . wn45 24 Wind R .. Idmb Cowhoy reach above Dubofs, Wyo ...... 55 M .no37 25 Du Noir Creek, above Duhois, Wyo ...... 93 M . onnm n Pop0 Agio R . Joyful reach near Hudson, Wyo ...... 700 M .on184 28 Litt1ePipcC;eekncar Avondale, Md ...... 8 M . 00473 30 Watts Branch, Viers pmtnre, ncar Rockvillr, M(1-...... 4 M . no31 31 Srnrcn Creek at Dawsonville, Md ...... inn S . nom 33 Scnwa Crrek: at Rifaeford near Rockville, Md ...... 15 S . no21 36 Mississippi R., at Tamm Bend nrar Rlythcville, Ark ...... M . nnooag 42 Raldwin Creek ncar Lander, Wyo...... 21 M . 00093 43 Brandywine Creek, at Cornog. pa^ ...... 26 S .0038 48 -at Emhrecville, Pa ...... 117 S . 00068 65 Christians Creek, at Oranarbridgenear Staunton, Vn ...... 24 M . 0015 68 MiddleR . atBethlehemChurchnear Staunton, Va ...... 18 M . no21 71 South R., black Bull reach south of Mt. Vernon Church near Lipscomb, Va.~...... 69 M .000x4 89 YellowstoneR.,at Rillings. Mont-----.-.- ...... 1i.m R? .oonB Bo WindR. nearRurris Wyo ...... I, 220 S . on4 125 Middle Piney Creek'helow South Forknear Big Piney, Wyo.--.- ...... 34 M . 0091 128 Little Sandy Creek, near Elkhorn, Wyo ...... 21 S . nin 151 KansasR.,at Lemmpton.Kans--~-~-...... 58, 420 M .000370 152 -at Ogden, Kans ...... 45, 240 M .000379 151 -atWamngo,Kans ...... 55, 240 M .000316 a7 Fall Creek near Pinedale, Wyo...... 37 S .036 229 West Pork' Rock Creek helow Basin Creek, near Red Lodge, MonL...... 60 S . 035 230 Rock Crrek, near Red Lodge, Mont ...... in0 S . 021 231 ClarksFork,nearEdgar,Mont...... 2, 115 S .nom 232 ClearCrwk nearBuffalo Wyo...... 120 S .024 233 North Fork'Clcar Crcek, hear Rangor station near Ruffalo, Wyo...... 29 S .028 234 RedFork,nearBarnum, Wyo ...... 142 S .0038 235 RockCreek atRoherts, Mont ...... 4 270 S .0086 24o Pole Creek,').$ mile below Little Half Moon Lakenear Pincdale, Wyo~-~-...... 87 S .0018 256 BullLakc Creek,ncarLenore, Wyo ...... 222 S .on81 2bl Smke R.,ncar Wilson, Wyo ...... 2, nnn B .no43 266 Big Sandy Creek, ncdr Leckir ranch, Wyo ...... 95 S .00425 267 Hams Fork, near Frontier, Wyo ...... 298 M .0013 268 NorthForkPowderR .. nearKaycer.Wyo ...... 980 S .no38 269a Bagmati R., above Dhang, India ...... 13 .00057 269b -below Dhang, Indis ...... M .oonig moa Kosi R., above Dhamarghat,. India ...... B,no0 B . 00095 270b -above Dhamargbat, India ...... B . 00038 noc -belowDhamarghnt,Indi:~ ...... M . no038 271 QangesR.,nearPatna India.~~ ...... B . 000066 286 Yukon R., ncar Holy Crrss, Alask:%...... M . noon95 287 ChenaR..nearFairbsnk s.Alaskn...... M .eons I Estimated from generalized regional relations of discharge of 1.1Gycer recurrence 3 Interpolated in regional curve relating known bankfull discharge to drainage area . Interval plotted against drainage arra . 4 Estimated . 1 From rating curve; value of hankfull stage estimated in field. 80 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS APPENDIXG.-Distribution of bed-particle size in various stream cross section8 .. I Perccnt Aner than (millimeters’ percent percent Serial Stream and location - - __ __ - -. - ._. ier than ier than No. feet)- feet)- 1-7; 1 2 4 8 18 32 64 (2s !58 - - - - - ._ . _- 6 Little Popo Agie R. ncar Lander Wyo ...... ----..... -.-. 5 9 13 22 46 83 96 100 ...... - - - -.- 0. I1 n. 24 8 Ireen R., at War& bridge ne& Daniel, wyo...... 5 6 8 9 9 9 10 16 48 84 100 -... .. - -.-. - .46 . R4 9 Beaver Crcek. near Daniel, Wyo .._..______.3 3 5 F 6 13 24 49 82 96 100 ...... - -... .IO .21 1la Eorse Creek near Daniel, Wyo ______..._..._.___..__.___. 2 6 7 22 53 88 100 ___ ...... -..- - - .09 .m 1% :ottonwood’ Creek, near Daniel, Wyo. (meander) -.__ .. ______._. __ .-. __ __ . 10 18 21 29 34 52 71 92 99 100 .. . -...... -. . . . .05 . I6 12b Danicl, Wyo. (braid)_._.____...... ___. .._._.__10 10 11 17 27 42 77 96 100 ...... -. -...... OB .12 14h 3reen R. at Daniel Wyo __._.....___...... --...... 2 2 2 2 12 58 96 100 .18 .Go 18s New Foik R.. at American Gothic reach near Pinedale, Wyo __.....____.....____-...... -. 4 12 15 16 23 31 88 100 --. .I2 .20 23 Buffalo Fork, Flyhox reach ncar Ranger station Jackson Wyo .____..______...... ____._._ ._._ --.. .___ 2 25 83 100 ... .14 .21 24 Wind R.: Dumb bowboy reach near Sheri- dan Ranger station above Dubols, Wyo...... 2 4 4 5 20 41 73 96 100 .I3 .27 25 Du Noir Creek, above Dubois, Wyo ._....._....-... 10 23 37 82 100 .___..- .-. ,035 .056 26 Vorth Pop0 Agic R. near Lander, Wyo ...-__.___.. 