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