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MICHAEL A. GORYCKI Department of Geology and Geography, Herbert H. Lehman College of the City University of New Yor\, Bronx, New Yor\ 10468

Hydraulic Drag: A -Initiating Mechanism

ABSTRACT INTRODUCTION

Previous work has shown that meandering is The natural tendency of to meander an intrinsic property of flow that is has interested numerous investigators, and as essentially independent of the effects of sedi- a consequence various theories to account for ment. This can be easily demonstrated on a meandering may be found in the literature (see simplified -free stream "table" or Morisawa, 1968, p. 139-141, and Leopold and plate composed of an inclined hydrophobic others, 1964, p. 298-303, for reviews). Attempts plane surface on which a small stream of water have been made to equate stream meandering is allowed to flow. Development of a meander with such factors as energy loss or gain, grade, series from a straight and then sinuous stream and , morphology, is induced by increasing water flow. A study grain size of stream sediment, proportion of bed of water motion by injecting ink into the versus , velocity, channel ob- stream reveals a genetic relationship between structions, condition and composition of the sinuous water motion (meandering thalweg) channel, helical flow, and centrifugal forces. In of straight reaches and the bends of meandering spite of all that has been written on the subject, streams. Dimensional ratios of wave length of however, some workers conclude that there is meandering thalweg to stream width in the no satisfactory or complete explanation for straight stream or stream width to meander meandering (Leopold and others, 1964; King, length and radius of curvature in the meander- 1966; Morisawa, 1968; Schumm and Khan, ing stream closely match those of larger streams 1972). The fact that meander patterns are in nature. seen in some sediment-free streams on glacial ice (Knighton, 1972) or on solid rock well above Variations of water depth along straight or , in the meandering thalwegs of meandering experimental streams match, more straight reaches of some streams and also in or less as mirror images, the familiar and the Gulf Stream, suggests that it is an intrinsic pool undulations of the in straight property of streams to meander. This leads to reaches or the crossings and deeps of meander- the consideration that the role played by ing streams in nature. Pools apparently are sediment during erosion, transportation, and analogous to deeps, and to crossings. deposition during development and migration Introduced silicon carbide granules form point of is essentially collateral (Leopold bars spaced approximately two to three times and others, 1964). To reinforce this concept, an the stream width in the straight stream and five examination of Tanner's (1960, 1962) labora- to seven times the stream width in the me- tory stream apparatus was made which demon- andering stream in accordance with field obser- strates the meandering nature, in the absence vations. of sediment, of a nondissipating water . Reversing helical flow can be demonstrated in the meander bends but this is an exaggeration of sinuous water motion or hydraulic drag MATERIALS AND METHODS already present in the straight stream. A The general form of the stream plate is simi- physical model demonstrating the initiation of lar to the "model" designed by Tanner (1960, meandering is also described which apparently 1962) but differs in regard to the type of is, in essence, similar to the initiating mecha- surface and the use of an ink injection system nism responsible for production of beach cusps and dissecting microscope to study and describe and other evenly spaced longitudinal current- water motion within straight, sinuous, and formed structures. meandering streams. The stream plate is basi-

Geological Society of America Bulletin, v. 84, p. 175-186, 16 figs., January 1973

