Bed-load Transport of Mixed-size Sediment: Fractional Transport Rates, Bed Forms, and the Development of a Coarse Bed-surface Layer

Transcription

1 Utah State University Watershed Sciences Faculty Publicatins Watershed Sciences Bed-lad Transprt f Mixed-size Sediment: Fractinal Transprt Rates, Bed Frms, and the Develpment f a Carse Bed-surface Layer Peter Richard Wilcck Utah State University J. B. Suthard Fllw this and additinal wrks at: Recmmended Citatin Wilcck, P.R. and Suthard, J.B., Bed-lad transprt f mixed-size sediment: fractinal transprt rates, bed frms, and the develpment f a carse bed-surface layer. Water Resurces Research, 25(7): This Article is brught t yu fr free and pen access by the Watershed Sciences at DigitalCmmns@USU. It has been accepted fr inclusin in Watershed Sciences Faculty Publicatins by an authrized administratr f DigitalCmmns@USU. Fr mre infrmatin, please cntact dylan.burns@usu.edu.

2 WATER RESOURCES RESEARCH, VOL. 25, NO. 7, PAGES , JULY 1989 Bed Lad Transprt f Mixed Size Sediment' Fractinal Transprt Rates, Bed Frms, and the Develpment f a Carse Bed Surface Layer PETER R. WILCOCK Department f Gegraphy and Envirnmental Engineering, The Jhns Hpkins University, Bahimre, Maryland JOHN B. SOUTHARD Department f Earth, Atmspheric, and Planetary Sciences, Massachusetts Institute f Technlgy, Cambridge Fractinal transprt rates, bed surface texture, and bed cnfiguratin were measured after a mixed size sediment had reached an equilibrium transprt state fr seven different flw strengths in a recirculating labratry flume. Fractinal transprt rates were als measured at the beginning f each run when the bed was well mixed and planar. The start-up bservatins allw us t describe the variatin f fractinal transprt rates with bed shear stress fr a cnstant bed surface texture and bed cnfiguratin. The start-up and equilibrium bservatins tgether allw, fr the first time, an unambiguus descriptin f the mutual adjustment amng the transprt, the bed cnfiguratin, and the bed surface, as the transprt system mves tward equilibrium. We find that a substantial interactin exists amng the transprt, bed surface, and bed cnfiguratin. Bed frms and a carse surface layer cexist ver a range f bed shear stress. Under sme flw cnditins the size and shape f the bed frms are cntrlled by the presence f the carse surface layer. At higher flws the carse surface layer is eliminated by scur in the lee f the bed frms. If the bed surface is defined as that ver which the bed frms mve, a cherent relatin between the bed surface texture and the transprt grain size distributin may be defined. At equilibrium the transprt rates f all fractins were nt equally mbile, defined as identical transprt and bed grain size distributins, althugh equal mbility was apprached fr runs in which the bed shear stress was mre than twice that fr initial mtin f the mixture. Under sme flw cnditins the transprt was bserved t adjust away frm equal mbility as the bed adjusted frm a well-mixed start-up cnditin t an equilibrium state. Develpment f a partial static armr, wherein sme individual grains becme essentially immbile even thugh ther grains in the same fractin remain in transprt, is suggested t explain these adjustments between the transprt and bed surface grain size distributins. Cnstraints n equilibrium mixed size sediment transprt are defined. The special cnditins fr which equal mbility must hld and the relevance t natural cnditins f flume results and the equal mbility cncept are discussed. INTRODUCTION When sediment f a single size is transprted in the presence f bed frms, a strng interactin exists between the sediment transprt and the bed cnfiguratin. Bed frms are created by the mving sediment, and their size, shape, and speed depend n the sediment transprt rate. But the magnitude and directin f sediment transprt als varies in space and time with migratin f the bed frms. In the absence f a unifying mdel f sediment transprt and bed frm genesis and stability, transprt and bed cnfiguratin are best cnsidered as tw classes f mutually interacting, dependent variables: effrts t understand ne depend n an understanding f the ther. When a sediment bed cntains a mixture f grain sizes, an additinal class f dependent variable, the grain size distributins f the bed surface and the immediate subsurface, may vary during transprt. The transprt rates f individual size fractins (as well as the ttal transprt rate) depend n the ppulatin f grain sizes available fr transprt n the bed surface. At the same time the grain size distributin f the bed surface depends n the mbility f the varius grain sizes in the bed. Similarly, the texture f the bed surface may influence the grwth f bed Cpyright 1989 by the American Gephysical Unin. Paper number 89WR /89/89 W R frms by cntrlling the depth t which bed frm trughs may be scured, but intense flw in the lee f bed frms may als serve t break up srted bed surface layers at flws that might therwise prduce vertical bed srting. All three classes f dependent variable, that is, fractinal transprt rate, bed cnfiguratin, and bed grain size distributin, may have a strng mutual interactin, and the predictin f any ne cannt be accmplished withut predictin f the ther tw. In the past decade, renewed interest in the transprt f mixed size sediment has prduced imprtant new empirical and theretical results. Althugh sme f this wrk has included a discussin f the interactin between the grain size ppulatin f the bed and the fractinal transprt rates [e.g., Parker and Klingeman, 1982; Andrews and Parker, 1987; Iseya and Ikeda, 1987; Sutherland, 1987], few clearly interpretable data have been presented, a result f the difficulty f btaining and interpreting samples f the bed surface texture and f cmparing surface samples t vlumetric samples f the transprt r the bed sediment [Kellerhals and Bray, 1971; Day and Eggintn, 1983; Church et al., 1987; Diplas and Sutherhtnd, 1988]. The influence f bed frms n the mean fractinal transprt rates and vertical bed srting has been discussed nly recently [e.g., Klaassen et al., 1987; Wilcck and Suthard, 1987]. This paper intrduces new data taken t illustrate mre clearly the interac- 1629