3 5 5 8 8 12 17 42 90 .49 .79 30 Watts Branch, Vicrs’pasture near Rockville. Md ..---..-....---.-..~-----..------.-....3 6 9 14 31 46 72 93 99 ,082 .31 31 Seneca Creek. at Dawsonville, Md ...... 2 3 29 69 97 ion --. ,075 .15 33 At Riffleford near Rockville, Md -.-.-.. 6 19 31 48 70 92 1M) --. ... ,026 ,079 37 Brandvwine Creek, at Lenape, Pa ._.....__. 11 17 18 26 40 61 89 99 100 ,072 .lR 43 ACCornog, Pal .__.....- _._.. .. . _____._...... -...- 7 9 14 21 32 48 75 97 .22 .48 44 At Seven Springs, Pa ..__._....______._...... -. 4 5 0 9 13 26 49 77 94 .21 .49 45 Near South Downingtown. Pa .______...... -..-. 9 11 11 12 14 24 39 64 86 .34 .R4 48 At Embrecville, Pa ._...._.__...... _._...... -..- .-. . ..__ 5 7 14 40 64 91 1W .-. ,072 .17 49 At Wnwasct. Pa .____...__.__...._._--...... _.__...... _ 4 5 9 17 33 66 92 100 .I6 .33 65 Christians Creek, at Orange Bridge near Staunton Va ___.....__...._.__._...... ---6.5 7.‘ 14 21 21 29 41 58 74 91 100 ,075 .29 GG At Rt. b54 near Staunton Va ....____...~ ...... -- .--. 4 11 23 37 61 82 97 100 .085 .21 67 Barterhrook Creek, at Rt. 254 near Staun- ton Va _...______.______..-..----...... 5 II 24 36 52 66 78 94 97 1W ___ .0125 .069 68 Middle River, at Bethlehem Church near Staunton Va ___._.___._..____...... _._._ ...... 15 16 m 27 32 3’3 59 81 9F 100 .07R .24 69 Eidson Creek. near Mt. Tabor Church near Staunton, Va. ______...__...... _.--...... ~._.._ 13 16 25 31 37 51 74 02 9E 99 .049 .15 8s Yellowstone R. at Billings, Mont.. - -.____. .-.-.- .. .-.-_. 1 1 1 1 E lfi 39 71 99 .27 .47 w: Wind R. near kurris Wyo.. _._.....______._.__._...-.-._ .___ _.__ .._.-__. m 35 6€ 98 .27 .Go 121 Middle hey Creed. below South Fork near Big Piney Wyo ..____...._..__...... -...... _...... 1 3 12 29 65 100 .31 .58 1B Littlc Sandy Cr&k, near Elkhorn, Wyo .... .-...-....-... 1 4 7 9 11 16 31 71 82 .29 .95 18: Rio Galistco, at Cerrillos (Lamy), N. Mer.- 27 42 46 60 87 79 RE 04 100 ..- .-. ,0038 .042 1% Rio Santa Fe, at Old Albuquerque Rd., west of Ssnta Fe, N. Mcx ...._.___.._..... 1 4 34 81 (js 76 O( 96 I00 ... -.- .0046 ,039 184 Arroyo de 10s Chamisos, near Mt. Carmel Chapel (Sunmount) at. Santa Fe, N. Mer- . .. ..-~. 6 20 52 72 86 94 97 99 IO( ... .006F ,0227 18! Cafiada Aneha (Eulcr), near El Rancho Montoso near Santa Fe N. Mex ..._.___..9 17 30 59 83 93 Of 08 Loo ...... ,0016 .0132 18( Anch Chiquita, near EI’Rancho Montoso south of Santa Fe N. Mex _____.._._._____2 14 48 78 87 R3 9; 98 98 IO( .-. ,0033 .OlOl 18: Tributary t.0 Herdanas Arroyo, near Las Des, northwest of Santa Fe, N. Mex _____.1 11 37 51 70 81 8s 97 95 1M .... ,0057 ,037 18! Rio Oa!isteo, at Domingo, N. Mex ..._.__...11 36 71 91 96 9: 1M -.--.... -__ .-. ,0021 .0046 1.25 2z Fa11 Creek, near Pinedale, Wyo .__._...____.-..-...... -. -... ..-. 4 E 21 6t .69 .42 28 Green R. Fontcnclle Wyo ____....____...._...... -.- .-.. ..__.-.. ____ .-__ 8 I( 8‘ lo( .29 28 West Fo;k Rock Crkk, near Red Lodge, .88 2.4 Mont ______...______._..____..-__ ._____.- .. __._. . --.-. - .____.__.-.- 1 5 2 4f 23 Rock Creek, near Red Lodge, Mont ...... -..-.... -.-. _.__.__. -.. .-__ 1 f 31 6: .67 1.93 2. 15 23 Clear Creek near Buffalo Wpo ______.-...... --..--.-__ .... ._. 1 E 1( 4 61 .58 23. North Fork’Cleer Creek,’near Ranger Sta- tion, Buffalo, Wyo .____...... _.____._..-..... _.._----_. --.. .-. -... ..- IC 2: 4 71 .47 1.0 .21 23 Red Fork, near Barnum, Wyo ._.______...... -~.-..- .---_. ___. -.. ._._-.. 1 42 SI 9 1M .12 23 Rock Creek at Roberts Wyo .___.__._...... _____...... -. -.- ._...... -.- , 3: 81 m .27 .46 241 Polo Creek,’J‘r mile heldw Little Half Moon .51 Lake ncar Pinedole. Wyo ._..___.____...... ---.-...-. ___. 2 I( 2; 5 7r .42 25 Bull Lakc Creek near Lenore Wyo- .._.___...... ___.. .-. ... --...... -. 2 6 .69 1. 92 26 Big Sandy Creed, at Leckie rjnch, Wyo __._._..._._ .__._ 1: 1‘ 1 2: 31 6 81 .25 .72 ~ RIVER CHANNEL PATTERNS 81 APPENDIXH.-Values of hydraulic factors at various stream cross sections [e, Estimated. For deflnition of b, f, and m see page IV; for discussion see Leopnld and Maddock, 19531 __ ~ At mean annual discharge Slope __ awe ___ __ height Drainage Jeloc- vledian rt hank- Serial full No. Stream and location rea (square Discharge ity led size b J m miles) (cubic feet Width Depth (feet Map 1 Field 2 (feet) stage per second) (feet) (feet) per (fcet) sec- ond) _- ______I North Platte R., North Platto, 32, 000 2,300 540 1. 7 2. 4 0.00135 0.0014 n. 0006 n. 35 n. 48 n. 18 ...... -.Nnhr ...... 