175

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cally a smooth plane surface (Masonite) about 22 X 40 cm that has been rendered hydropho- bic to a degree by giving it a fresh coat of white high gloss enamel paint and supporting it on a frame so that its long dimension makes an angle of about 25° with the horizontal. An adjustable but stable water supply in a draina- ble 2-1 container is supported above the upper edge of the plate. Water is conveyed from the container through a 20-cm length of rubber hose terminating in a thin-walled cylinder or nozzle about 5 cm long and 3 mm in diameter. The nozzle rests tangentially on the plate to which it is fixed near the plate's upper edge and the axis of the nozzle points directly down- slope. A suitable water collection and disposal trough is also installed along the lower edge of the plate. An ink injection system was used to study water motion within the experimental streams. Figure 1. General view of stream plate apparatus The system consists of a polyethylene squeeze consisting of a black-painted wooden frame, supporting bottle filled with washable ink and connected a 40-cm-long piece of Masc nite, which has a fresh coat of white high gloss enamel paint. Water, colored for by polyethylene microtubing to a pipette visibility, draining from container meanders down drawn by flame from glass microtubing. The stream plate, inclined 25° from the horizontal. Col- pipette is held in a suitable mount so that its lecting trough and drain ;tt the lower edge of plate. orifice can be held either against or slightly Ink injection system, composed of ink-filled squeeze above the surface of the plate and accurately bottle connected by polyethylene microtubing to glass positioned anywhere on it but with enough micropipette held in support, rests on apparatus. flexibility in the mount so that the pipette Dissecting microscope rests on platform attached to does not break if in contact with the plate. underside of wooden frame. Ink can be injected in the form of numerous filaments into the stream flowing on the plate therefore, increases from 1 to a maximum of surface. Single filaments can also be produced nearly 1.8 (see Fig. 7) (Leopold and others, by gentle pressure on the ink bottle. Paste 1964) and the wave length of the curves as well composed of water and silicon carbide granules as the channel length also increases. Close in- (2F grade) and added to the upper end of the spection shows that as the meanders develop stream allows observations to be made of sedi- and the stream deviates from the original ment motion and deposition within the stream. straight course the wettsd surface of the plate A frame for attaching a dissecting microscope abandoned by the migrating current becomes can also be constructed on the underside of the dry because of surface tension effects of the apparatus if close observation of the ink fila- water and the hydrophobic property of the ments or carbide granules is desired (Fig. 1). plate. As a result, the si:ream maintains a dis- creet course of fairly constant width. It is im- Experimentation portant to stress that the condition of the A gentle stream of water is allowed to flow stream plate surface is critical to meander down the plate. Initially, the stream has essen- formation. It must be clean and dry and the tially a straight course (Fig. 2). As the flow of water used should be free of wetting agents such water is slowly increased, however, a series of as soaps and detergents. A freshly painted symmetrical curves slowly but simultaneously smooth surface is best but polyethylene and develops along the length of the stream (Figs. other plastic or treated surfaces may be suitable. 3, 4). With increased flow one or more of these Tanner (I960, p. 993) suggests that ". . . glass curves develop into meanders which tend to which had been collecting dust lightly for one migrate downstream and from which new me- or two years" was necessary to the production anders appear to be generated farther down- of meanders on his apparatus, and that ". . . stream (Fig. 5). The of the stream, After many experiments had been run on a

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Figure 2. A gentle flow of water issuing from noz- Figure 3. An increase in water flow produces sinu- zle on left produces straight stream on the stream plate. ous stream. Each curve seen was present as sinuous Ink filaments {see Fig. 8) reveal that lower water levels water motion within the straight stream (see Figs. 2, in this stream have sinuous course (meandering 8, 9, 10, 12). Stream width, 3.5 mm. thalweg), the result of hydraulic drag. Stream width, 3 mm. (In this and all other photographs and diagrams except Figs. 1, 6, 12, and 14, water motion is from left to right.)

Figure 5. Meanders produced by further increase of water flow. Sinuosity is only 1.43, but becomes greater with increased flow (SM Fig. 7). Note curvature variation within meander bends (see Figs. 7, 15, 16). Stream width, 4 mm; average meander length, 50 mm. Figure 4. A more sinuous stream than in Figure 3. As water flow and sinuosity increase, overrolling of developed in the hose or exit nozzle. Tanner water filaments (reversing helical flow as seen in Fig. (1962) indicates this by allowing water to flow 16) occurs at bends. Stream width, 3.5 mm. down a clean glass surface along which the single glass sheet, meanders became more diffi- water takes a straight path and then across a cult to obtain, . . ." because "... the sheet was coated (hydrophobic) surface on which me- washed clean. . . ." He maintains that "... the anders develop. In one of my experimental pro- dust appears to serve the purpose of providing cedures, water flowed into and overflowed from a slightly roughened surface, thereby setting a glass cylinder reservoir, 21 mm in diameter up turbulence . . ." which induces helicoidal and 5 mm high, resting near the upper edge of flow and thence meandering. In a later paper the stream plate. The overflow initially formed Tanner (1962) describes meander production a straight stream and, with increasing flow, de- on artificially roughened glass surfaces which veloped a sinuous and then meandering pattern were coated with plastic cement, varnish, or identical with those formed without employing lacquer, sprinkled with sand grains, and al- the reservoir. This proves that these patterns lowed to dry. In both situations the dust or are the result of interaction of the water and sand apparently is not necessary to meander the stream plate surface and that a considera- production but, rather, the hydrophobic nature tion of Reynolds Criteria which govern the of the contaminated or coated glass surface. transition from laminar to turbulent flow It should also be mentioned that meandering within the nozzle or hose is not necessary. does not depend on any sort of Also, if the nozzle were turned to any angle