3 1630 WILCOCK AND SOUTHARD' BED LOAD TRANSPORT OF' A MIXED SIZE SEDIMENT tin amng all three dependent variables. Experiments were made with a single mixed size sediment fr which the fractinal transprt rates, the bed surface grain size distributin, and the bed frms were measured. Measurements f the fractinal transprt rates were made when the bed surface texture and bed cnfiguratin had reached an equilibrium state. Because experimental runs were made at different flw strengths, we can investigate the adjustments amng the dependent variables fr different values f flw strength and ttal transprt rate. We als tk samples f the fractinal transprt rates at the beginning f the runs, when the bed was well mixed and planar and identical frm run t run. The start-up samples permit cmparisn f fractinal transprt rates at different values f bed shear stress fr cnstant cnditins f bed surface texture and bed cnfiguratin, and they allw the adjustments amng the three dependent variable grups t be clearly defined as the system changed frm a fixed start-up cnditin t a final equilibrium cnditin. By taking bed surface samples fr the start-up cnditins, we were als able t cmpare samples f the equilibrium bed surface texture t equivalent samples taken at start-up, thereby aviding the persistent and difficult prblems assciated with cmparing surface samples t vlumetric samples f the sediment bed r the transprt. As a cnsequence, we were able t measure unambiguusly the adjustment f the bed surface texture as the system adjusts tward an equilibrium cnditin. T ur knwledge the cmbinatin f bservatins presented in this paper has nt been made befre. Therefre these data prvide a unique pprtunity t describe the interactin amng bed cnfiguratin, bed surface texture, and fractinal transprt rates. The primary gal f this paper is t demnstrate this interactin and t prvide sme interpretatin f it that may serve as a basis fr further develpment f a general mdel fr mixed size sediment transprt. Because the fcus f this paper is n the interactin amng bed cnfiguratin, bed surface texture, and fractinal transprt rates as these variables underg a mutual adjustment t reach an equilibrium state, we must als clearly define any cnstraints n that equilibrium state. Central t this discussin must be the cncept f equal mbility which states that, fr equilibrium transprt cnditins, the grain size distributin f the bed and the transprt must be identical [Parker et al., 1982b]. That is, bulk samples f bed and transprt wuld be identical. If equal mbility were generally true, the directin and end result f a transprt system's adjustments tward equilibrium wuld be largely predetermined; the adjustments discussed in this paper culd fcus nly n the rate f adjustment and sme detail f the final bed texture that wuld prvide equal mbility fr all size fractins. That we d nt, in fact, find the transprting system adjusting in this way, indeed, under sme cnditins the system adjusts "away" frm equal mbility as it adjusts tward equilibrium, is nt a direct cntradictin f the equal mbility hypthesis, which, as nted by Parker et al. (1982a), is strictly true nly fr the special case f a sediment feed flume wherein the sediment bed is used as the feed material. Fr the field data f Milhus [1973], Parker et al. [1982b] suggested that equal mbility prvides a first apprximatin fr the relatin between the bed and transprt grain size distributins. In the discussin and debate f the equal mbility cncept that has fllwed, many have failed t appreciate that the hypthesis was nt ffered as physical necessity but as an apprximatin. It is wrth pinting ut that a majr sectin f the seminal paper [Parker eta!., 1982b] was devted t bserved deviatins frm equal mbility, including, fr example, plts f the variatin with bed shear stress f the fractinal transprt rates and D5 f the transprted sediment. Despite this, the equal mbility cncept is nw evlving int ne that states that a transprt system is nt at equilibrium unless the bed and transprt grain size distributins are equal. This is nt the case unless ne is willing t accept that a particular system perates strictly as a sediment feed flume that has adjusted t a cnstant sediment input. Because f the cntinued debate and ptential misunderstanding regarding the nature and cnditins fr equal mbility, and because the results f this paper wuld be impssible if equal mbility were generally true, a secnd gal f this paper is t set ut sme cnstraints and cnditins fr the equilibrium transprt f mixed size sediment. CONSTRAINTS ON EQUILIBRIUM MIXED SIZE SEDIMENT TRANSPORT Fr a transprting system t perate at equilibrium the sediment supplied t it must als leave the system at the same rate. If the transprted sediment cntains a mixture f grain sizes, the transprt rate f each size entering the system must be identical t that leaving the system. The surce f the sediment input t the system prvides a particularly imprtant cnstraint. The nature f this cnstraint can be illustrated using tw end-member cases: ne in which an input mixed size sediment transprt rate is independently impsed n the system and ne in which the input sediment lad is entirely determined by the sediment and flw prperties within the system. It is useful t examine these end-members because their impact n equilibrium mixed size sediment transprt can be replicated exactly in labratry flumes. Natural transprting systems cntain varying prprtins f these tw systems, depending n the time and space scales under cnsideratin. Here we try t define clearly the influence f the tw input mdes n the equilibrium transprt state and develp implicatins fr natural transprt systems. If the sediment input is independently impsed n the system, a strng cnstraint n the interactin between fractinal transprt and bed surface texture exists. If, fr a given flw and bed surface, the transprt rate f any fractin in the input sediment is smaller than its input rate, the system must adjust t increase the mbility f that fractin in rder t achieve equilibrium, because a state f equilibrium requires that all fractins are transprted at the rate with which they are input. As illustrated by the wrk f Parker and clleagues [e.g., Parker and Klingeman, 1982; Andrews and Parker, 1987], less mbile fractins may becme verrepresented n the bed surface, thereby increasing their mbility and permitting the system t apprach equilibrium. If significant amunts f the less mbile fractins are depsited, the slpes f the bed surface and water surface may als increase, thereby changing the system hydraulics in a directin that increases the mbility f the less mbile fractins, A Cmbinatin f bed surface texture and energy slpe is determined by the input sediment transprt rate and the inherent mbility f the different fractins in the mixture. A mre particular cnstraint exists if the bed sediment is fed

4 WILCOCK AND SOUTHARD: BED LOAD TRANSPORT OF A MIXED SIZE SEDIMENT 1631 la) lb) FINE COARSE % BED IN FINE COARSE FINE COARSE % BED IN F E CO RSE 1 [ FINE I COARSE I Fig. 1. Hypthetical transprt experiments using tw different bimdal sediment mixtures. Each mixture is run in tw different flumes, ne with the bed sediment fed at a cnstant rate (left) and the ther with the sediment recirculated (right). The carse fractin in bth mixtures is assumed t be immbile at the start f the experiment, the fine fractin is assumed t be mbile. (a) Bed sediment is 80% fine and 20% carse grains. (b) Bed sediment is 20% fine and 80% carse material. See text fr discussin f the develpment f cntrasting equilibrium bed and transprt states. int the system at a cnstant rate. In this case, the grain size distributin f the bed and transprt must be identical at equilibrium. This cnditin has been defined as equal mbility [Parker et al., 1982b; Parker and K!ingeman, 1982]. As made clear in the discussin by Parker et al. [1982a], equal mbility is a requirement nly under the special circumstances f equilibrium transprt in a perfect feed system where the bed sediment is used as the feed material. In a recirculating transprt system the input sediment is an intrinsic prduct f the system itself. The input and utput fractina; transprt rates must still be identical at equilibrium, but the input fractinal transprt rates are determined slely by the flw and the sediment within the system. There is n cupling between fractinal transprt rates and bed surface impsed by mass cnservatin requirements and the inherent mbility f the different fractins. The equal mbility cnstraint in a feed system can prduce equilibrium transprt cnditins very different frm thse f a recirculating system, even when the initial cnditins are made as similar as pssible. The different equilibrium cnditins arise frm variatins in mbility f the different size fractins and frm size-dependent vertical srting that ccurs when finer grains are able t wrk their way beneath catset grains in the bed. The impact f bth these prcesses n the equilibrium transprt state is illustrated with tw hypthetical experiments shwn in Figure 1. Tw identical flumes are used in each experiment, the nly difference being that ne is perated in a recirculating mde and the ther in a feed mde (using feed material equivalent t the sediment bed). Bth experiments invlve a mixture f tw size fractins, ne small and the ther large. Fr illustrative purpses we assume the small fractin t be mbile and the large fractin t be immbile under the initial flw and bed surface cnditins. The sediment in the first experiment (Figure la) cnsists f 80% (by weight) fine grains and 20% carse grains. In the recirculating system the immbile fractin simply remains n the bed in the prprtin represented in the bulk mixture. If the space between carse grains is entirely filled with fine grains, n vertical srting can ccur, and the transprted sediment must cnsist entirely f the fine fractin. In cntrast, the immbile carse fractin in the feed flume must be depsited n the bed. T reach an equilibrium state the carse fractin must becme mbile, either by increasing its prprtin f the bed surface r by building the bed slpe r bth. At equilibrium the carse fractin must cntribute 20% f the transprted sediment. The equilibrium fractinal transprt rates and the cmpsitin f the bed surface are very different in these tw cases, even thugh the same sediment bed and flw were used as initial cnditins. In the secnd experiment the bed sediment is changed t 20% fine grains and 80% carse grains (Figure lb). The fine grains are mbile and the carse grains immbile at the start f the run, as in the first experiment. In the recirculating flume the equilibrium bed surface and transprt rate are likely t nt remain the same as the initial cnditins, as they did in the first experiment. Vertical srting f the sediment may ccur in this case because the prprtin f fine grains is small, and there is sufficient space between the carse grains fr the fine grains t wrk their way beneath the carse, immbile bed surface. The final transprt rate can be zer in this case if the final bed surface cnsists nly f carse grains. In the feed case the bed surface and bed slpe must again adjust s that the equilibrium utput is the same as the input. In this case the bed surface will presumably build up with a depsit f carse grains until the shear stress is sufficient t mve them. At the same time the sediment bed must becme significantly verrepresented with fine grains s that the pre space is sufficiently filled and fine grains traversing the bed surface are nt immediately lst t the subsurface. Bth experiments shw that, even when starting with the same sediment bed and the same initial flw cnditins, the adjustments between fractinal transprt rates and bed surface texture, and the final equilibrium cnditin, differ strngly between the tw types f sediment input. Althugh the experimental cnditins in the first tw experiments are highly simplified, the interdependence amng grain mbility, bed surface texture, and bed slpe impsed by the feed system, as well as the vertical bed srting prcess, shuld als perate in mre realistic systems. Any feed system, including thse with a cntinuus grain size distributin and all sizes in mtin, are still subject t the equal mbility cnstraint. Vertical bed srting shuld prceed mre rapidly in a system where bth carse and fine fractins are in mtin because the mvement f carse grains will increase the number f fine grain depsitinal sites. Once equilibrium has been established in bth systems, ne culd begin a secnd phase f the experiments by