2 Near Sutherland, Nebr- .... .~.. 31,300 537 340 .92 1.7 ,00115 ,0011 ,0005 .48 .34 . zn 3 Near Lisco, Ncbr ...... 26.900 1,137 400 1. 35 2. 1 ,00105 ,00125 ,0016 .% .50 .21 ...... 4 Near Douglas, Wyo ...... 14,300 1,493 310 1. 7 3. n . m5 .no095 .n2 .n5 .65 .28 ...... 5 Wind R., at Riverton, Wyo ...... 2, 320 1. 108 160 2.0 3. 6 ...... ,0038 .16 .05 .65 .31 ...... 6 Little Pop0 Agie R., near Lander, 108 e 100 39 1. 1 2. 7 ...... ,0049 .ll .n4 .4n .47 R W"n 7 NeGYork R., Jenkins ranch near 45 ...... ,0047 ,023 ...... Cora Wyo. 8 Green 'R., at Warren Bridge near 408 509 120 1. 8 2.4 .- - -.. -. - ,0034 .46 .12 .34 .52 ...... Daniel Wyo ...... 9 Beaver kreek, near Daniel, Wyo. . 141 32. 1 42 .88 .86 ,0066 .MI14 ,097 . in .40 .5n 10 New Fork R., below New Fork 36. 2 50 ...... 0051 .017 ...... Lake near Cora, Wyo. lla Horse Creek, near Danlel, Wyo.-.. 124 63. 2 61 .61 1.6 ...... ,00227 .09 .12 .42 .43 ...... llb ....do.3 ...... 124 ...... ,0073 ...... ~.~~...... 1% Cottonwood Creek near Daniel, 204 ...... M)11 .049 ...... wyo. 204 67. 4 43 .8 1. 8 ...... on405 .06 .30 .26 .44 ...... 12b ...-do.a-...... 14a Green R. at Daniel, Wyo ...... 680 ...... -...... ,0005 ,056 ...... 14b ....do.3 ...... -. - . -. . .0029 . in ...... 14c .... do.3 ...... 00m . in ...... 1% New Fork R. at American Gothic 372 ...... ,00125 . 121 ...... reach near Pinedale, Wyo...... 00286 ...... 18b ....do.3 ...... 18C ..--do.3 ...... on286 ...... ~.. 21 Duck Creek near Cora Wyo ...... 5 ...... ,000193 ' ,004 ...... 2: Snake R., &low mouth of Hoback 3,440 ...... on21 ...... ~.~...... R. near Jackson, Wyo. ..~.~..-. z Buffalo Fork, Flybox reach near 345 ...... ,00071 ,000455 . 14 ...... Jackson, Wyo. 24 Wind R Dumb Cowboy reach 55 ...... 0037 .I31 ...... near Sberidan Ranger station above Dubois Wyo...... 93 ...... no098 . a35 ...... 2: DuNoir Creek, &ve Dubois. Wyo...... 2f North Fork Pop0 Agie R., near 140 in3 41 1. 75 1. 5 ...... 007n .48 . 13 .20 ,6C Lander, Wyo...... 2i Pop0 Agio R., Joyful reach near 700 ...... 00184 .10 ...... Hudson, Wyo. 5. 5 2! Little PiDe Creek. near Avondale, n ...... w473 ,049 ...... Md...... z Rock Creek. Rt. 115 near Redland. 7. 4 ...... I3 ...... Md. .47 .M 3. 3 3( Watts Branch. Viers nasture near 4. 2 e 4.2 13. 1 .52 .62 ...... ,0031 ,082 .03 in0 93 53 1. 06 1.7 .00133 . no06 ,075 . 16 .50 .3( 5. 1 31 ...... 3: .53 ...... ,0005 ...... x 15. 5 ...... ,0023 . 0% ...... Rockrille Md. .~~.~...... ~~...... 3t Mississippi' R., at Tamm Bend 1,000. no0 7 c 580,000 ...... onon89 ,002 near Blvtheville. Ark. .4: ...... 3s 21 21. 5 26 .92 .84 ...... 15 .42 ...... 4: 21 ...... -.__...... ,00093 . ny -..--...... 5; .4? .!M ...... wyo...... I, ,710 70 38 1. 5 1.4 . m947 ...... 3( ...... 1f .48 .4: ...... 5t At Hnlett Wyo ...... 2, %Q 60. 5 50 .8 1.8 .onlati ...... 5s At Wydming-South Dakota 1m ...... ,000947 ...... - -.- - - - ...... State line ...... ______.3: ...... 61 Near Elm Springs S. Dak 7,210 447 112 1. 5 2. 7 ...... 3f .35 ...... 6: ...... --.__...... oniin ...... -. - - - - Near Fruitdale S.'Dak .3( .45 . 3( ...... 6: Arikaree R. at Haigler Nebr ...... 1.400 31. 7 45 .5 1. 4 .onin9 ...... 64 Seneca Creek, near Wdodfleld, Md...... (1 mile north of Woodfleld)...... 2. 1 ...... OWJ2 .06 -..-.. 6: Christians Creek, at Grange Bridge ...... near Staunton Va ...... 24 ...... -.-.-...... ,0015 ,075 ...... G( Christians creek, at Rt. 254 near ...... Staunton Va ...... 82. 5 ...... on30 .085 ._.._.- . . - -. 6: Barterbrook Creek, at Rt. 254 near ...... Staunton. Ve ...... 6. n ...... __._.-.---...... nn23 ,0125 ...... 61 Middle R., at Bethlehem Church .-. .-...... near St,aunton Va ...... 18 ...... 0021 .076 _____ 61 Eidson Creek ' mar Mt. Tabor ...... Church near'Staunton, Va...... 2. 2 ...... - -.-. - - ,0083 ,049 ..... 71 Tributary to Christians Creek near St. James Church near Fisheiville, ...... no07 ...... Va. - -.-. .-. . ------.- - - __- - - -.- - 1. 6 ...... -..-.. 7 South R. Blnek Bnll reach south of Mt. Vkrnon Church nenr Lips- ...... -.. -.-._-.-.-...... ,00034 .0032i ...... -.~.. . comb Va ...... 69.2 ...... - - - ...... 7 South +ark Tyc R. above Naeh Va 14. 2 ...... - - -.- -...... ---__...... ,051 1. 15 .-..-...... 7 TYCR.. culvcrt-bridge near St&- ...... G. 4 -. -.-. - -.- -.-...... - -.- - -.. .O67 1.31 ._.___ ton, Va ...... - - -. ~.~~~...... 12. 3 ...... 068 1. 65 ...... ~..~.~ Picnic rcsch near Stsunton, Ye...... ? .- - - .- - -...... 0% .75 .