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other than directly downslope the stream Increasing water flow beyond that necessary would tend to flow off the plate's lateral edges, to induce meandering results in production of especially as the flow is increased, but more unstable meanders that migrate wildly across importantly, the shapes of initial meanders the stream plate surface (Fig. 7); they eventu- would be influenced by a lateral (downslope) ally have a proper meander length to radius of component of gravity; this could be construed curvature ratio, but also have a meander length as the mechanism of meander initiation. As to channel width ratio too large to fit Leopold Schumm and Khan (1972) state, discussing and Wolman's graph. The stream dimensions meanders that were produced in the laboratory presented in this paper are average figures as under straight entrance conditions, "... a per- measured on the stream plate, but they can turbation or disturbance of the flow may not vary depending on the condition of the plate be an essential cause of meandering." All that surface. is required to produce meanders on the stream plate is that the flow be sufficient, constant at any value, and issue from a fixed point. Mechanism of Meandering A measure of the dimensional ratios of the Straight Reaches and Sinuous Flow (Hy- meanders (that is, meander length [50 mm] to draulic Drag). A st jdy of the initially straight channel width [4 mm] and meander length to stream on the stream plate (Fig. 2) employing mean radius of curvature [9 mm]) appropri- the ink injection apparatus and dissecting ately fits the graphs presented by Leopold and microscope reveals an interesting aspect of Wolman (1960) but on a scale two orders of water motion under these conditions. Sub- magnitude smaller than the meanders on gla- merging the orifice of the pipette just below cial ice or the smallest or meanders the water surface in the middle of the stream (Fig. 6). Also, when comparing meander ex and applying gentle pressure on the squeeze perimentally produced patterns with aerial bottle causes a relatively straight single fila- photographs or topographic maps of stream ment of ink (laminar flow) to be formed along patterns, it would seem safe to assume that a major portion of the stream length (Fig. 8). meanders have been experimentally produced By progressively submerging the pipette, how- in a short time and in the absence of sediment, ever, the ink filament will exhibit a series of and that forces involved in the experimental more or less evenly spaced symmetrical curves situation are similar to those responsible for that become progressively more sinuous and meander formation on a larger scale in nature. slow moving and which migrate a short distance upstream with depth (Fig. 9). These curve locations are fixed with respect to the stream X Gulf Stream 300,000 ( ) and A- o Glacier ice 30,000 • Stream plate / 3000 S ® 300 o E

/B

0.03 0.3 3 30 300 3000 30,000 Figure 7. Unstable meandering stream, which con- meters stantly changes course, procuced by increasing water Figure 6. Graphs showing relation of meander flow beyond that required to induce meandering. length (ordinate) to channel width (A) and mean Sinuosity, 1.79. Further increase in flow produces radius of curvature (B) extended two orders of magni- meanders having wave lengths and radii of curvature tude by inclusion of stream plate meander data. (Re- too large in relation to stream width. Width of the drawn from Leopold and Wolman, 1960.) stream, 5 mm.

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Figure 8. Micropipette injecting ink into straight Figure 9. High power view of a number of ink fila- stream. Note straight (laminar) water flow in upper ments injected simultaneously by heavy pressure on levels of stream (arrow 1) and sinuous flow of water squeeze bottle through a single micropipette into near plate surface (arrow 2) as indicated by ink fila- straight stream. Straight filaments (arrow 1) are fastest ments. Stream width, 3 mm. moving and are in uppermost stream levels. More curved filaments (arrow 2) are in progressively deeper slower moving stream levels. Note that bends on fila- plate surface; that is, if the pipette is shifted ment with greatest curvature (arrow 3) are located across or along the stream or if water flow is farther upstream than the less sinuous filament, indi- varied slightly, the curvature of the filament cating it is closer to stream plate surface and undergoing will vary but not the positions of the curves. greater amount of hydraulic drag. Secondary flow If a large cluster of wet silicon carbide gran- characteristics within hose or nozzle not responsible ules is introduced at the upper end of the for sinuous flow as evidenced, in part, by presence of stream the water becomes turbid. In a few straight filaments. No true turbulence seen in these streams. Stream width, 3 mm. moments it clears but a train of granules remains which follows the identical sinuous course taken by the lowermost ink filament streams in nature, the shallow to riffles (Leopold and, except for the stream edges, represents and Langbein, 1966). A central hump is also the slowest course of particle or water motion prominent in straight reaches of natural within the stream. Since this is where the streams (Leopold and others, 1964, p. 284). greatest friction between water and plate sur- Another point of correspondence is that the face occurs, it follows that this is where the spacing between the sinuous curves or point greatest amount of erosion (meandering bars in straight streams (see Figs. 3, 8, 9, 10, 13) thalweg) would be in nature. A few particles is approximately two to three times the stream also tend to accumulate at the edges of the width, which is in fair agreement with data stream in discreet equally spaced clusters (Kel- presented by various workers. Leopold and ler's [1971] point bars) on alternate sides ini- others (1964, Fig. 7-6) show gravel accumula- tially at positions only slightly upstream of, tions in the channel of an ephemeral wash, a and on the same side as, each curve. As the portion of the de los Frijoles near Santa sinuosity of the stream increases, these clusters Fe, New Mexico. The spacing between the become more apparent and tend to form slight- nine right-hand accumulations of gravel for ly farther upstream from the curves (Fig. 10). July 1959 averages approximately two to three A side view of the stream reveals that its upper times the average stream width as shown in surface undulates slightly at periodic intervals the diagram. This is also true for Creek equivalent to the spacing of the sinuous curves. near Downington, Pennsylvania, as described Water depth is greater at the curves than at by Leopold and Wolman (1970, Fig. 7.8), in the intervening locations (Fig. 1 IB). These which they show meandering thalweg curves undulations are independent of the sediment spaced approximately 3.3 times the stream and form whether or not sediment is intro- width as shown. Diagrams presented by Dury duced into the stream; they are also essentially show spacing of riffles or pools in a drainage a mirror image of the variations of water depth ditch and in McDonald Creek, Scott County, seen in straight reaches of streams (Fig. 11 A). Iowa (Dury, 1964, Figs. 26, 28) to be approxi- The deep water locations on the stream plate mately three times the stream width. apparently are analogous to pools in straight Keller's (1972, p. 1534) statistical study of

