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<br />
<br />SCOUR AND FILL IN STEEP, SAND-BED EPHE~IERAL STREAMS
<br />
<br />The sedimenr-inpur rare for simulated floods was of [he form Gsi
<br />::::: Q~. With flume slope Jdjusrcd {O 0.0106, this sedimenr-inpur reo
<br />la.rion \....ould give maximum discharge conditions similar [0
<br />steady-scare runs. Thus, for the first 6 min of the flood [here would
<br />be approximately equilibrium flow. However, when the exponen-
<br />rial dec3.Y of the flood began, the sedimenr-inpur rate was propor-
<br />tional to Q~ while the sedimenr.ccansport rate was proportional CO
<br />QU, This difference would result in scour for the remainder of the
<br />flood unless a transition to a lower flow regime with a lower
<br />sedimenr-rransporr (;Ire and formation of ripples rempor:uily de-
<br />cceased transport rate below input rate. To establish a graded
<br />channel, this behavior required that flume slope be lowered co
<br />0,0089 so rhat fill wok place in rhe first 6 min of the flood w bal-
<br />ance the scour occurring later. This balancing resulted in mean-bed
<br />fill and scour, bur rime-dependenr hydraulic effects may have pro-
<br />duced simila r resules.
<br />Time-Dependenr Hydraulic Effects. The depth versus velocity
<br />curve for run F-I-Il (Fig. 7) exhibits :1 transition from the upper
<br />now regime to the lower flow regime as depth and mean velocity
<br />dl:crease. This discontinuity is of the type first described in the laba-
<br />,awry by Bwoks (1958) and in the field by Colby (1960), In those
<br />instances, transition from flow over anridunes or a flat bed co flow
<br />over ripples or dunes caused thl: disconrinuiry. In che experimenrs
<br />reported here, data suggest mat transition is first from normal an-
<br />cidunes moving upstream CO anridunes chat migrate downstream,
<br />rhen to ripples. Figure 8 shows Froude number, F, bed Darcy-
<br />Weisbach fricrion factor fb. bed friction faccor rario ftit' Ih and
<br />minimum bed-fonn trough depression below initial mean-bed ele-
<br />vation as functions of time for run F-I-II. Bed friction factor f b
<br />was deterrninl:d using the sidewall correerion technique of Van ani
<br />and Brooks (1957), which allows for the effect of the smooth flume
<br />walls on overall flow resistance. [nrerrelations berv.reen rhese var-
<br />iables can aid in recognizing rime-dependent hydraulic effecrs mat
<br />may affect mean-bed behavior.
<br />In Figure 7, che break in slope for the F-l-11 depth versus veloc-
<br />ity curve occurs a&er 20.67 min and before me next sample poine at
<br />22.67 min. The bed-form trough elevation (Fig. 8) shows that bed-
<br />form amplitude reaches a minimum in chis same rime interval. Less
<br />than 2 min larer, ft/t' b exceeds 2 and signals me end of true an-
<br />tidune flow as defined by Taylot and Btooks (1961), The time dif,
<br />ference berween the break in slope of the depm versus velocity
<br />curve and (rJ'f'b exceeding 2 is probably nor significant, since me
<br />slope of ftlt b versus time in mis area is so gende mar a very small
<br />error in (~.f fJ produces a rime error of severa! minuees. The region
<br />labeled transition 1 in Figures 7 and 8 is 3. flow regime where the
<br />bed form is small uanridunes" moving downstream. These bed
<br />forms resemble ripples, bur have in-phase stationary waves charac-
<br />teristic of anridunes.
<br />A sha'1' slope break in the F,(,,(,i(',, and bed-form trough depth
<br />curves (Fig, 8) OCCUtS at 33_67 min, which indica reS the onset of
<br />ripple fonnation. The region of ripple formation is labeled transi-
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<br />567
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<br />rion.! in Figures 7 and 8. Ripple formarion appears complete by 44
<br />min, although Figure 7 suggests th:u it acrually continues undl 48
<br />min. After ripple formarion is completed, ft! continues co increase
<br />because rhe depth is decreasing.
<br />The effecr of transitions 1 and 2 on mean-bed fill and scour is
<br />that increase in fb and ftJf' h n:quires a finite amount of time owing
<br />(0 the amount of sedimenr thar has (0 be moved to increase bed
<br />roughness."Thus, whenever a decrease in discharge requires an in.
<br />crease in bed roughnes:> CO achieve equilibrium flow conditions, the
<br />increase does not occur instanrJ.neously, and a time lag may exist
<br />between discharge change and equilibrium flow. The same instan-
<br />taneous decrease in low discharges should have a longer time lag
<br />than Ole higher discharges because me sediment-transport: rate is
<br />lower and more rime is required to increase bed roughness. Since
<br />discharge is steadily decreasing during the waning flood, the rime
<br />lag in roughness development should increase through borh transi.
<br />tion regions, although it eventually should disappear as ripples
<br />reach maximum development. This lag between bed roughness re-
<br />quired for equilibrium flow and actual bed roughness means chat
<br />flow velocities and sediment-transport: rates will be higher than
<br />equilibrium values during me transition parr of the flood. Water-
<br />s~rface slope relative to the flume (Fig. 9) suPPOrtS this interpreta-
<br />non. Comparison between water-surface slope and a linear inrerpo-
<br />lation between initial and final mean-bed slope shows a peak posi-
<br />rive relarive slope at 25 min in transirion 1, and from 40 co 50 min
<br />in transition 2. These positive values suggest mat bed roughness is a
<br />less man equilibrium value. The dip in relarive slope at 35 min
<br />suggests chat flow equilibrium is achieved temporarily between
<br />transition __1 and transition 2.
<br />This dynamic rime-lag effect means mat, even if the sedimenr-
<br />input rare is adjusted to steady-scate equilibrium transport, mean-
<br />bed scour \....ill seitl occur on me waning flood used in these experi-
<br />ments. Thus, an excess of sediment inpUt at the beginning of the
<br />flood is required to balance scour and achieve overall equilibrium.
<br />and chis adjusrmenc produces mean-bed fill and scour. Sediment-
<br />transport: rare at the very end of the flood is coo low to allow
<br />equilibrium co be achieved by a sediment-input excess, so mean-bed
<br />scour and fill is nOt possible unless a power-law sedimene-input re-
<br />larion with an exponenc less than 1.5 is used. However, considering
<br />me actual magnitude of mean-bed devation fluctuations (Fig. 6),
<br />rhe question of mean-bed fill and scour versus scour and fill is
<br />academic in praerical terms, and me dominant faeror in bed re-
<br />working is bcd-form amplitude.
<br />
<br />Applicability of Laboratory Scudies to Field Sicuarions
<br />
<br />Laboratory flume flows were less than 4 an deep in rhese exper-
<br />imentS. Middleton (1965) has run antidune flows as much as 20 cm
<br />deep in the 40-m flume in the Keck Hydraulics laboratOry. In
<br />Middleton's experiments, the antidune behavior was similar co that
<br />reported here and by Kennedy (1961). Simons and others (1965)
<br />
<br />F.f-Il WATER SURFACE SLOPE
<br />
<br />Figure 9. W;:Her-surface and mean-bed
<br />slopes fot run f-1-11.
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<br />.00896
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<br />.008760
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<br />"EAM 8E.O SLOPE.
<br />F-l-lI ~
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<br />o ~ ~ Z5 ~ ]5 ~
<br />HYOROGRAPH ELAPSED TIME (m;n)
<br />
<br />55
<br />
<br />60
<br />
<br />"
<br />
<br />50
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