______._._ Below Nash Va ...... 31.4 ...... 7 Campbdl Crud, above Tyro, Va.. 1. 1 .._.._..... I::::::::. .I1 1.77 ._.___ 7 Stony Run, above mouth at Little .31 -..-.-_.___...... R. near Staunton, Va ___.._.___.._ 1. 1 ...... om See footnote at end of table. 82 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS APPENDIXH.-Values of hydraulic factors at various stream cross sections-&ntinued - - At mean annual discharge Slope 1 Gage -- height Drainage eloc- ~ vPedian at bank- Serial led size m full No. Strcam and location area (square Discharge ity 0 miles) .cubic feet Nidth lepth feet Asp 1 Field 2 (fect) stage er second) (feet) (feet) per (feetj see- ind) ____ - - 78 Mines Run, at mouth near Staun- ton Va ...... 2. 8 n. 038 0.22 ...... -. ... 79 3kidmore Fork, Rt. 95 near Staun- ton Va ...... 4.8 ...... ,025 .25 ...... _._. .... an Little( R., Grooms Ridge near Staun- ton Va ...... 16 ...... ,0048 .2G ...... 81 Norti) R. near Stokesvillc Va ______2% 4 ...... -. -. . ,015 .38 ...... -.- 82 North River Gap ne& Stokes- villr Va ...... 66.4 ...... no81 .43 ...... -..~ .... 84 Slab Cab& Creek, west. of Lamont, Pa- ...... 16 ...... - .-...... _.. ,0032 ...... - 11, !wo 1,950 258 2. 5 3.0 00004: ...... 0.55 0.35 ...... 86 BIK Horn R. at Mandenon, Wyo-- .4R .40 ...... Wind R. ne& Crowheart, WYO..... 1.920 1,315 155 2.4 3.6 ..-...... 87 .27 .MI .47 .46 ...... 89 Yellowsthe R. at Billings, MontL- ii,wn 6,331 420 4.6 3. 2 00152 .00083 1,220 853 130 2. 7 2.5 on4 ...... 27 .05 . aa .62 ...... 90 Wind R,. near Burris, yo ...... 8& 6 91 Near Dubois, Wyo ...... 233 179 68 1.4 1.9 0063 ...... n2 .5u 92 Little Righorn R., at Statc line near .37 .M Wyola. Mont ...... 199 152 29 2.0 2.5 0095 ...... o 93 North Platte R. at Wyoming- 22,100 767 270 1. 4 2. 1 00118 ...... 22 A .16 Nebraska State !:ne. Wyo- ...... 10 .33 .57 94 At Samtorra Wyo ...... 2,880 1. 204 210 2. n 2.0 00146 ...... 95 Medicine hdgk Creek, Hyattville, .15 .31 .5: 3. 4-3.9 wvo...... ne 3i 25 .9 I. 7 ...... 86 Ooodeberry Creek, near Grass Creek, . ~ ~-~.~ . .~~ . OD .45 .4? ...... wy[, ...... 155 . 19 19.5 .6 1.9 ,0099 I North Fork Owl Creek, near An- 97 ...... 31 .24 .4i 7.3- 8.8 chcr Wyo...... 58.1 16 17 .58 1. 7 0114 98 Yello\;stone R., at Corwin Springs, ...... 49 .4: Mont ...... 2, &XI 2,950 242 3.4 3.6 . onzx .OF ...... ,134 .37 .5t 99 Near Sidney Mont ...... 69,450 11,860 308 11.9 3.2 .00018 loo Little Bighorn ' R., below Pa.% 429 202 57 1.5 2. 4 ,00316 ...... o: .55 .4: Creek near Wyola Mont ...... 04 .44 .5( in1 Near Crow Agency, Mont ...... 1, 190 294 96 1.2 2.5 . on118 ...... 102 Republican R., near Bloomington, ...... at .52 .4( 16 Nehr.-...... 20,800 724 230 1.7 1. 8 . OOORF ...... 1; .4c .4( R. 4,600 185 60 1.4 2.2 .00167 ...... 103 Laramie near Ft. Laramie, WyO...... a 2: ...... 104 South Platle R. at Paxton, Nebr.-. 23,700 438 140 1.5 2.0 .onm .s . 105 North Platte 8.. near Keystone, ...... % .2f . I! ...... 30,000 340 ...... OOllE Ncbr ...... O! .7: .2 ...... 106 Platte R., near Grand Island, Nebr. 59,500 960 670 .n 1.8 ,0012~ ..~~~...... 2: .% .2 ...... 58,800 937 550 .96 1.8 ,0012f 107 Near Odessa, Nebr ..~~~.~ ...... o .6! .2 ...... 108 Near Overton Nebr ...... ~,4on 2,583 780 1.55 2.2 .0012( in9 North Platte R.', near Mitchell, .3; .12 ...... Nehr 24,300 1,495 280 2. 0 2.6 .00118 ...... 3 ...... 4: .2: .32 ...... 110 Below Whalen, Wyo...... 16,350 1,111 ...... a0111 ~..,.~~. 12,600 1,358 250 1.9 3.0 .ooono ...... 2! .2: .20 ...... 111 Below Casper, Wyo...... o' .3! .62 ...... 112 Pop0 A ie R near Riverton, Wyo.. 2, nin fi83 123 3.3 1.7 ,00126 ...... 11 .5( .37 ...... 113 Oreybufl R..'hear Basin, WYO...... 1,130 200 90 .96 2.4 . on6a 87 1.4 3. n ,00947 ...... 21 .3! .35 ...... 114 Near Meeteetse, Wyo ...... 690 364 ...... 26 .9 1.9 ...... ~~ . .~.. . 21 .2! .5n 115 Owl Creek, near Thermopolis. WYO. 484 45...... ~~.. ~. ~ ...... 0 .4: .58 ...... 424,300 35,440 863 11.5 3. 6 ,000227 116 Missouri R., at St. Joseph, Mo .4: .50 . ~~..~~~ 528, mn 69,170 1,578 14. 5 3.0 .oonim ...... o 117 At Hermann, Mo...... 11 .4 .47 ~~.~~..~ At Pierre S. Dak ...... 243,500 22, nao 962 9.1 2.5 ,00018Y ...... 118 ...... 0 . 5! .37 ...... At Kand City. Mo-..-- ...... 489,200 43,710 1,093 11.7 3. 4 ,000146 119 ...... n .5l .45 ...... 120 At Bismark, N. Dak ...... 186,400 20,320 1, 202 G. 1 2.9 .oonm 121 East Fork R., near Big Sandy R., .4 .50 ~.~~ .~.~ wyo...... 79. 103 70 1.3 1. 15 .o 122 North Piney Creek, near Mason, ...... I . 