5 1632 WILCOCK AND SOUTHARD: BED LOAD TRANSPORT OF A MIXED SIZE SEDIMENT switching the feed and recirculating peratinal mdes between the tw flumes. The riginal feed system wuld have the feed input replaced by the flume utput. The new sediment feed t the riginally recirculating flumes wuld be set at the final equilibrium rate and cmpsitin achieved in the first part f the experiment. We expect that bth flumes wuld maintain the same equilibrium cnditins f hydraulics and transprt. These cnditins wuld be different between flumes because the tw systems evlved t a different equilibrium cnditin in the first phase f the experiment. Given these cnditins, a change in the input mde shuld nt be expected t prduce a change in the equilibrium develped between the bed and transprt. T say that each system can maintain the equilibrium results f the ther system als implies that the final equilibrium result is unique and culd be achieved by either system, even if the necessary initial cnditins are unknwn. T ur knwledge the independence f equilibrium transprt and sediment supply has nt been cnfirmed, in part due t the difficulty f arranging bth types f sediment peratin n a single flume. The bservatin that the adjustments amng transprt and bed surface texture may vary between feed and recirculating systems requires careful cnsideratin because natural transprt systems cntain aspects f bth sediment input systems in cmbinatins that depend largely n the time and space scales under cnsideratin in any particular prblem. Fr example, transprt ver lng time perids thrugh an entire river basin r acrss the cntinental shelf is clearly a feed system, althugh in these cases transprt will nt generally be at equilibrium. Many transprt prblems, r mdels, perate at a much smaller scale. A typical prblem might invlve predictin f sediment transprt rates ver a perid f minutes r hurs, given the bed grain size distributin and the flw cnditins. This prblem invlves mre f a recirculating cmpnent and appraches an entirely recirculating state if the bed sediment is relatively cnsistent ver distances cmparable t the distance traveled by the sediment under the time perid f interest. In such a case the transprt system may reach an equilibrium state ver a perid f hurs, and the prblem f predicting the transprt, given the bed and flw prperties, wuld be exactly mdeled by a recirculating flume. The purpse f this sectin is nt t advcate feed r recirculating simulatin f natural transprting systems r t shw that natural systems cntain either input cmpnent in sme knwn prprtin. Rather, this sectin is intended t present the cnstraints n equilibrium sediment transprt prvided by these tw end-member transprt systems and t draw implicatins regarding natural transprt. The hypthetical experiments were presented t illustrate that equilibrium transprt cnditins fr the tw input systems are, in general, nt equivalent and can be very different, even when starting frm initial cnditins that are as similar as pssible. Once equilibrium is established, the tw input mdes shuld maintain the equilibrium transprt cnditins prduced by either input mde. An additinal bservatin cncerning equilibrium mixed size sediment transprt cntributes t this discussin. Many mixed size sediments with unimdal r weakly bimdal grain size distributins perate clse t equal mbility in perfectly recirculating systems in the labratry [Wilcck and Suthard, 1988]. Nearly equal mbility in a recirculating system is nt the result f a cnstraint impsed by the sediment input but reflects a balance between mixture effects n fractinal transprt rates (grain hiding/expsure, relative bed rughness) and vertical srting. One can imagine anther experiment similar t thse in Figure 1 in which a cntinuus grain size distributin is used and all fractins are mbile. The bservatin given abve is that bth flumes wuld evlve t essentially the same equilibrium transprt cnditins. This bservatin, if general, is a disadvantage fr determining hw natural systems perate: if the mbility differences between fractins were enrmus, it wuld be bvius if a natural system had a predminantly feed r recirculating character as it adjusted t a near-equilibrium state. Hwever, the fact that many mixed size sediments appear t perate naturally near equal mbility is als an advantage in that the advantages f bth flume methds, and the cncepts behind them, may be applicable t natural transprting systems. The directin in which the transprt and bed surface texture adjust in appraching an equilibrium cnditin can be very different in feed and recirculating systems. This implicatin directly cncerns the results f this paper. In a feed system the adjustment is frced t an equal mbility cnditin. In a recirculating system this cnstraint des nt exist, and the adjustment is determined by the bed sediment, the flw, the mbility f the different fractins, and the vertical srting. If nly the sediment bed and flw cnditins are knwn, the final equilibrium cnditin cannt be determined withut knwledge f the type f input mde. The experiments reprted in this paper use a recirculating system. It shuld be clear frm the preceding discussin that the adjustments amng transprt and bed surface texture reprted in this paper are nt subject t any particular cnstraint due t the nature f the input sediment. A secnd imprtant implicatin regarding natural transprt cnditins cncerns the nature f equilibrium transprt: except fr perfect feed systems in which the bed sediment is used as input, a transprting reach need nt achieve equal mbility t achieve equilibrium. The recirculating experiments in Figure I reached an equilibrium state fr the flw and bed sediment invlved, but the equilibrium grain size distributin f the transprt and bed were cnsiderably different; the equilibrium system was nt clse t equal mbility. Natural transprt systems may apprach such a cnditin f equilibrium but nnequal mbility. Labratry bservatins suggest that equilibrium is reached in a perid f a few hurs fr recirculating systems [Wilcck, 1987]. When natural flw cnditins are cnstant fr a similar perid and the bed grain size distributin is relatively cnsistent ver distances crrespnding t the mean transprt f sediment during that perid, a natural transprt system can achieve a shrt-term equilibrium between the sediment bed and prevailing flw. This shrt-term equilibrium is best mdeled by a recirculating system and crrespnds well t the typical transprt prblem in which the initial cnditins f bed sediment and flw are given and the sediment transprt is t be predicted. The bservatin that the transprt grain size distributin is clse t the bed grain size distributin in sme field data led t the riginal frmulatin f the equal mbility hypthesis [Parker et al., I982b]. Because equal mbility can be strictly true nly fr a perfect feed system, the bservatin f nearly equal mbility in the field wuld supprt the cncept that sediment feed flumes prvide a gd apprximatin f