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P Pool ft Riffle

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Figure 10. Silicon carbide granules following path of slowest water motion within fairly straight stream. Sinuous flow, the result of hydraulic drag due to couple between stream plate surface and faster upper Figure 11. A, Side view sketch of straight stream in levels of stream is where (at stream bottom) greatest nature showing periodic variations in water depth and amount of friction and, therefore, erosion would be in riffle and pool locations. (Redrawn from Leopold and a natural stream (meandering thalweg). Note accumula- Wolman, 1966; copyright C> by Scientific American, tions of sediment slightly upstream of points of maxi- Inc. All rights reserved.) B, Side view sketch of straight mum deviation of sinuous flow which correspond in stream on stream plate. Note undulatory nature of location and spacing to point bars in nature. Water upper surface of water and near mirror image of varia- depth greatest at sinuous curves (see Fig. 11). Stream tion in water depth with diagram above. Low points width, 3 mm. (riffles) located between sinuous curves as seen in Figure 10. pool or riffle spacing shows that during the development of alluvial stream channels the p. 154) is exhibited ty the experimental tendency is for incipient pools or riffles to be stream. This is determined by noting the spaced about three to five channel widths apart velocity of the ink filaments as the orifice of (although in some streams they may be as close the pipette is moved farther from the stream as one to three channel widths), and that only plate. The slower the filament the closer it is in later stages of development is the spacing to the plate surface. The folded structure (Fig. generally five to seven channel widths. Schumm 9) revealed by the ink filaments suggests a and Khan (1972), in studying streams in sand distortion of laminar flow as the result of a on a 100-ft-long flume, produced meandering combination of fractional resistance of the thalwegs in a straight stream upon attaining a water flowing in contact with the plate surface critical slope. Their Figure 5C (p. 1761) is re- and the water moving at high velocity in the markably similar to Figure 10 presented here upper levels of the stream. This structuring is both in appearance and in the ratio of stream the initial manifestation ci a reversing helical width to spacing of sinuous curves (twice the flow structure seen in the more sinuous stream stream width), but their stream is approxi- and meander bends descriaed later, which de- mately 575 times as wide. Finally, Leopold and velops as the velocity differential is increased Wolman (1970) present a graph which shows with increased flow on the stream plate. I call that for streams approximately 100 ft wide suc- this sinuous water motior. "hydraulic drag." cessive riffles or pools are spaced about five It is important to note that the transition from times the stream width but only three times laminar to sinuous flow is in a direction opposite the stream width for streams approximately 0.8 to that generally accepted in a consideration of ft wide. By plotting on Leopold and Wolman's laminar and turbulent flow. As the stream plate graph the stream width (3 mm) and spacing surface is approached, the flow becomes less (7 mm) of sinuous curves seen in Figure 10 laminar and more sinuous. Consequently, it presented here, the point falls on the curve and does not seem appropriate to consider Reynolds extends it two orders of magnitude. Water Criteria here since there is also a reduction in depth and motion, sediment motion and accu- velocity in the more distorted zone of sinuous mulation, and dimensional ratio of stream flow and the stream lines c.o not become con- width to spacing of successive sinuous curves fused through heterogeneous mixing but remain in a straight stream on the stream plate closely discreetly visible. In this situation, since turbu- correspond to the meandering thalweg, point lent flow (sensu stricto) does not occur, a con- bars, riffles, and pools of straight streams in sideration of the Froude number becomes inap- nature. propriate and hydraulic drag seems an apt descriptive term for the mechanism of me- The normal velocity gradient of water flow- ander initiation. ing over a surface (Leopold and others, 1964,