41 .42 ...... wy"...... 58 60. 29 .94 2. 2 ...... 123 Bou der Creek, below Boulder Lake e 66 .n .4 .47 ...... near Boulder, Wyo...... 130 196 130 1. 8 .84 ...... ooon ...... 1 . 41 .27 ..~~.~~.. 124 Silver Creek near Big Sandy Wyo.. 45. 43. 29 .n 1.9 ...... 12: Middle Piniy Creek below' South 34. 26. 21 .a 2. 0 ...... no91 .31 .1 .4 .48 7. 7 Fork near Blg Piney, Wyo ...... 2 .4 .30 ...... 1% New Fork R. near Boulder Wyo ... 552 403 98 1.8 2.2 ...... 12i Fontendle Cieek, near Fohenelle, ...... 2 .2 .50 ~~~ ~..~~. wyo...... 224 64. 42 .9: 1.7 ...... 1% Little Sandy Creek, near Elkhorn, ...... 22 19 1.5 .7G ...... 010 .29 .2 .4 .33 wyo...... 20. ' ...... 2 .3 .43 ...... 140 6. 2 1.03 ...... A. 1Z Pecatonica R at Freeport, 111 .______1,330 906 ...... o .6 .35 15 1X Iro uois R Chebanse Ill-..--. 2, 120 1,mfI .330 3.2 1.5 ...... lkar .9 1.5 ,00947 ...... 1 .2 .67 ...... 131 Caaeys C;eek near Brevaid N. C- 11. 34 25. : ...... 154 64 1. n 1.3 ...... 1 .4 .50 13: watauga R ndar sugar Grovl N. C. 90...... u .4 .53 ...... 13: Davidson near Brevard, NI C---- 40. 125 55 1.6 1.4 ,00374 ...... $1, ...... u .2 .65 ...... 134 Noland Creek, near Bryson City, 13. 42. 30. ' 1.9 .n N.C ...... a .6 .28 ...... 131 Tennessee R. at Knoxville, Term-. 8,934 12,820 933 14.4 1.0 .woo95 .-. .-. _. 13f French Rrosd R., near Newport, ...... c .3 .Fk, 10 Te ...... 1,858 2,764 346 5.3 1. 5 .00237 ...... nn ,00108 ...... c .5 .45 ...... 13; At Calvert, N. C ...... 103 335 92 1.8 2.0 ...... 67. 229 77 2.0 1.5 ,00252 _.___.-...... I .5 .45 11 At Rosman N. C...... c .I .47 ...... 13< At Bent CGek, N. C ...... 676 1,589 296 2.8 1.9 ...... 1H Buttahatcbee R., near .Caledonia, .a .75 ...... Miss- ...... 823 1,066 13.0 .5 . MX)G&7 ...... ' 2,863 11.5 1. . ooO142 ...... I .5 .3n ...... 141 Tombigbee R., at Aberdeen, Miss-- 2,210 n ...... I .3 .m ...... 14: Near Leroy, Ala ...... 19, loo 26,250 26. n 2.0 . m19 ...... 21.450 22.3 2.2 ,033376 ...... I .4 .35 --._.__. .- 14: Near Coatopa, Ala...... 15, 500 ...... I .z .52 ...... 14 Near Columbus, Miss ...... 4,490 5,791 11.9 1.8 .m95 ...... 7.0 1.1 ...... ooo63 ...... 4 .3u ...... 141 Sipsey R., near Elrod, Ala ____ ~ ___._.51 5 715 See footnotes at end of table. RIVER CHANNEL PATTERNS 83 APPENDIXH.-Values of hpdraulic factors at various stream cross sections-Continued ~. ~ At mean annual discharge _- ____ mgc - height Serial Drainage eloc- rledian It hank- No. Stream and location area (square Discharge ity w?d size b f m full miles) cubic feet Nidt.h epth feet rlap I Field 2 (feet) stase cr second) (feet) eet) Per (feet) jet- ind) - - _____ ~ _- --- I 146 le ublican R., at Clay Center, &!arts.. -. -.- - - - -.-. . - - - ___.- -. 2pv 570 1,093 272 2.0 2.0 000541 ...... 37 .45 .20 15 147 moky Hill R.. at Elkader, IEans .... 3,555 36 41 . 6 1.5 ...... I7 .58 .30 ...... 148 At Lindshorx, Kans ...... 8.110 292 8n 2. 4 I. 5 000545 ...... x? .% .20 ...... 149 At Enterprise, IEans ...... 19,200 1.419 102 7. 2 1.9 000303 ...... - - -.-. -. .I0 . 17 .72 ...... 150 Cansas R.. at Bonncr Springs, Kans- 59,890 5,874 563 5.9 1.8 000379 ...... -.-. -. -. .06 .45 .48 ...... 151 At Lccompton, Kans ...... 58.420 7,836 7% 4. A 2.3 000379 ...... 07 .70 .25 -..- -..-. 02 .55 , ...... 152 At Ogden, ICans ...... 45,240 2.514 342 3.8 1. 9 000379 ...... - - -.-. -. . 40 2. 1 0430 .~--._. .- ...... 07 .61 .30 21 163 At Topeka, Kans ...... 56,710 4,655 481 4.6 ...... 154 At Wamego IEans ...... 55,240 4,114 525 4.1 i. 9 000316 ...... 17 .55 .25 156 Plathead R., ndar Columhia Falls, Mond ...... 1,553 2,855 290 2.5 4.0 ...... 30 .32 .38 At Columbia Falls, ...... 4,464 9.112 450 7.1 2.9 ...... - .- -.-. .04 .40 .55 ...... 157 Monk .4(! ...... i5n Near Polson Mont ...... 7,096 11,330 444 7.6 3.4 ...... 08 .50 159 :lark Fork R., kt St. Regis, Mont..- 10. 500 7,341 340 6.0 3. 5: ...... 09 .4c .44 ...... Above Missoula ...... 5,740 2.659 232 4.7 2.4; 00158 ...... 05 .42 .51 ...... 160 MonL ...... _-. -. 8, 4,897 370 5.8 2. 2 ...... 03 .a .77 161 Below Missocla,' MonL - - GW .27 ...... Near Plains, ,...... 19. A00 18,6!IO 495 L4.3 2. 6 ...... 04 .69 162 Mont .3s ...... 163 Near Heron Mont ...... 21,no0 20,400 328 12.0 5.3 00079 ___.-..- -...... 20 .36 164 'end Orcille Jil, below Z Canyon, near Metaline Falls, Wash ...... 25, 200 26,190 293 11.7 7. G ...... 30 .34 .34 ...... Embarrass R.. at St. Maric, Ill ...... 1.540 1.239 110 4.8 2. 