6 WILCOCK AND SOUTHARD: BED LOAD TRANSPORT OF A MIXED SIZE SEDIMENT 1633 TABLE 1. Hydraulic and Transprt Parameters Bed Shear Stress Ttal Transprt Rates Mean Velcity, Depth, r, Initial Equilibrium q,, Run cm/s Slpe cm Pa rdr q,, g/ms g/ms Bed Cnfiguratin n.a n.a plane plane tw-dimensinal tw-dimensinal tw-dimensinal tw-dimensinal tw-dimensinal dimensinal dunes dunes dunes dunes t threedunes quasi-equilibrium field transprt r that natural systems have a predminantly feed character. The bservatin that equilibrium mixed size sediment transprt in recirculating systems als prduces nearly equal mbility suggests that either kind f flume may represent natural systems, which cntain a cmbinatin f bth input mdes. The chice f input mde shuld depend n the specific questins t be addressed. The gal f this paper is t examine the free adjustment amng fractinal transprt rates, carse surface layers, and bed cnfiguratin, fr which the uncnstrained recirculating methd prvides a clear and efficient arrangement. Fr a given bed sediment, flw depth, and discharge we examine the adjustments amng fractinal transprt rates, bed surface texture, and bed cnfiguratin. EXPERIMENTAL METHODS We reprt here n seven experimental runs made with a single sediment. General hydraulic and transprt parameters fr each run are given in Table 1. The sediment had a mean size f 1.83 mm and a srting f 0.99, if grain size is expressed in 0 units (O84/O16 = 4.0). The grain size distributin was lgnrmal. The cumulative grain size distributin f the bed sediment is given in Figure 2. The sediment cnsisted almst entirely f quartz and near-quartz density minerals, and the density used in transprt cmputatins is 2.65 g/cm 3. The central prtins f the sediment mixtures are slightly mre angular (subangular versus subrunded) and f lwer sphericity than the tails. Apparatus The experiments were made in a flume with a rectangular channel 23 m lng, 0.6 m wide, and 0.3 m deep, with transparent sidewalls. Water and sediment were recirculated separately. The upstream 6 m f the channel cntained a false bttm at the same elevatin as the sediment bed. Sand mm in diameter (the mean size f the sediment mixture) was glued t the dwnstream 4.9 m f the false bttm t allw the bundary layer t develp befre it reached the mvable bed. The 16.2-m wrking sectin f the bed ended in a sediment trap that extended 25 cm in the flw directin and acrss the full width f the flume. All the transprted sediment fell int the trap and was returned, with a small discharge f water, t the head f the channel by an air-driven diaphragm pump thrugh a 2.5 cm (1 in.) tube. The trap caught virtually 100% f the passing sediment. Channel slpe was cntinuusly adjustable. The flw passed int the tailbx with n free verfall, s the vlume f water in the flume determined the mean depth f flw. Unifrm flw was maintained by adjusting the flume slpe. Water discharge was determined frm the calibrated head lss in a straight sectin f the return pipe. Mean flw depth and water surface slpe were determined frm water surface and bed surface elevatins read with a pint gage munted n a cart that traversed rails parallel t the flr f the channel. Transprt Sampling Sediment transprt was sampled by passing the watersediment mixture in the sediment return system thrugh a 20.3 cm (8 in.) sieve that trapped the sediment and allwed the water t return t the headbx thrugh the diaphragm pump. This was achieved by clsing a valve in the sediment return line between the trap and the pump and allwing the water-sediment mixture t flw under gravity thrugh a flexible tube int a large funnel that was itself cnnected t the sediment return system between the diversin valve and the pump. Sediment culd als be returned t the recirculatin system via the sample funnel, s that sampled sediment culd be replaced. During sampling perids all f the transprt was measured vlumetrically by emptying the sample frm the sampling sieve int a graduated cylinder. While a secnd sampling sieve was filling, the vlume f sediment in the graduate was measured, and the sample was returned t the recirculatin system. During the sampling perid all f the transprted sediment was sampled, except at very high transprt rates when we were nt able t keep pace and culd sample nly 30 s ut f every minute. The duratin f the individual samples varied frm 30-s subsamples t 1-hur samples f lw transprt rates. Sme vlumetric transprt samples were nt returned but saved t be dried, weighed, and sieved at 1/4-4> intervals. The retained samples were replaced by equal vlumes f sediment; usually this replacement sediment was material sampled earlier in the same run r during the previus run, s its grain size distributin was nt substantially different frm the sampled sediment. If bed frms were present, transprt rates were cmputed nly fr whle numbers f bed frms. The number f bed frms sampled varied frm ne (150-min. sample perid) t 17. The mean grain size distributin f the transprted lad was determined as a weighted mean fr many samples taken ver individual bed frms.

7 1634 WILCOCK AND SOUTHARD: BED LOAD TRANSPORT OF A MIXED SIZE SEDIMENT Bed Surface Texture Samples f the bed surface were taken using tw different techniques. The first invlved spray painting an area f the bed 12.7 cm in diameter with a mixture f paint and fine magnetite. Surface grains (defined as thse having any paint n them) were remved frm the sample with a strng hand magnet. Sme additinal separatin was necessary t remve unpainted grains that had adhered t painted grains during remval f the sample frm the bed. This technique [Wilcck and Stull, 1989] was develped because manual remval f painted grains finer than 1 r 2 mm was fund t be impssibly tedius. The secnd sampling methd invlved pressing a circular cylinder filled with mist clay nt the bed. The cylinder was the same size as that used as a mask fr painting the bed. The clay technique has been used by numerus authrs [e.g., Dhamtharan eta!., 1980; Kuhnle and Suthard, 1988]. We cllected samples using bth methds and fund them t give cmparable results, althugh the magnetic sampler appears t recver a slightly greater percentage f grains frm the middle and carse prtins f the grain size distributin. The slight difference between the tw samplers is presumably due t the inability f the clay sampler t pick up carser grains that have nly a small amunt f clay adhering t them. We prefer the magnetic paint technique because it allws direct bservatin f the sample and thereby prvides an accurate check that all grains n the surface have been sampled and that the sample cntains nly thse grains that were n the bed surface. A cnsiderable cntrversy exists as t whether areal surface samples, such as thse cllected by the paint r clay techniques, may be cmpared with samples taken vlumetrically, such as by remving a predetermined vlume f sediment frm the bed (see Church et al. [1987], and accmpanying discussins and reply, fr a recent summary f the prblem). The essence f the prblem is whether the prprtin in each fractin must be multiplied by the factr I/D, as riginally prpsed by Kellerhals and Bray [1971] and recently cnfirmed by Church et al. [1987]. A number f authrs have fund the 1/D crrectin t give results that are biased tward the finer sizes [e.g., Prffitt and Sutherland, 1980]. Diplas and Sutherland [1988] prvide theretical and experimental supprt fr a crrectin factr based n D /2 Unfrtunately, the cntrversy regarding crrectin factrs fr surface samples has becme intermeshed with the issue f whether the surface f a mixed size sediment bed may carsen during equilibrium transprt [e.g., Parker eta!., 1982b; Day and Eggintn, 1983]. Because the adjustment f the bed surface texture is f direct imprtance t this paper, and because we d nt have a definitive slutin t the prblems f crrectin techniques fr bed surface samples, we have chsen t sidestep the prblem by making cmparisns nly amng samples taken with identical techniques. Transprt samples are cmpared nly with each ther and use the vlumetric grain size distributin f the sediment mixture as a reference. Surface samples are cmpared nly t ther surface samples and then nly t samples taken with the same sampling device (clay r paint). These samples use as a reference the mean f five surface samples taken With each methd frm the bed at its start-up cnditin. Althugh limiting urselves in this fashin prevents us frm making direct cmparisns between particular transprt and bed surface grain size distributins, it des allw us t make unambiguus cmparisns f the different transprt and bed surface grain size distributins, which is ur intentin in this paper. Prcedure The sediment bed was mixed and screeded t a plane bed 7 cm thick befre each run. A mixing prcedure was fllwed in which the sediment was first hmgenized by hand in half-meter segments alng the channel, then half the sediment in each segment was exchanged with that f ther segments fllwing a predetermined recipe, and finally the sediment was rehmgenized in each segment. The flume was then filled slwly with ht and cld water t achieve a temperature between 24 ø and 26øC. This temperature was maintained during runs by adding small vlumes f ht r cld water t the flume; a cnstant water vlume (and hence flw depth) was maintained with an verflw pipe in the tailbx. T prduce an initial sediment bed that was cnsistent frm run t run, the flume was next run fr 30 min. at a mean velcity f 41 cm/s and a flw depth f 11.2 cm. This flw prduced a very lw transprt rate (<<0.01 g/ms) that was just sufficient t mve grains (f any size) that were left in particularly unstable psitins by the screeding prcess. Fllwing this preparatin, the run was immediately begun by adjusting the flume slpe and discharge t the desired values. Previus experience with the flume and sediment allwed the slpe t be set immediately t the value necessary fr unifrm flw at the start f the run. One run cnsisted nly f the 30-min. preparatry flw, after which the flume was drained and samples f the bed surface were taken. Sampling f the transprt rate began five min. after the start f the run. The duratin f these samples varied frm 1 t 30 min., depending n the transprt rate. N bed frms were present during any f the initial samples included in this paper. Measurements f equilibrium flw and sediment transprt were made nly after lng-term steady transprt became established. In previus experiments [Wilcck and Suthard, 1988], equilibrium was judged by the absence f lng-term variability in the flw prperties (related t the develpment f a stable bed cnfiguratin) and in the size distributin f the transprted sediment (related t the develpment f a stable grain size distributin n the bed surface). T avid any significant impact n the sediment bed and transprt rates during the run, intermediate samples were nt taken, and final equilibrium was assumed t have been established when the run duratin was greater than r equal t sufficient values in previus runs. While the transprt sampling was underway, the water surface elevatin was read, and the head lss in the return pipe was measured fr later cnversin t water surface slpe and discharge. After each run the flume was drained, the bed was described, a prfile f the bed elevatin alng the flume centerline was made, and bed surface samples were taken. Initial Cnditins EXPERIMENTAL RESULTS The grain siz e distributins f the transprt Samples taken at the beginning f each run are shwn in Figure 2. Data fr the range 1.0 < r/% < 1.7 are available, where r is the mean bed shear stress and r = 0.9 Pa was determined as the value