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A simple physical model of hydraulic drag mechanism responsible for the production of or the initiation of sinuous distortion of laminar beach cusps, parabolic , and other evenly flow can be produced by placing a very thin spaced longitudinal current-formed structures. cylinder of elastic rubber 5 cm long and 0.5 mm As the leading edge of a fluid sheet traverses a in diameter (taken from an elastic cloth band) plane surface it tends to extend laterally in a on a piece of plate glass. A second glass plate is direction perpendicular to current motion. placed over the first and, by pressing down and This lateral extension is relieved by regularly forward, parallel to the axis of the cylinder, the spaced invaginations separated by salients and cylinder will be flattened and thrown into a it is this structuring of the sheet edge which is series of more or less equally spaced sinuous responsible (in the appropriate geologic envi- curves (Fig. 12) very much like the lowest ink ronment) for the multiple structures. In a filament closest to the stream plate surface as similar fashion, hydraulic drag is responsible the straight stream is flowing. The model func- for the initiation of sinuous flow and meander- tions best if friction between the rubber and ing in streams, but here the extension is in a glass is reduced by slightly soiling the glass direction parallel to current flow. surfaces with oil from the finger tips. In this Continued pressure on, and translation of, model, the lower glass plate simulates the the upper plate causes the rubber cylinder at stream plate (or lower slower moving water), the curves to twist and overroll and the sinu- the rubber cylinder, the lowest slowest ink fila- osity and distortion of the cylinder to increase. ment (or an upper faster moving, but distorted As previously mentioned, this distortion (the ink filament) and the upper glass plate, the familiar reversing helical flow structure) pre- faster moving upper levels of the stream. vails as the stream becomes more sinuous and The distance between the ends of the rubber as meanders develop. The general average cylinder remains essentially unchanged even movement of the rubber, however, is in the after distortion. Elongation induced by the direction of motion of the upper glass plate, couple is relieved by the simultaneous forma- the movement of which is analogous to the tion of a number of equally spaced sinuous downstream motion of the water. It is likely curves. In another paper (Gorycki, 1973) I that a mathematical model of hydraulic drag have presented evidence for the existence of a could be designed to quantify this mechanism. Ink filaments progressively farther from the stream plate surface suffer less distortion since the velocity differential is less; their structure is also translated a short distance downstream because of decreased frictional resistance and increasing velocity with decreasing depth, but they in turn affect and aid in distortion of the lower filaments. At the uppermost levels in the stream, friction between water filaments and the stream plate surface is minimal. Conse- quently, this water flows most quickly and with the least distortion. It is likely that the folded structure or hydraulic drag of the water seen in the experimental stream (Fig. 9) is Figure 12. Physical model of hydraulic drag which present in the proper proportions in the straight causes sinuous flow in straight streams, eventually reaches of natural and laboratory streams be- reversing helical flow and meandering. View is through cause of the presence in them of meandering two pieces of plate glass between which is thin (0.5-mm) thalwegs, and that the stream plate closely rubber cylinder (here flattened). Glass pieces have been reproduces natural conditions during stream moved relative to each other in direction parallel to flow but on a much smaller scale. axis of originally straight cylinder. This relative motion has caused elongation of the rubber and has conse- Sinuous Reaches and Reversing Helical quently thrown it into a series of more or less equally Flow. Increasing water flow on the stream spaced sinuous curves. Continued plate motion causes plate as the straight stream is flowing produces cylinder at curves to overroll in manner analogous to only a slight increase in wave length of the water motion at bends of sinuous and meandering sinuous filaments but causes the straight streams on stream plate (see Fig. 16). stream to become sinuous (Figs. 3, 4). Ink fila-

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ments or carbide granules reveal that each ing (see Leopold and others, 1964, p. 301-302, curve seen within the straight stream enlarges for a short review) and that this downward and distorts the stream itself (Figs. 10, 13). As motion of the water at the concave in the wave length increases from approximately streams is responsible for overdeepening at that 14 mm to 16 mm there is a downstream migra- point. As noted here, ink filaments do reverse tion of the stream's curves as well as a decrease direction at meander ber.ds by overrolling but in their number and a slight increase in stream this is merely an exaggeration of sinuous water width. At this critical velocity, when the motion already present in straight streams. stream itself becomes sinuous, ink filaments Overdeepening at the concave side of meander approaching the concave sides of the bends bends is also clearly seen on the stream plate change direction by a helical flow motion or but as a more or less mirror image of the varia- overrolling, in the proper direction as the tion of water depth at bends in nature (Fig. twisting in the rubber cylinder model, and 14), the difference here and in the pool and head for the concave side of the next down- riffle system in straight streams previously stream bend. described (Fig. 11) due :o the nonerodibility As previously described, frictional resistance of the stream plate surface. This suggests that between the faster moving upper filaments of the local overdeepening at pools or deeps as the stream and the stream plate surface pro- well as bank curvature is the result of stream duces the folded structure near the plate sur- flow being intrinsically structured and not vice face and within the boundaries of the straight versa. stream. With increasing velocity of the upper During transition from straight to meander- filaments, however, progressively more of the ing the systematic deflection of the stream cross-sectional area of the stream becomes in- causes the fast central zone of flow to be volved in sinuous flow. This, coupled with an brought into more intimate contact with the increase in amplitude of sinuous flow, causes dry surface of the stream plate or the slower the stream itself to become distorted. Possibly filaments at the edges of the stream. There, in the sinuous water motion also serves as a sys- accordance with the rubber cylinder model, the tematic impediment alternately diverting the slower moving edge of the current on the con- faster overlying straight filaments to either vex side (concave bank) of each sinuous curve side of the stream. is slowed, overrolls, and its direction changed Meanders and Nonuniform Curvature. very much like a billiard ball striking the edge Further increase in the stream's velocity and of the table at an angle. This "reflected" fila- distortion of the reversing helical flow structure results in meanders developing (Fig. 5) and 1.5 mm T attaining a maximum sinuosity of about 1.79 (Fig. 7). Several workers have suggested that reversing helical flow is important to meander-

