mcdonald paper

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Flow patterns, sedimentation and deposit architecture under ahydraulic jump on a non-eroding bed: defining hydraulic-jump

unit barsROBERT G. MACDONAL D*, JAN ALEXANDER*, JOHN C. BACON* and MARK J. COOKER *School of Environmental Sciences, University of East Anglia, Norwich, Norfolk NR4 7TJ, UK(E-mail: [email protected])School of Mathematics, University of East Anglia, Norwich, Norfolk NR4 7TJ, UK

ABSTRACT

This paper presents results from two flume runs of an ongoing seriesexamining flow structure, sediment transport and deposition in hydraulicjumps. It concludes in the presentation of a model for the development ofsedimentary architecture, considered characteristic of a hydraulic jump over a

non-eroding bed. In Run 1, a hydraulic jump was formed in sediment-freewater over the solid plane sloping flume floor. Ultrasonic Doppler velocityprofilers recorded the flow structure within the hydraulic jump in fine detail.Run 2 had identical initial flow conditions and a near-steady addition of sand,which formed beds with two distinct characteristics: a laterally extensive,basal, wedge-shaped massive sand bed overlain by cross-laminated sand beds.Each cross-laminated bed recorded the initiation and growth of a single surfacefeature, here defined as a hydraulic-jump unit bar. A small massive sandmound formed on the flume floor and grew upstream and downstream withoutmigrating to form a unit bar. In the upstream portion of the unit bar, sand finerthan the bulk load formed a set of laminae dipping upstream. This set passeddownstream through the small volume of massive sand into a foreset, which

was initially relatively coarse-grained and became finer-grained downstream.This downstream-fining coincided with cessation of the growth of theupstream-dipping cross-set. At intervals, a new bed feature developed aboveand upstream of the preceding hydraulic-jump unit bar and grew in the sameway, with the foreset climbing the older unit bar. The composite architectureof the superimposed unit bars formed a fanning, climbing coset above themassive wedge, defined as one unit: a hydraulic-jump bar complex.

Keywords Backset beds, cross-bedding, flume, hydraulic jump, submergedwall jet, unit bar.

INTRODUCTION

Hydraulic jumps occur naturally in a variety ofsubaerial environments such as in rapids andcascades, at levee breaches during floods andwhere steep channels enter lakes or reservoirs.These hydraulic jumps are characterized by amarked increase in free water surface level be-tween a supercritical incident flow and a deeper,slower, subcritical flow. Hydraulic jumps formspontaneously in natural flows and are subject to a

finely balanced interaction between inertia, pres-sure gradient and gravity. The Reynolds number,Re, is the ratio of inertial to viscous forces(Re = qud/l) where q is the density and l thedynamic viscosity. Re can occur over many ordersof magnitude (Chanson, 2007a). In natural waterflows, the Froude number, Fr = u/(gd)1/2 has rarelybeen observed to exceed 4 and is usually lowereven in steep mountain streams (Jarrett, 1984). Inunconfined (and shallow) flow over steep non-cohesive slopes, Fr rarely increases much above

Sedimentology (2009) 56, 13461367 doi: 10.1111/j.1365-3091.2008.01037.x

1346 2008 The Authors. Journal compilation 2008 International Association of Sedimentologists


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critical value (i.e. 1) (Grant, 1997). Comparison ofsediment behaviour in natural settings with that inengineered settings (e.g. Fr = 5 to 9 achieved withundershot sluice gates; Chanson, 1999) could bemisleading. Here, flow structure (Fr = 273), sedi-ment transport and deposition and deposit char-

acter associated with a hydraulic jump aredescribed towards a model that can be used ininterpretation of ancient deposits.

A range of sedimentary features in alluvial fan,fan delta and jokulhlaup deposits contain backsetbeds, attributed to hydraulic jumps (e.g. Postma &Roep, 1985; Massari & Parea, 1990; Nemec, 1990;Russell & Knudsen, 2002; Cassidy et al., 2003;Breda et al., 2007). Steep-sided scours, rapidlyfilled with massive or diffusely graded deposits,have also been attributed to hydraulic jumps,notably in sites downstream of glacial debouch-

ment (e.g. Gorrell & Shaw, 1991; Russell et al.,2003). Normally gradedand cross-stratified gravelswith scoured bases have also been described atsuch sites (e.g. Hornung et al., 2007). Despite thefairly common occurrence of hydraulic jumps innatural flows, the deposits associated with themare poorly documented or quantified and identifi-cation in ancient deposits is problematic.

In one of the few previous laboratory studies ofsedimentation under hydraulic jumps, Jopling &Richardson (1966) demonstrated how backsetbedding formed under a hydraulic jump in a smallflume (02 02 m cross-section, 06 slope, non-

recirculating). Alexander et al. (2001) described

how sedimentary structures (termed chute andpool structures after Fralick, 1999) formed in awell-sorted sand bed by the rapid upstream move-ment of trains of hydraulic jumps in a flume.Neither of these studies could present detailedmeasurement of the associated flow but subse-

quent technological advancements have deter-mined turbulent structure (e.g. Liu et al., 2004)and aeration (e.g. Murzyn et al., 2005; Lennon &Hill, 2006; Chanson, 2007b) in sediment-free set-tings. The two companion flume runs presentedhere stand independent to: Run 1 monitor thedetailed flow structure; Run 2 (i) monitor thesediment transport behaviour and its effect on theflow behaviour; and (ii) document the depositarchitecture. The constant flume slope and widthmake the final model ideal for application inenvironments of flow expansion, gradually chang-

ing slopes, slope breaks and where water bodiesinteract, to generate hydraulic jumps.