3 ...... !XI .N .20 18 167 .44 168 Cankakee R. at Mcmence, 111. ___~.2,340 1, 8lf< 4311 2. 3 1.8 ...... 15 .38 169 Lock R. at 6omo Ill ...... 8,700 5,174 500 3.6 2.8; ...... -. .-. . .10 .4E .45 172 jangamdn R. at hiverton III...... 2,560 1,806 125 6.0 2. 5 ...... 35 .5i .15 173 2onneoticut k., at First bonnecti- . 198 57 1. 25 2.6 ,01136 ...... 10 .34 .56 cut Lake near Pittsburgh, N. >I.. 83.0 .5Ei At North Stratford, N. H ...... 798 1.570 160 3.7 2.7 . ooin9 ...... 15 .L 174 . 5: .42 175 Near I)alton, N. €I...... 1,514 2, W2 380 4.0 2.0 00189 ...... OR 176 At White River Junction, Ver- mont ...... 4,092 7,217 485 4.2 3. 5 . 00063 ...... 04 .a .30 ...... 08 .4: .46 ...... 178 At Montague City, Mass ...... 7,865 13.670 450 11.5 2.6 ,00034 ...... 160 1.3 2.3 . ooing ...... OH .5: .36 12 179 White R., near Bethel, Vt...... 241 487 ...... At Wet Hartford, Vt ...... 6W 1,169 235 4. 1 1.2 ,00114 ...... 05 .32 .57 180 .4! .49 ...... 181 Arkansis R. at Salidn Colo. - --..~. 1,218 622 104 2.0 3.0 ...... -1. .:oo5B...... c4 .I8 .a .29 ...... 182 Rio Oalistco: at Cerrilios, N. Mex. .. e 100 ...... -- ...... 0038 183 Rio Santa Fe at Old Albuquerque .4 Rd. west oi Santa Fe, N. Mex --.. e 175 .. ..~-. ..~- .OM6 .2E .35 184 Arroyo de Ias Chamisos, near Mt. Carmel Chapel (Sunmount) at --I .0151 .. .6' .2E Santa Fe N Mex.-...... 2.5 ...... ~~~-...~. ,025 ,0066 . 0s 185 Catiada Akcha (Euler), near El Rancho Montos:, near Santa Fe, 31 .2! N.Mex ...... 1. 5: .-.-...... 0175 ,0046 .31 . 1 86 Ancha Chiqnita, near El Rancho Montoso. south of Santa Fe, N. Mex ...... 0! ...... ~. ,0286 .0033 .1: . €1 .3: 18i ...... ~...... ,032 .0057 .3: .% .4: ...... M .31 ...... 360 ...... ~.~...... 2i .3f 186 ...... 3! .24 ...... 181 e 600 ...... ~~..~..- ,0055 ,0022 .3: ...... 3: . 3, .34 1K .x .4: 191 .-.- ...... 2: 19: .fr Iowa ...... 380 141 100 1. 21 1. 1 ...... 0 .4t 65 46 1. 5 .8 ...... 2 .4 .a ...... 19: Turtle Creek new Austin Minn.-.. 144 .fr .34 ...... 194 Cedar R.. at 'Cedar Rapid. Iowa ____ 3,093 460 2.8 2.3 ...... a 4,259 430 4.7 2.0 ...... % .4 .2: ...... 19f Near Conesville, Iowa ...... ?E .2 ...... 1% Iowa R., at Wapello, Iowa ...... 12,480 6,135 480 8.1 1.6 ...... 4l .41 94 1.3. 1.3 ...... 01 .5 .3( ...... 19; Cedar R., near Austin, Minn ...... 425 172 .4! ...... 198 Lime Creek at Mason City Iowa.-- 535 209 94 1.9 1. 1 ...... a .5 1sI West Fork Shell Rock R., & Finch- 5 10 ford, Iowa...... 860 461 112 2. 4 1.7 ...... -.2.--. .2 .1' 675 190 1.6 2.3 ...... 2, .5 . l! m Cedar R., at Janesville, Iowa.-...... 6 .2 201 At Waterloo Iowa- ...... :E 2,988 440 2.3 2. g ...... -. - -.-. .o 20: Tributary to Seieca Cr. at Hawkins Creamery rd. near De'mascus, Md. 0.8 ...... w ..... Seneca Creek at Holstein 20: pasture ...... near Wooddeld. Md ...... 7.9 ...... 00467 .os At Poison Ivyreach. Brunt road XI...... bridge near Woodfield, Md-..- .. _...... _...... 00345 ,074 201 At Pretty Flooa Plain near ...... 26 ...... W16 ,037 ...... Prathertown, Md.. .2 .1 201 Kankakee R at Davis, Ind ...... 5of, 470 75 3.6 1. i ...... 6 130 2. ( ...... 1 .5 .2 m At S held;, Ind-.- ...... 1. wo 1.m 5.0 8 201 Auglaize R. near DeEance Ohio--.- 2,329 1,598 285 3.7 1. : .000189 ...... o .4 .4 W13 ...... -.-. - - - .2 .4 .2 17 20' Near Fdrt Jennings, Ohio...... 333 278 100 2.8 1...... Blanchard R., near Dupont, Ohio-.. 749 452 120 5.4 ., .000090 ...... -.~..... 211 ...... 5 .3 ...... 92 1.5~.~ 1. f ,000237 ...... 0 21 Near Findlay, Ohio...... 343 219 K .2 ...... 21 At Glendorf, Ohio ...... 643 548 77 3.7 2. ( ,000146 ...... 1 ... 202 4.3 1. i . ooo2/1 ...... I .4 .3 ...... 21 Maumee R., at Antwerp, Ohio ...... 2,049 1.547 .5 ...... 21 Near 1)eflance Ohio...... 5,530 3,612 620 3. 1 l.I .000189 ...... 0 .. .& .2 ...... 21 At Waterville 'Ohio ...... 6,314 4,269 670 2. 1 3. 1 .Mw)947 ...... 1 ...... 52 1. 2. 1 . ooo631 ...... 2 ... .4 211 Ottawa R., at Allkown, Ohio __.___168 119 a ...... --. 21'. At Kalida, Ohio...... 315 141 80 1.6 I. 1 ,000473 ...... See footnotes at end of table. 84 PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS APPENDIXH.-Values of hydraulic factors at various stream cross sections-Continued __ At mean annual discharge Slope ______Gage height Serial Drainage Jeloc- Median at bank- NO. Stream and location rea (squar Discharge ity bed size b I m full milos) (cuhic feet Width Depth (feet Map 1 Field * (feet) stage ier second) (feet) (fect) per (feet) scc- ond) -1- -1- /-- 218 3t. Joseph R., near Blakeslee, Ohio.. 369 292 95 2.8 1. 