4 mm

560 m 1 O-r

30 m

Figure 14. A, Cross section at bend of stream plate meander. Horizontal line represents stream plate sur- face. Curved line (arrow) is lateral component of over- rolling water filaments in bend. No vertical exaggera- tion. B, Cross section of bend on Mississippi River. Vertical exaggeration, X2.85. (Redrawn from Fisk, Figure 13. Sinuous stream in which slow moving 1947.) Note near mirror image relation between dia- silicon carbide sediment forms sinuous thread (me- grams; left-hand side of each is at concave bank of andering thalweg). Note sediment accumulations on meander bend. Low width to depth ratio of Figure 14A alternate sides of stream ; compare with Figures 3, 8, 9, is result of hydrophobic nature of stream plate surface 10, 15. Stream width, 3 mm. and surface tension in stream.

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merit then underflows the main current and fourth classification, helicoidal motion, is also heads for the convex side (concave bank) of evident on the stream plate, but is an exag- the next sinuous curve farther downstream. gerated form of sinuous flow or hydraulic drag. Faster moving, more central filaments override Comparing Figures 10, 13, and 15 and this slower filament and are similarly reflected studying the transition from one type of flow but, being faster, are able to deviate farther regime to the other reveals a genetic relation- from the central axis of the original straight ship between sinuous water motion (meander- stream. Progressively slower filaments on the ing thalweg), zones of deeper water (pools), concave side of the same sinuous current curve intervening shallows (riffles), and point bars of are reflected downstream from the point where straight streams, and the reversing helical flow the central filament changed direction, but (meandering thalweg), deeps, crossings, and again, deviate progressively less. This process point bars, respectively, of meandering streams. is repeated at each curve in the stream and the As a result, each of these features in the straight curves become increasingly sinuous with higher stream has an analog in the meandering stream velocity. Consequently, a meander curve is both in function and number but not in down- created, the form of which is more or less re- slope position because of the increase in wave lated to the variation in velocity across the length with downslope migration of the devel- stream. Water filaments at crossings (points of oping meanders. This is in direct disagreement inflection) generally have subparallel paths. with Keller's (1971) concept of constant pool or riffle spacing for both straight and meander- fust upstream of the maximum curvature of ing streams and the addition of new pools to each meander bend, on its convex (concave keep pool spacing constant as ". . . channel bank) side, some of the slowest water filaments length increases due to lateral migration of the fail to overroll and, as a consequence, a back- meanders. . . ." Tinkler (1971, p. 281) offers a water eddy develops appearing as a whirl of reverse circulation of carbide granules or ink filaments (Morisawa, 1968, p. 139). It is at and just upstream of these eddies that point bars form (Fig. 15) at positions comparable to the younger and growing downstream portions of point bars in nature. Also, the distance between point bars in Figure 15 is approximately five to seven times the stream width which is in agreement with point spacing in nature (Leopold and others, 1964, p. 297). The me- andering thalweg seen as a dark thread of slow moving carbide granules at the bottom of the stream in Figure 15 is, paradoxically, "the line of maximum velocity" (Morisawa, 1968, p. 139) in the near surface levels of natural me- andering streams. This is reasonable, however, since it is along this line that water depth is Figure 15. Slightly asymmetrical meanders in greatest. stream turbid with silicon carbide sediment. Dark thread of slow moving sediment slightly out of phase Matthes (1947) has proposed a classification (downstream) with center line of stream can be dis- of eddy phenomena or secondary flow in cerned (compare with Figs. 10, 13) and marks location streams. His surge phenomena do not exist on of meandering thalweg in nature. This is also the line the stream plate because flow is held constant. of maximum velocity of surface waters since, in nature, Eddies or vortices are easily observed and have water depth is greatest along the meandering thalweg. already been described here. Bank and bottom Point bars just upstream of concave sides of bends are water rollers, which have vertical or horizontal at, and just upstream of, whirls of reverse flow where axes, respectively, were not observed. Bottom slow moving water filaments unable to overroll and rollers in straight streams have been the subject head for opposite side of stream take a reverse direction of flow and form eddies. They are also at positions of much speculation (see Leopold and others, comparable to younger and growing downstream por- 1964, p. 282-283; and Leliavsky, 1966, p. tions of point bars in nature. Downstream distance be- 177-187, for discussions), but I do not consider tween point bars is five to seven times stream width, them to be responsible for, or involved in, depending on where stream measured. Stream width, meander initiation (Gorycki, 1973). Matthes' —4 mm.