8 WILCOCK AND SOUTHARD: BED LOAD TRANSPORT OF A MIXED SIZE SEDIMENT z zz: GRAIN SIZE (mm) GRAIN SIZE (mm) Fig. 2. Grain size distributin f transprt samples taken at the beginning f five flume runs. The size distributin f vlumetric samples f the bulk sediment mix is given as a reference. Fig. 3. Grain size distributin f transprt samples taken at the end f all flume runs, when the bed surface and bed cnfiguratin had reached an equilibrium state. The size distributin f vlumetric samples f the bulk sediment mix is given as a reference. f r where the ttal transprt rate appraches zer [Wilcck, 1988]. At the lwest transprt rates the finer fractins f the sediment mixture are underrepresented in the transprt cmpared t their prprtin in the bed sediment mix. The prprtin f finer fractins in transprt increases with shear stress until it is essentially equivalent t the bed mixture at r -> 1.5r,.. The carser prtin f the sediment mixture is als underrepresented in the transprt at the lwer transprt rates, and its prprtin f the transprted sediment increases with shear stress but is still underrepresented at the higher transprt rates measured. These results shw that near incipient mtin the finer and carser size fractins are less mbile than the central size fractins. This difference in mbility decreases with r, disappearing altgether fr the finer fractins, but nt the carser fractins, at the higher values f r/r,. we measured. The data available d nt make clear whether the carser fractins wuld achieve equal mbility at a higher shear stress, althugh the trend f the data pint in that directin. Because the bed surface is the same fr each run in Figure 2, it may be seen clearly that the mbility f individual size fractins varies with grain size and that this size-dependent variatin in mbility itself depends n the shear stress acting n the bed, with the prprtin f bth finer and carser fractins increasing in the transprted sediment at higher shear stresses. Equilibrium Cnditins Fractinal transprt rates. The grain size distributins f transprt samples taken after the transprt reached equilibrium are shwn in Figure 3. The variatin f the transprt grain size distributin with bed shear stress is mre cmplicated than in the start-up case. At the run nearest incipient mtin the prprtin f the finer fractins is very clse t that in the bed. As the shear stress increases, the prprtin f the finer fractins first decreases, but then, abve the prprtin f the finer fractins increases and slightly exceeds that f the bulk sediment mix at the tw highest flws tested. The carsest fractins are underrepresented in the run clsest t incipient mtin. As r increases, the prprtin f carse fractins decreases until abut then increases with further increase in r and appraches, but des nt reach, equal mbility even at the highest shear stresses tested. As in the start-up case, the mbility f the varius fractins changes with bed shear stress, althugh in the equilibrium case the bed surface texture als varies frm run t run. Figures 2 and 3 allw a cmparisn f transprt grain size distributins between a well-mixed sediment bed with a cnstant grain size distributin and a bed allwed t reach an equilibrium bed surface texture. In bth cases there is a general increase with bed shear stress in the prprtin f fine and carse fractins in transprt. The finer fractins reach equal mbility in bth cases, althugh at a higher shear stress when the bed has reached an equilibrium bed surface texture. The carse fractins in bth cases d nt reach equal mbility ver the range f r/r,. we measured. The relative mbility f the different sizes in a mixture clearly varies with bed shear stress, whether ver a cnstant bed surface grain size distributin r ver a bed surface texture that is allwed t adjust t an equilibrium state. The equilibrium samples differ frm the start-up samples in that the prprtin f bth fine and carse fractins decreases with increasing shear stress fr the runs immediately abve incipient mtin. The implicatins f this bservatin will be discussed further, nce the adjustments f the ther dependent variables are presented. An alternative presentatin f the transprt grain size distributins is given in Figure 4, which plts the fractinal transprt rates as a functin f grain size. Fractinal transprt rates are cmputed as q, = (p/f,.)q,, where p is the prprtin f each fractin in transprt, i- is its prprtin in the bulk bed sediment mix, and q, is the ttal transprt rate. Because the value f q, is the same fr each fractin in a run, Figure 4 gives the transprt grain size distributin in the frm f P/Ji' scaled by the ttal transprt rate. Figure 4 prvides a very clear presentatin f the shift in transprt grain size distributin with increasing shear stress and transprt rate and makes the prprtins f the middle size fractins clearer. Bed sm /bce grain size distributin. Samples f the bed surface texture were taken fllwing each run. When bed frms were present, the samples shwn here were taken

9 ß. _ WiLccI AND SOUTHARD: BED LOAD TRANSPORT OF A MIXED SIZE SEDIMENT 8 mm 4 mm 2 mm 1 mm 0.5mm 100 : -': '_. [ P, 10 z (g/ms) 1 it' ' FO Run1 (4 samples) Iv Run 2 (5 samples) [ Ja, Run 3 (3 samples) / /' [O Run 4 (3 samples) /!,4', [[3 Run 5 (3 samples) / [# Run 6 (1 sample) / [4. Run 7 (1 sample) l 40'.1 muj.01 20'. '... i GRAIN SIZE (mm) GRAIN SIZE (1 UNITS) Fig. 6. Grain size distributin f equilibrium bed surface samples taken with the clay sampler at the end f all flume runs. When Fig. 4. Fractinal transprt rates at the end f all flume runs. bed frms were present, the surface sampled was the bed frm Because qb is a cnstant fr each fractin in a run, the trends trugh. The mean size distributin f clay samples taken frm the represent the grain size distributin f the transprt in the frm p/f,.. start-up bed is given as a reference. The number f samples used t Plt symbls same as Figure 3. prduce the pltted grain size distributin is shwn in the figure legend. frm the bed frm trughs. The trughs frm the expsed prtin f the surface ver which the bed frms mve and therefre represent the surface n which, r thrugh which, size-dependent exchange f sediment may ccur as the bed adjusts tward equilibrium. Figure 5 presents cumulative grain size distributins fr magnetic paint samples taken frm runs I thrugh 5. Each grain size distributin curve represents the mean f a number f samples, which is shwn in the figure legend. The bed surface grain size distributin fr the 30-min. start-up run is shwn as a reference. The fine and carse fractins shw a similar and cnsistent increase in prprtin with increasing bed shear stress, althugh the prprtins f the fine and carse fractins present in the bed are different. The finer loo Run 1 (4 samples) i Run 2 (5 samples) Run 3 (3 samples) Run 4 (3 samples) Run 5 (3 samples) Start-up (5 samples GRAIN SIZE (mm) Fig. 5. Grain size distributin f equilibrium bed surface samples taken with the magnetic paint sampler at the end f five flume 0 fractins are underrepresented with respect t the start-up cnditin at the lwest flws and then apprach the wellmixed start-up cnditin as the flw increases. In cntrast, the prprtin f carse fractins n the bed surface after the first run is essentially identical t the start-up cnditin. As the flw increases, the carse fractin becmes increasingly verrepresented with respect t the start-up cnditin. Previus discussins f the develpment f an equilibrium carse surface layer have been criticized because bed surface samples were cmpared t the bulk mix, thereby invlving a cmparisn between areal and vlumetric bed samples [Parker, 1980; Parker et al., 1982b; Day and Eggintn, 1983]. Because f this sampling prblem the actual existence f an equilibrium carse surface layer was questined [Day and Eggintn, 1983]. Because the same sampling methd was used fr bth the start-up and equilibrium samples, Figure 5 clearly shws that the bed surface layer carsens during adjustment tward equilibrium. The magnetic paint methd had nt been devised at the time runs 6 and 7 were made, althugh individual samples f the bed surface were taken with a clay sampler. Figure 6 presents cumulative grain size distributins fr these individual samples, as well as the mean f clay samples taken after the five runs shwn in Figure 5. The trends fr the lwer five runs are similar t, if mre scattered than, thse in Figure 5, but the equilibrium bed surface texture in runs 6 and 7 is cnsiderably finer and similar t the well-mixed start-up bed surface. Because nly single samples were taken f the bed after these tw runs, the exact grain size distributins are less accurate than thse fr the weaker-flw runs. The surface textures fr runs 6 and 7 d, hwever, appear t represent faithfully the equilibrium bed cnditin, which we bserved t be distinctly finer at the strngest flws and nt particularly different frm the bulk sediment mixture. runs. When bed frms were present, the surface sampled was the Figures 5 and 6 bth shw thathe prprtins f fine and bed frm trugh. The mean size distributin f magnetic paint samples taken frm the start-up bed is given as a reference. The carse fractins in the equilibrium bed surface texture innumber f samples used t prduce the pltted grain size distribu- crease with flw strength up t rughly 2r,.. With increasing tin is shwn in the figure legend. r, the fine fractins apprach a prprtin equivalent t that