1 .00021n ...... 219 Bcioto R., at Chillicothe Ohio ...... 3,847 3.289 200 9. 2 1.8 .000316 ...... 12 .30 .53 17 220 Near Circleville, Ohio...... 2,635 1,815 280 in. 8 .6 .Ow271 ...... IO .21 .Fd ...... 221 At Columbus, Ohio ...... I, 624 I, 386 280 3.7 1.35 .ooo473 ...... n2 .52 .46 ...... m Near Dublin, Ohio.-...... 988 797 205 2. n 1.95 .OOO94, ...... 18 .40 .40 ...... 223 At La Rue Ohio...... 255 198 90 3.8 .6 ,000316 ...... 13 .32 .50 ...... 214 Near Prosbet Ohio...... 571 489 130 2.5 1. 5 ,000237 ...... na .50 .42 ...... 225 Tiffin R., near Brhnerhurg, Ohio.... 766 448 85 3.9 1. 4 .nonio5 ...... 226 At Stryker. Ohio...... 444 292 77 5.6 .69 .wo189 ...... 20 .32 .43 ...... m Fall Creek near Pinedale, Wyo.. -.. 37. 36. 2 24. ! .35 .42 ...... ,036 .69 ...... 8.5 228 Green R. hear Fontenelle Wyo .... 3,970 1,838 250 3. 2 2.3 ...... no02 . 29 .n5 .35 .m 7. 1 228 West Fork Rock Creek, beiow Basin Creek near Red Lodge, Mont ...... Ro 85 33 1.25 2. n ...... ,035 .88 .04 .36 .58 ...... 230 Rock Creek near Red Lodge, Mont. inn 166 28. t 2.4 2. 3 ...... ,021 . 67 n .29 :; ~3:o. 231 Clark Fork 'near Edgar Mont...... 2,115 1. no8 115 4.2 2. n ...... ,00295 .21 .n8 .31 I..... 232 Clear Creei near Buffaio Wyo.. ... 120 70 42 .9 1.8 ,0316 ,024 .58 .14 .37 .48 ...... 233 North Fork'Clear Creek,'near Buf- falo (near Ranger station), Wyo. .. 16 21 .R .8 ...... 028 .47 ...... 234 Red Fork R. near Barnum, Wyo ... 29 21 .97 1. 34 ,0038 ...... l2 ...... 235 Rock Creek 'at Roberts Mont ...... ,0086 .27 -..-...... 236 Illinois R. it Kingston'Mines, Ill-.. 14,220 600 15. n 1. B ...... 16 .32 .54 ...... 237 At M&eilles, Ill ...... 11,6711 620 4.1 4. 5 ...... 1 ...... 1...... 03 .M .4n ...... 238 bt Meredosia Ill ...... 20,950 wn 11.5 1.9 ...... n8 .57 .35 ...... 239 Kankakee R., neir Wilmington,.Ill.. 4, no9 840 2.4 2. n .04 .50 .46 ...... 240 Pole Creek, % mile below Llttle Half Moon Lake near Pinedale, wyo...... 87. in8 60 1.23 1.4 ...... Gill8 .42 ...... 245 Cedar Creek near Winchester, Va.- in1 86. 7 60 1.1 1. 2 ...... 06 .58 247 North Fork bhenandoah R., at Mt. Jackson. Va ...... 509 368 iin 2. 7 1.2 ...... in .33 .52 ...... 248 Near Strasburg Va ...... 772 575 160 2. 4 1. 5 ...... 13 .52 .35 ...... 249 South Fork Shedandoah R., at Front Royal, Va ...... 1,638 1.671 275 3. 2 1.9 ...... n4 .42 .54 ...... 250 Near Luray, Va ...... 1,377 1,264 315 4. 7 .87 ...... 04 .33 .59 ...... 251 1,076 1, om in9 2.9 1.9 ...... n6 .53 .38 ...... 252 m 217 86 1. 5 1. 8 ...... in .30 .60 ...... 253 144 146 78 1. 4 1.34 ...... 04 .43 .50 ...... 254 Va ...... 76 e 74 70 1. 2 .9 ...... m .45 .31 ...... 255 Ant.ietam Creek, near Sharpsburp, Md ...... 281 258 72 2. 7 1.3 ...... ,00055 ...... ,135 .35 .57 ...... 254 Bull Lake Creek, near Lenore, %'yo 222 285 92 1.65 1.9 ...... ,0081 .69 .14 .33 .50 ...... 1 1 -.-..- ...... 257 Cheyenne R. at Edgemont, S. Dak. 7,134 126 90 .a 1. 9 ,0013 e.ooO16 Lance Creek 'at Spencer. WYO.-..... 2,070 30.7 43 .53 1.4 ...... ,00073 e.0099 .I3 .53 .34 7. 5 258 ...... 264 Snake R. ne'ar Wilson, Wyo ____.~.. 2, 000 ...... ,0043 I ...... 1...... 266 Big San(dy Creek, near Leckie ranch Wyo...... 95 ...... 1 :E;5 I .25 ...... 5.5 267 Hams F'ork R. near Frontier Wyo.. 298 ...... ,086 .--..-._.~...... 3.8 268 Middle Fork Powder R., ne& Kay- w, wyo...... 980 ...... -.-..-.-.- ,0038 ...... 15 ...... 4.e5.1 ...... 212 Bighbrn R. near Custer, Mont 22,350 4,441 390 4.65 2. 4 ...... in .50 .40 273 Near St. Xavier, Mont ...... e m,Ow 3,758 264 4.9 2.8 . 00271 ...... --.-...... 274 Missouri R. at Toston Mont ...... 5,322 3i0 4. 5 3. 2 ...... 04 .47 .48 ...... 215 Powder R., ;ear Locst& Mont ...... 12,900 727 165 1.6 2. 8 .m47 ...... 28 .42 .3n ...... 276 At Moorhead Mont ...... 8, 030 511 124 1.7 2. 5 ,00114 ...... 277 Middle R. nesr drottoes Va ...... 360 314 84 3. n 1. 3 ...... 15 .34 .53 ...... 278 North Fdrk Shenandoih R., at Cootes Store Va ...... 215 187 73 1.4 1.8 ...... 30 .28 .42 ...... 279 Passage Creek'at Buckton Va ..... 87 70.1 40 1.75 .95 ...... 26 .28 .47 ...... 280 Shenandoah R., at Millvilfe, W. Va 3, om 2, 561 .tm 3.85 1. 4 ...... n4 .40 .56 ...... 281 Bighorn R., at Kane, Wyo ...... 15, 900 2,413 175 3.8 3. 35 ,000847 ...... 06 .51 .43 ...... 282 At Thermopolis. Wyo ...... 8,080 1.900 210 2. 7 3. 33 . Wl8D ...... ne .35 .59 ...... Powder R., at Arvada, Wyo ...... 6, n,w 410 112 1.27 2. 77 ,000947 ...... 44 .27 .XI ...... m .30 ...... 