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possible explanation for the addition of pool- -riffle sequences as being "a function of variable effective discharges." That is, if the flow of a stream varies and at times its width becomes, and remains, reduced for a period of time, the retention of a certain pool spacing to stream width ratio would necessitate the devel- opment of additional pools along the stream channel. This suggests also that conditions of straight stream flow might be obtained in a channel having a meandering form as shown by / the pool and riffle form of the bed profile of both the straight and meander-like curved reaches of Rio del Ranchos near Talpa, New Mexico (Leopold and others, 1964, Figs. 6-7, Figure 16. Enlarged view of meander bend show- 6-8, p. 164-165) which could then develop ing main current overrolling (reversing helical flow) and changing direction at point (arrow) on concave into the "manifestly underfit" meandering bank where curvature radius is smallest compared streams "... contained in more amply mean- with rest of bend. It is h ire, and where other filaments dering valleys . .." as described by Dury (1970, farther downstream are overrolling, that in nature the p. 265). greatest amount of bank and channel erosion takes place and where water depth is greatest (see Fig. 14). However, no increase in the number of pool Stream width, 4 nun. sites occurs on the stream plate as meanders develop from the straight stream, nor can they main current occurs. Many aerial photographs be induced by varying the flow, for once the and topographic maps exhibit this generally meander pattern develops on the stream plate, ignored feature, suggesting the rate of change pool sites and associated structures remain in of direction in meander bends is not uniform. their proper positions with respect to the me- Unstable Meanders and Braided Streams. ander pattern. Even simulating low flow The instability of the experimental meandering stream conditions by reducing the flow and stream which rapidly changes course as the relative stream width for a fixed meander flow of water is increased beyond that necessary pattern or adding detergent to the water to induce meandering (Fig. 7) is reminiscent (which reduces the surface tension thereby of braided stream behavior in nature. Further, permitting the meandering stream to retain if the slope of the stream plate is increased for its width as the flow and depth are reduced) a fixed flow of water that is producing me- did not induce development of sinuous flow anders, there will be a transition to the unstable and, thus, an increase in pool number on condition. That meandering is an intrinsic established meander bends. In fact, there is property of stream flow suggests that braided always a reduction of pool sites during the streams result from the inability of easily transition from a straight to meandering stream eroded plain to contain an as shown by the change in pool spacing from unstable meandering stream in a single, more two to three stream widths to five to seven or less stable channel. That is, the stream has stream widths. This is the only point of ap- enough energy to anastomose and maintain parent noncorrespondence between natural several meandering or sinuous channels. Leo- streams and those produced on the stream pold and others (1964, p. 292-293) see "a close plate. relationship between braiding and meander- Another interesting aspect of the meanders ing" on the basis of mear.ders being commonly produced on the stream plate is that their radii present in braided streams. Leopold and Wol- of curvature generally are not constant within man (1970, Fig. 7.L4, p. 218) present data each meander bend. There often is a point on which indicates that if bankfull or each bend where the radius of curvature is slope (and presumably velocity) (Morisawa, quite small compared with the rest of the 1968, p. 149) are increased in streams in nature bend (Figs. 5, 7, 15, 16). Handy (1972) con- there will be a transition from a meandering siders the positions of meander loops best de- to a braided regime. Si.humm and Khan's fined by this point of maximum curvature — (1972) data taken from a laboratory flume also where overrolling of the fastest portion of the show that with increased slope there is an