10 WILCOCK AND SOUTHARD' BED LOAD TRANSPORT OF A MIXED SIZE SEDIMENT 1637 loo 200 8O (Clay Samples: Reference 81%<4.0 mm ) 180 Z G 160 (Magnetic Samples: Reference 80%<4.0 mm,) (/) 140 6O 4O %<4.0 mm (clay) [] %<1.0 mm (clay) 4, %<4.0 mm (mag) # %<1.0 mm (mag) u_ 100 rn 80 2O 0 1 (-Clay Samples: Reference 13%<1.0 mm ) ;;.g '"'- [] a m R ( Magnetic Samples: Reference 10ø/<1.0 mm ) 115 ' % / ' ½ Fig. 7. Variatin in equilibrium bed surface texture with r/r,, the rati f mean bed shear stress t the critical shear stress fr incipient mtin f the sediment bed. Plt symbls represent the percent finer than 4 and 1 mm fr bth clay and magnetic paint samples. Crrespnding values fr the start-up cnditins are prvided as a reference and are represented by hrizntal lines. 600 f the well-mixed start-up bed, while the carse fractins becme increasingly verrepresented. At r > 2r, the carse surface layer is cmpletely brken up; bth fine and carse fractins are present n the bed surface in a prprtin clse t that f the well-mixed bed. Figure 7, which shws the percent in the bed surface samples finer than 4.0 and 1.0 ms, illustrates these pints mre clearly. The reference lines crrespnd t the mean values determined frm five samples f the start-up bed surface using the magnetic and clay samplers. The prprtin f grains finer than 1.0 mm increases frm arund 3% near incipient mtin t the wellmixed cnditin (10% fr the magnetic samples, 13% fr the clay samples) at r < 2r,.. The prprtin f grains carser than 4.0 mm increases frm near start-up cnditins (21% fr the magnetic samples; 19% fr the clay samples) clse t incipient mtin t rughly 35% at r 1.4r,.. At the highest flw strengths the prprtin f these carse grains drps t less than 20%, which is cmparable t the reference value within the errr assciated with these tw individual samples f the bed surface texture. Bed cnfiguratin. Figure 8 presents the dimensins f the equilibrium bed frms fr each run with bed frms in Table 1 plus additinal runs made with the same sediment mixture. The bed was planar in the lwest runs. Abve r 1.3%, lng, lw dunes frmed with relatively straight, flwperpendicular crests. The bed frm crests became mre irregular in shape and rientatin at the highest flw strengths, althugh they remained essentially flw perpendicular at all flws. The variability in bed frm height and trugh depth als increased with flw strength. In the strngest flws, bed frm height cmmnly varied frm 1 t 6 cm acrss the 60 cm width f the flume. The spacing f the bed frms decreased with flw strength frm almst 200 t cm. The height f the bed frms increased with flw strength frm apprximately D,,, (0.185 cs) at lw flws t 8D,, (1.5 cs) at the highest flws. The changes in spacing and height caused the bed frms t increase in steepness, with the rati f spacing t height decreasing t a fairly cnstant value f at r > l.sr, MEAN CHANNEL VELOCITY (cm/s) Fig. 8. Bed frm spacing, height, and height-t-spacing rati fr all runs with bed frms. Fr better cverage the plt includes results frm three runs with the same sediment that are nt discussed in this paper. ADJUSTMENTS OF FRACTIONAL TRANSPORT RATES AND BED SURFACE TEXTURE As shwn in Figures 9 and 10, mst f the apparent adjustment between the fractinal transprt rates and the bed surface texture ccurs in the finest and carsest frac- tins. Figure 9 presents the initial (slid symbls) and equilibrium (pen symbls) fractinal transprt rates fr runs 1-5, as a functin f grain size. Again, because q, is a cnstant fr each fractin in a run, plts f q,i prvide a grain size distributin in the frm f p/f,. versus grain size. The equilibrium fractinal transprt rates fr runs 6 and 7 are als shwn in Figure 9. N initial transprt samples were taken fr these runs. Figure 10 presents the initial and equilibrium bed surface grain size distributins fr all runs. Magnetic samples are used fr runs 1-5; clay samples fr runs 6 and 7. The initial bed surface samples shwn are the mean f five magnetic samples fr runs 1-5 and the mean f five clay samples fr runs 6 and 7. The equilibrium bed surface grain size distributins fr runs 6 and 7 represent nly a single clay sample fr each run, s mre errr may be assciated with these tw equilibrium distributins than with the equilibrium distributins in runs 1-5, which represent the means f several bed samples. Figure 11 presents the variatin with r/r, f the percent finer than I and 4 mm in bth initial and equilibrium transprt samples. It is similar t Figure 7 in that it illustrates

11 1638 WILCOCK AND SOUTHARD: BED LOAD TRANSPORT OF A MIXED SIZE SEDIMENT 8mm 4 mm 2 mm 1 mm.5 mm loo Run 7 lo lo un mm 4mm 2 mm 1 mm 0.5 mm -, Run 5 lo 1 10 Run 6 Run Run 5.Ol Run 3 z uj uj Run 4 : : : : : ß : ß :! :!.' I -' I -' Run 2,Ol.Ol Run GRAIN SIZE (O UNITS) Fig. 9. Fractinal transprt rates fr initial and equilibrium cnditins in all runs. Slid symbls are initial fractinal transprt rates; pen symbls are equilibrium fractinal transprt rates. Transprt rates were nt sampled at the beginning f runs 6 and 7; initial fractinal transprt rates fr these runs may be assumed t be clse t equal mbility and hence clse t the final fractinal transprt rates. the variatin f the amunt f fine and carse sediment in transprt with bth shear stress and time. Carser Fractins Runs 1-5. As the bed and transprt adjusted tward equilibrium in these runs, the prprtins f the carse fractins in transprt and in the bed surface adjusted in ppsite directins. The percent f carse fractins in transprt decreased with time fr these runs (Figures 9 and 11). The prprtin f carse fractins present n the bed surface increased with time (a carse surface layer develped; Figures 7 and 10). This result cautins against the simplistic cnclusin that an increase in the representatin f a particular fractin n the bed surface represents a crrespnding increase in its fractinal transprt rate. The degree f this cunterintuitive adjustment decreases with r. That is, the extent f develpment f a carse surface layer increases with r, and the time-dependent decrease f carse fractins in transprt decreases with r. This suggests that the cause f the seemingly cntrary adjustment f carse fractins n the bed surface and in transprt is mre prevalent as r appraches r,.. Our explanatin invlves tw pints: the prprtin f immbile grains n the bed surface and the depth f the bed GRAIN SIZE (O UNITS) Fig. 10. Bed surface grain size distributins fr initial and equilibrium cnditins in all runs. Pltted is the percent in each fractin against grain size. Slid diamnds are initial cnditins. Open symbls are equilibrium cnditins. Magnetic paint samples used fr bth initial and equilibrium cnditins fr runs 1-5. Clay samples used fr runs 6 and 7. Only ne sample was taken frm the equilibrium bed surface in runs 6 and 7; the means f multiple samples were used fr all initial cnditins and the equilibrium cnditins in runs 1-5. layer cntributing t the transprt. Even thugh sme grains f all size fractins are fund in transprt in all f ur runs, sme f the individual carse grains will, as the run prgresses, find stable resting places and becme essentially immbile, frming a partial static armr. A similar partial armring was described by Prffitt and Sutherland [1980; 1983]. althugh in their case the partial armr was bserved during the prcess f cmplete armr develpment (n sediment input), whereas the partial armr suggested here is present n an equilibrium transprt surface. The prprtin f immbile grains in any fractin presumably increases as r appraches r,. Althugh we made n explicit test f the number f immbile carse grains, we did nte n ccasin that particular grains in the carse surface layer did nt