284 At Sussex, Wyo ...... 3, n9n 134 100 . 82 1.85 ,000842 ...... 44 .m 285 South Fork Owl Creek, above Curtis .52 ...... ranch at Thermopolis. Wyo. ____.139 29.1 21 .84 1.65 ...... 21 . 24 1 Slope measured from topoprghic map. Elope determined by field survey. 1 Divided channel. INDEX Acknowledgments ...... 40 Meanders. profi1coftypic;rl ...... 57 Aggradation, relation to slope of water surfam ...... 48-50,6 9-70 wavelength ...... 55, 57 Meandering channels, values distinguishing hraided fro!n ...... 59, 60 b (width-to-discharge relation), values at various cross sections ...... 81-84 Meander River, Turkey ...... 59 Bedconfiguration, relationofresistance to--..^----.- ...... 66 MiddleRiver,Va.- ...... 53,55, 57 Bed.materia1, data on size distribution of ...... 80 Mud bars, relat.ion to thalwcgs ...... ~~~~~~~ ~53 resistance controlled by size of ...... 6546 Braided channels, valws distinguishing meandering from ...... 59 New Fork River, Wyo ...... 53. 57 Braidedreaches, development inflgme ...... 45-48 develo-ment in Horse Creek ...... 4344,48, 53 Pcale, A . C., quoted ...... 40 proflle of typical ...... 57 Pools ...... 53-59 ratio of hydraulic factors...... 50 Pop0 Agie River, Wyo ...... 53,5F, 57 Braided rivers, general discussion- ...... 40-53 Purpose of study ...... 40 data on divided and undivided reaches...... 77 Brandywine Creek . Pa ...... 65, 66 Quasiequilihrium . in braided stream pattcrns 53 Channel adjustments, relation of dependent hydraulic variables ...... 71 Resistancc, relation of bcd configuration to ...... 66 Channel division, hydraulic factors affccted...... W .53 relation of hed-material sizc to .. ~ ~ ~ ~ ~ ~~~~ 65-66 Channel patterns, relation to hydra!ilic variahlcs...... 59-63 Rimes ...... 53-59 Climate, influonce on channcl patterns- ...... 63.71 Rio Clrande, Bernaliilo, hT. Mes .. ~ ~ ~ ~ ~ ~ ~ .70 Cottonwood Creek, Ryo...... 60,61, 62 Roughness, definition of relative ...... 65 relation of load movement to channcl .... . 71 Darcy-Wcishach resistance coefficient...... 65 Runoff, inflncncc on channel patterns- . . ~ ~~71 Depth, values at various stream cross .sections-.--...... 81-84 Discharge, data on hankfull ...... 78, 79 Sedimcnt, influence on channd patterns ~71~~~~ values at various stream cross sections ...... 81-84 Scdimcnt transport ...... ~~ (i7-69 Shcar ...... t17 Elkhorn River, Ncbr.-- ...... 70 Sinnosity, defined ...... 53 Equations, No . 1, relationofslope to discharge ...... 60 value defining meandering channels .~ .. ~ ~ ~~ 60 No . 2, Darcy-Wieshach resistance factor ...... 65, 72 Skewshoals~...... 53 No . 3, rclation of resistance to depth: sizr ratio ...... 65 Slope, relation to braids ...... ~~ 48-51 No . 4, relation of slope to dischargr ...... 70 relation to changes in load..-.----^---^- ~~~ ~ ~~ lis-i0 valucs at various streem cros ...... 81-84 /(depth-to-discharge relation), values at various cross sections ...... 81-84 Son Itivrr, Ritiar, India ...... ~~ ~~ ~~ ~~ 02 Flume experiments, development of braided reach ...... 45-48 Straight charuicls ...... 53-59 flume described-..- ...... 4M5 Straight reach . profilcoftypicni ...... 51 sizes and distribution of sancl ...... 75 Symbols cqil.tined...... iv slopeofaatersurface.~~.~...... 48-51 summaryofdata ...... 76 Thal\r.eg, ~wndering...... 53,54, 64 Ganges River, Bihar, India ...... 62 Valloy Crcck, Fa ...... ~~ $3, 54 Green River, Wyo ...... 40,41,50,51,53,60, F2 Vcprtation, influence on channel \vidtti-----.-~. ~ ~ ...... (14 Velocity, nteofchangeu,ithdepth...... lii Horse Creek, Wyo ...... 4044,48, 53 values at variousstream cross sections ...... 81-81 IIydraulic factors, values at various stream cross srctions ...... 81-84 \..avrlengt. 11, data ...... 78 Inglis, C . C., wavelength-discharge relation plot.tcd ...... 58 defined ...... 5.5 plotted against channel width ...... 58 Kosi River, Bihar, Indk ...... 62 plotted against dischargr.- ...... ratio towidth ...... Lithologic factors, influence on channel patterns ...... 71 ...... 5X.5!) Load, hydraulic adjustments related to suspended ...... 50 relative effect of width and discharge on ...... iR sediment band in relation to introduced...... 69 Width . data on bankfull-.--- slope in relation to introduced ...... 69-70 factors, influencing ...... 63-65 interpretation ...... 71 m (velocity-to-discharge relation), values at wrious cross sections ...... 81-84 valnes at. varions cross sections~...... 81-XJ 85 0