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increase in velocity and shear or tractive force hydraulic drag and meandering, these inex- and a transition from a straight to meandering pensive, easily studied stream systems are thalweg to a braided channel occurs. They also especially suitable for classroom demonstrations show that increased sediment load causes an of the meandering process. increase in slope which results in the same ACKNOWLEDGMENTS transition. Therefore, the transition to unstable meanders on the stream plate apparently simu- I wish to thank Robert Gelber and George lates the initiation of the braided condition in Gorycki for their assistance in preparing the sediment absence. photographs used in this paper. CONCLUSIONS REFERENCES CITED The large number of points of correspon- dence between the experimental streams de- Dury, G. H., 1964, Principles of underfit streams: scribed here and those in nature and in hydrau- U.S. Geol. Survey Prof. Paper 452-A, 67 p. lic laboratories strongly suggests that the forces 1970, General theory of meandering valleys and underfit streams, in Dury, G. H., ed., involved in all are essentially similar. Conse- Rivers and river terraces: New York, Praeger quently, meanders apparently evolve from the Publishers, 283 p. sinuous flow effect of hydraulic drag already Fisk, H. N., 1947, Fine-grained alluvial deposits present in straight streams and require the and their effects on Mississippi River activity: attainment of a critical velocity and discharge U.S. Waterways Exp. Sta., 2 vols., 82 p. more commonly found in the lower reaches of Gorycki, M. A., 1973, Sheetflood structure: Mech- streams as shown by Leopold and Maddock anism of beach cusp formation and related (1953, p. 5, 13). Sinuous flow patterns and phenomena: Jour. Geology, v. 81. meander development will be inhibited if the Handy, R. L., 1972, Alluvial cutoff dating from subsequent growth of a meander: Geol. Soc. stream profile is too irregular or if the stream America Bull., v. 83, p. 475-480. is actively cutting downward and is deeply Keller, E. A., 1971, Pools, riffles and meanders: incised. Discussion: Geol. Soc. America Bull., v. 82, By definition (Leopold and others, 1964, p. p. 279-280. 281), meanders have been produced on the 1972, Development of alluvial stream chan- stream plate since the maximum sinuosity at- nels: A five-stage model: Geol. Soc. America tained (1.79) is greater than 1.5. Schumm and Bull., v. 83, p. 1531-1536. Khan (1972) state, "Experiments in the hy- King, C.A.M., 1966, Techniques in : draulic laboratories of the world have con- New York, St. Martin's Press, 342 p. Knighton, A. D., 1972, Meandering habit of supra- centrated on the phenomenon of meandering, glacial streams: Geol. Soc. America Bull., v. but, in fact, it has not been possible to induce 83, p. 201-204. a laboratory channel to develop a truly me- Leliavsky, S., 1966, An introduction to fluvial andering course." If we modify our concept of hydraulics: New York, Dover Publications, the meaning of the term "channel," Tanner 257 p.

(1960, 1962), with his simple apparatus, appar- Leopold, L. B.( and Langbein, W. B., 1966, River ently may have produced "a truly meandering meanders: Sci. American, v. 214, no. 6, p. course," but does not present quantifying 60-70. proof. The sinuosity produced on the stream Leopold, L. B„ and Maddock, T„ Jr., 1953, Hy- plate does not approach the value of 4 or more draulic geometry of stream channels and some physiographic implications: U.S. Geol. Survey occasionally seen in nature (Leopold and others, Prof. Paper 252, 57 p. 1964, p. 281). As a result, cutoffs and oxbow Leopold, L. B., and Wolman, M. G., 1960, River lakes cannot be simulated on the stream plate. meanders: Geol. Soc. America Bull., v. 71, This suggests that other influences such as the p. 769-794. inertia of moving stream water, condition of 1966, River meanders: Sci. American, v. 214, the banks, centrifugal forces, meander stability, no. 6, p. 60-70. and the like may affect meander forms in 1970, River channel patterns, in Dury, G. nature. H., ed., Rivers and river terraces: New York, Praeger Publishers, 283 p. It is surprising that Tanner's experiments Leopold, L. B„ Wolman, M. G„ and Miller, J. P., (1960, 1962) are not cited more often by 1964, in geomorphology: San workers interested in stream flow. Aside from Francisco, W. H. Freeman, 522 p. providing an insight into the mechanics of Matthes, G., 1947, Macroturbulence in natural

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streams: Am. Geophys. Union Trans., v. 28, 1962, Inexpensive models for studying helical no. 2, p. 255-261. flow in streams: Jour. Geol. Education, v. 10, Morisawa, M., 1968, Streams, their dynamics and no. 4, p. 116-118. morphology: New York, McGraw-Hill, 175 p. Tinkler, K. J., 1971, Pools, riffles and meanders: Schumm, S. A., and Khan, H. R., 1972, Experi- Reply: Geol. Soc. \merica Bull., v. 82, p. 281. mental study of channel patterns: Geol. Soc. America Bull., v. 83, p. 1755-1770. Tanner, W. F., 1960, Helical flow, a possible cause MANUSCRIPT RECEIVED BY THE SOCIETY JANUARY of meandering: Jour. Geophys. Research, v. 65, 26, 1972 p. 993-995. REVISED MANUSCRIPT RECEIVED JULY 6, 1972

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