12 WILCOCK AND SOUTHARD' BED LOAD TRANSPORT OF A MIXED SIZE SEDIMENT 1639 z "r' I- n' 60 z LLI 40' loo] 20 BULK MIX: 86%<4.0 %<1 mm equilibrium! %<4 mm initial! %<4 mm equilibriurnj ; / 1; c mm BULK MIX: 19%<1 mm Fig. 11. Variatin f initial and equilibrium transprt grain size distributins with 'h',. Plt symbls represent the percent finer than 4 and I mm in transprt. Crrespnding values fr vlumetric samples f the bulk sediment mix are given as hrizntal lines. mve ver perids f hurs r did nt mve as successive bed frm trughs mved past them. As a run prgressed, the number f carse grains in the static armr shuld have increased, as individual grains fund stable resting places n the bed surface, s the prprtin f carse grains in transprt can decrease with time. These time-dependent relatins shuld becme less apparent at strnger flws if fewer carse grains becme immbile as -increases. Bed frms were present in runs 3, 4, and 5 and increased in size with -. The bed frms expsed a larger number f carse grains t active transprt. Size-dependent vertical srting can then serve t cncentrate these catset grains n the bed surface ver which the bed frms mve. The bed frms act t "mine" the bed fr catset grains, a disprprtinate number f which are left n the bed surface. Runs 1 and 2, which had a plane bed at equilibrium, shwed nly negligible carsening f the bed surface. The next three runs, which had lng, lw dunes, shwed a distinct carsening f the bed surface. Althugh a partial static armr explains the decrease with time f carse fractins in transprt, any decrease in this trend as -increases can be explained by bth bed frm "mining", increasing the prprtin f carse grains n the bed surface, and increased -, reducing the prprtin f immbile grains n the bed surface. It is wrth nting that this interpretatin f the mutual adjustment between the bed surface and the transprt wuld nt be pssible within the paradigm that the prprtin f each fractin present n the bed surface reflects an adjustment that prduces equal mbility fr each fractin. This prblem is well illustrated by the fact that we bserve the carse surface layer t becme better develped with -, a trend that cntrasts with the mbile armring mdel ffered by Parker and Klingeman [1982] and Andrews and Parker [1987]. This mdel is based n the premise that inherent size-dependent differences in mbility are greatest at -,. and decrease with increasing -, a trend we als bserve, mst clearly in ur start-up samples. If equilibrium transprt requires equal mbility, the bed surface texture must cmpensate fr these differences, and the carse surface layer shuld be best develped near -,. and decrease in strength as -increases. We d nt bserve this trend in ur data because a recirculating system need nt achieve equal mbility t achieve equilibrium transprt. In ur runs the prcesses leading t a carse surface layer, which include the develpment f a partial static armr, vertical bed srting, and bed frm mining f carse grains, prduce a strnger carse surface layer as -increases, at least t the pint where the carse surface layer is entirely brken up by the intense flw in the lee f bed frms. Runs 6 and 7. N carse surface layer was evident at the cnclusin f these runs, and n verrepresentatin f carser fractins was fund in the bed frm trughs (Figures 7 and 10). The carse-fractin transprt rates apprached, but did nt reach, equal mbility in these strngest runs (Figures 9 and 11). Because n carse surface layer was present, these runs frm an apprximate cntinuatin f the well-mixed initial cnditin prtins f runs 1-5. The startup transprt size distributins f runs 1-5 and the equilibrium transprt size distributins f runs 6 and 7 shw a steady increase in the mbility f the carsest fractins. Finer Fractins Runs 1-5. The fractinal transprt rates f the finer fractins decreased with time fr each f these five runs (Figure 9). With the exceptin f run 1, the prprtin f fine fractins in transprt als decreased frm initial t equilibrium cnditins (Figure 11). The prprtin f fine fractins in run 1 was able t increase while its fractinal transprt rate decreased because the ttal transprt rate decreased dramatically with time, indicating the develpment f a partial static armr. The prprtin f fine fractins n the bed surface decreased with time in runs 1 and 2 and remained relatively cnstant in runs 3, 4, and 5. Fr runs 1 and 2, bth f which have planar equilibrium bed surfaces, the prprtin f fine grains in transprt and n the bed bth decreased with time. Fr runs 3, 4, and 5 the prprtin f fine grains in transprt als decreased with time, even thugh the prprtin f fine grains n the bed surface did nt change with time. This suggests that sme prprtin f the finer grains frm part f the partial static armr and are hidden frm the flw by larger neighbring immbile grains. The fine grains are cncentrated within and belw the carse trugh surface, having been preferentially extracted frm the transprting sediment which is mving as bed frms ver the bed (trugh) surface. It is wrth nting that in runs 3, 4, and 5 the fine fractins were nt preferentially remved frm the bed surface and depsited in a fine sublayer. Rather, their decreased mbility appears t be due t decreased flw expsure and increased relative bed rughness related t the carse partial static armr. Runs 6 and 7. The prprtin f finer grains n the bed surface was essentially unchanged frm the well-mixed start-up bed cnditins t the equilibrium cnditins (Figures 7 and 10). The equilibrium transprt f the finer fractins was clse t, r slightly greater than, equal mbility. Althugh we did nt sample the transprt at the beginning f these runs, it is likely that the prprtin f fine fractins in transprt was near equal mbility, because the fine fractins were near equal mbility fr the well-mixed start-up bed cnditins f runs 4 and 5, as well as fr the well-mixed equilibrium bed cnditins in runs 6 and 7. Thus it seems likely that the fractinal transprt rates f the finer fractins, like their prprtin f the bed surface, changed

13 1640 WILCOCK AND SOUTHARD: BED LOAD TRANSPORT OF A MIXED SIZE SEDIMENT little frm start-up t equilibrium cnditins. In these strngest runs, differences in mbility (whether inherent r related t vertical srting) disappeared as the bed surface became mre hmgeneus. THE ROLE OF BED FORMS IN THE ADJUSTMENT OF FRACTIONAL TRANSPORT RATES AND THE COARSE SURFACE LAYER Bed frms may bth influence and be influenced by the develpment f a carse surface layer. In runs 3, 4, and 5, well-develped dunes cexisted with a distinct carse surface layer. The carse surface layer, by prviding a relatively immbile surface belw which bed frm trughs may nt scur, may serve t limit the height f the bed frms, the depth f the bed frm trughs, and the variability in bed frm size. At these flw strengths the bed frms may actually play a rle in limiting their size range by increasing the number f carse grains expsed t active transprt, thereby prviding mre grains with which t armr the bed surface. Prir t these runs, it was nt clear whether bed frms and carse surface layers were mutually exclusive, with a carse surface layer inhibiting the develpment f bed frms r the intense flw in the lee f bed frms preventing develpment f any carse surface layer. At the highest flw rates we measured (runs 5 and 6), flw in the lee f the bed frms did becme sufficiently strng t break up the carse surface layer. Even withut the presence f bed frms, it is pssible that the carse surface layer wuld vanish at higher flws because the size-dependent differences in grain mbility and the strength f a partial static armr wuld bth decrease with r. The presence f intense flw in the lee f the bed frms may cause the carse surface layer t break up at a lwer r than wuld ccur withut bed frms. It is difficult t test the bed frm effect in any definitive manner because bed frms are an inherent and inextractable part f the transprt prblem fr thse sediments in which bed frms naturally ccur. Any means f suppressing bed frm grwth wuld invlve imprtant changes t the entire transprt system that wuld prevent direct cmparisns. LIST OF CONCLUSIONS 1. We measured fractinal transprt rates abve a wellmixed sediment bed that was identical frm run t run. We fund that the fine and carse fractins are smewhat less mbile (p/f. < 1) than the central fractins and that this size-dependent difference in mbility decreases as the bed shear stress increases. The fine fractins reach a cnditin f equal mbility (p/f. = 1) at r > 1.5r,.; the carse fractins apprach, but d nt reach, equal mbility fr the range f flws fr which we cllected transprt samples frm the well-mixed start-up bed (r < 1.75r,). Because the bed surface was identical frm run t run, we can clearly demnstrate that the mbility f individual size fractins depends n bth grain size and flw strength. 2. At values f r < 2r,, when the bed and transprt adjust frm the well-mixed start-up cnditin tward an equilibrium cnditin, the mbility f the fine and carse fractins cnsistently decreases with time, mving away frm a cnditin f equal mbility. This prcess cannt be explained with a cnceptual mdel that states that all size equal mbility nly in the special case f a perfect feed system in which the material f the sediment bed is used as the feed material. Feed and recirculating flumes can prduce very different equilibrium transprt cnditins, even when the same initial flw and sediment bed are used. In nnfeed systems, equilibrium transprt may ccur at cnditins far frm equal mbility, as demnstrated in ur experiments. 3. The decrease in mbility f the fine and carse fractins as the system adjusts tward equilibrium is explained by the develpment f a partial static armr, wherein sme prprtin f grains frm the carse fractins find stable resting places and becme effectively immbile, even thugh grains frm all fractins are still fund in transprt. The develpment f a partial static armr als appears t decrease the mbility f the fine fractins, which are underrepresented in the transprt even thugh they are nt underrepresented n the bed surface. 4. The degree t which the equilibrium transprt departs frm equal mbility decreases as the bed shear stress increases. This trend is attributed t a decrease in the size- dependent variatin in grain mbility at higher r (demnstrated by a similar variatin in ur start-up runs), the disappearance f a partial static armr as the prprtin f immbile grains decreases, and the scur f any srted bed surface by mving bed frm trughs. 5. We have clearly demnstrated that a carse surface layer can develp as a mixed size sediment bed adjusts tward equilibrium transprt. This carse surface layer need nt serve as a regulatr f the mbility f different size fractins except in the special case f a sediment feed flume. Its presence in ur recirculating flume data is a result f size-dependent variatin in grain mbility, develpment f a partial static armr, and a gemetrically necessary vertical srting prcess that ccurs when at least sme f all sizes are in mtin. Bed frms als cntribute t the develpment f a carse surface layer by increasing the supply f carse grains available fr transprt. We bserved the carse surface layer t becme better develped as r increases, up t the pint where intense flw in the lee f bed frms breaks up any surface grain size srting. This trend in the develpment f a carse surface layer is nt pssible in a feed system, which must perate at equal mbility t achieve equilibrium transprt cnditins. 6. The degree t which natural mixed size transprt systems may be represented by feed r recirculating flumes depends n the time and space scales f the prblem. Cases with very lng time r space scales will tend t be feed systems, but equilibrium transprt is rare in these cases. Cases with very shrt time r space scales have a larger recirculating cmpnent. In cases where the sediment transprt, bed surface texture, and bed cnfiguratin achieve a shrt-term equilibrium (n time scales f hurs), the equilibrium cnditins are determined primarily by the sediment bed and flw cnditins. This is a typical predictin prblem fr sediment transprt and is best mdeled by a recirculating flume. Uncertainty in the chice between feed and recirculating mdels f mixed size sediment transprt is partially reslved by the bservatin that unimdal and weakly bimdal sediment mixtures appear t perate at clse t equal mbility in bth feed flumes and recirculating flumes fr r > 2r,. fractins must adjust tward equal mbility fr equilibrium 7. A carse surface layer and bed frms cexist ver a transprt. An equilibrium transprt system must perate at finite range f r. When bth are present, the carse surface

14 WILCOCK AND SOUTHARD: BED LOAO TRANSPORT OF A MIXED SIZE SEDIMENT 1641 layer des nt cnstitute the entire bed surface that is visible at any time, but is expsed nly in bed frm trughs. The carse surface layer is the surface n which, r thrugh which, size-dependent exchange f grains ccurs. As such, the carse surface layer plays a rle in determining the grain size distributin f the transprted sediment and therefre f the bed frms. In the range f r where bth bed frms and a carse surface layer exist the carse surface layer may serve t regulate the size and variability f the bed frms by limiting the depth f scur in the bed frm trughs. Abve this range, bed scur in the lee f the bed frms is sufficiently strng t prevent the develpment f a vertically srted bed surface. Bed frms may limit the range f r ver which a carse surface layer may develp; the type and size f bed frms may als be cntrlled by the ccurrence f a carse surface layer. REFERENCES Andrews, E. D., and G. Parker, Frmatin f a carse surface layer as the respnse t gravel mbility, in Sediment Transprt in Gravel-bed Rivers, edited by C. R. Thrne, J. C. Bathurst, and R. D. Hey, Jhn Wiley and Sns, New Yrk, Church, M. A., D. G. McLean, and J. F. Wlctt, River bed gravels: Sampling and analysis, in Sediment Transprt in Gravelbed Rivers, edited by C. R. Thrne, J. C. Bathurst, and R. D. Hey, Jhn Wiley and Sns, New Yrk, Day, T. J., and P. Eggintn, Particle-size distributins fr the surface f alluvial channel beds, Curt. Res., Part B, Pap. 83-1B, pp , Gel. Surv. f Can., Ottawa, Dhamtharan, S., A. Wd, G. Parker, and H. Stefan, Bedlad transprt in a mdel gravel stream, Prj. Rep. 190, St. Anthny Falls Hydraul. Lab., Univ. Minn., Minneaplis, Diplas, P., and A. J. Sutherland, Sampling techniques fr gravel sized sediments. J. Hydraul. Eng., 114(5), , Iseya, F., and H. Ikeda, Pulsatins in bedlad transprt rates induced by a lngitudinal sediment srting: A flume study using sand and gravel mixtures, Gegr. Ann., 69(A), 15-27, Kellerhals, R., and D. I. Bray, Sampling prcedures fr carse alluvial sediments, J. Hydraul. Div. Am. Sc. Civ. Eng., 97(HY8), , Klaassen, G. J., J. S. Ribberink, and J. C. C. de Ruiter, On the transprt f mixtures in the dune phase, paper presented at Eurmech 215, Eurpean Mechanics Cmmittee, Genva, Italy Sept , Kuhnle, R. A., and J. B. Suthard, Bed lad transprt fluctuatin in a gravel bed labratry channel, Water Resur. Res., 24(2), , Milhus, R. T., Sediment transprt in a gravel-bttmed stream, Ph.D. thesis, Oregn State Univ., Crvallis, Parker, G., Experiments n the frmatin f mbile pavement and static armr, technical reprt, Dept. Civ. Eng., Univ. Alberta, Edmntn, Parker, G., and P. C. K!ingeman, On why gravel bed streams are paved, Water Resur. Res., 18, , Parker, G., S. Dhamtharan, and S. Stefan, Mdel experiments n mbile, paved gravel bed streams, Water Resur. Res., 18(5), , 1982a. Parker, G., P. C. Klingeman, and D. L. McLean, Bedlad and size distributin in paved gravel-bed streams, J. Hydraul. Div. Am. Sc. Civ. Eng., 108(HY4), , 1982b. Prffitt, G. T., and A. J. Sutherland, Self armuting n nn-unifrm alluvial sediments, paper presented at 7th Australasian Hydraulics and Fluid Mechanics Cnference, Institute f Engineers, Australia Brisbane, Australia, Aug Prffitt, G. T., and A. J. Sutherland, Transprt f nn-unifrm sediments, J. Hydraul. Res., 21(1), 33-43, Sutherland, A. J., Static armr layers by selective ersin, in Sediment Transprt in Gravel-bed Rivers, edited by C. R. Thrne, J. C. Bathurst, and R. D. Hey, Jhn Wiley and Sns, New Yrk, Wilcck, P. R., Bed-lad transprt f mixed-size sediment. Ph.D. thesis, Mass. Inst. f Technl., Cambridge, Mass., Wilcck, P. R., Methds fr estimating the critical shear stress f individual fractins in mixed-size sediment, Water Resur. Res., 24(7), , Wilcck, P. R., and J. B. Suthard, Bed cnfiguratin, bed surface texture, and fractinal transprt rates (abstract), Es Trans. A G U, 68, 1292, Wilcck, P. R., and J. B. Suthard, Experimental study f incipient mtin in mixed-size sediment, Water Resur. Res., 24(7), , Wilcck, P. R., and R. S. Stull, Magnetic paint sampling f the surface and subsurface f clastic sediment beds, J. Sediment. Petrl., in press, J. B. Suthard, Department f Earth, Atmspheric, and Planetary Sciences, Massachusetts Institute f Technlgy, Cambridge, MA P. R. Wilcck, Department f Gegraphy and Envirnmental Engineering, The Jhns Hpkins University, Baltimre, MD (Received December 29, 1988; revised March 31, 1989; accepted April 11, 1989.)