Experimental procedure

The two runs are from an ongoing series, exam-ining flow structure and sedimentation in sub-aerial hydraulic jumps using the tilting flume atthe University of East Anglia. This flume recircu-lates water and sediment in a closed pumpedloop (Fig. 1). The near-stationary hydraulic jump(Fig. 2) in Run 1 was the identical startingcondition for Run 2, which involved the contin-

uous addition of sand.

Fig. 1. The flume used for these experiments (not to scale). The inset box shows the pattern of UDVP probes, used inthe two different arrays along the flume centreline.

Defining hydraulic-jump unit bars 1347

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The 10 m, straight, test channel has a square(1 1 m) cross-section, glass sidewalls and a flatstainless steel floor. Channel tilt was set at 425to the horizontal. A 0100 m high overshot weirwas used at the downstream end of the channel

(Fig. 1). The water discharge was kept constant at026 m3 sec)1 throughout both runs (measuredwith electromagnetic flow meters in the recircu-lation pipes). The co-ordinate system used is xdownstream (parallel to the flume floor), y cross-stream and znormal to the floor; 0, 0, 0 was set atthe point of entry to the test channel, on the right-looking downflow and at the flume floor.Throughout this paper, flow is viewed left toright. The x and z components of velocity are uand w, respectively.

Repetition of runs with the same conditions

reproduced a hydraulic jump in the same meanposition, with the same free surface shape andinternal flow pattern that remained steady forprolonged periods (many hours). For the two runspresented here, the hydraulic jump was set suffi-ciently far down the flume for the supercritical jetfree surface to be uniform across-stream. Thehydraulic jump was sufficiently far up the flumefor sediment accumulation downstream of thejump in Run 2 to be largely unaffected by theflume end-wall conditions. There is a relationshipbetween any inflow characteristic and its devel-

opment length and this has a control on thecharacter of the flow or flow structure (here thehydraulic jump structure) and the behaviour ofsediment. A parabolic profile of streamwise veloc-ity takes some time and space to develop and,

once developed, the shape of the profile is main-tained downstream, assuming no change in chan-nel conditions. Kirkgoz & Ardiclioglu (1997)determined the distance, L, of development of aparabolic shape in their eq. (5), to be:

L

ds 76 00001

ResFrs

1

where ds is the supercritical flow depth and Frsand Res are the Froude and Reynolds of theinflow, respectively. In many natural settings, the

boundary conditions vary in space and time suchthat a fully parabolic profile will not develop. Ahydraulic jump will form upstream of the posi-tion where a parabolic velocity profile woulddevelop. Hydraulic jumps with a parabolic inflowvelocity profile may be considered a special caseattainable only in unnatural settings. The exper-iment was set up with a partially developedinflow to the hydraulic jump, which may be morecommon in nature.

Flow depth downstream of the hydraulic jumpwas determined at the downstream end of the test

A

B

Fig. 2. Still video images of thehydraulic jump in Run 1 at two timeintervals, taken from a consistent

distance, through the flume sidewall. The blue sidewall verticalsupports are 080 m apart. (A) Imageof surface splash. (B) Image taken032 sec after (A) without splash.The toe of the hydraulic jump is in amore upstream position.

1348 R. G. Macdonald et al.



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channel, dx=1000m, a position downstream of thevertical water surface fluctuations associated withthe behaviour of the hydraulic jump. UltrasonicDoppler velocity profiler (UDVP) probes, de-ployed in arrays, measured high-frequency timeseries of beam-parallel velocity components in

transects away from the probes. Vectrino acousticDoppler velocimeters recorded time series of allcomponent velocities at isolated points (Fig. 3).Outputs were monitored in real time to ensurethat aliasing was prevented and that the receivedsignals were acceptably clean. Data were recordedfor periods of at least 540 sec, to allow an accurateassessment of the time-averaged velocity allowingfor turbulent fluctuation (the average was takenover at least 500 readings at each spatial point). Inorder to maintain wet contact, UDVP probes weresubmerged by at least 005 m under the oscillating

free surface. The flow was recorded on a videocamera through a sidewall.

Run 1: Sediment-free hydraulic jumpThis run was undertaken to determine the waterflow structure within a particular hydraulic jump.Flow depths upstream and downstream of thehydraulic jump were 009 and 025 m, respec-tively. A UDVP array of 10 probes, parallel to theflume floor and pointing upstream (array 1; Fig. 1),was deployed at 13 positions along the channelcentreline to measure streamwise velocity (u) justupstream, within anddownstream of the hydraulic

jump. Two-dimensional (u and w) turbulent char-acteristics were assessed with data from a secondUDVP array (array 2; Fig. 1) at four positions.Velocities in the supercritical flow were measuredwith a single probe and mean velocities are theaverage of 12 000 readings at each point.

Run 2: Hydraulic jump with sand additionThis run was undertaken on an initially flatinclined flume floor so that deposition would becontrolled by the flow, not the channeltopography.Well-sorted, quartz-dominant sand was added to

the flume at approximately 4000 kg h)1

over theduration of the 75 min run by conveyor feed (theduration was limited by the volume of sandavailable and the input rate). Sand was loaded byhand onto a conveyor at as steady a rate as could bemaintained by shovelling, from five crates. Therewas a short hiatus in sand loading when each fullcrate was manouvered into place. The hiatus was5 min before crate 2 and crate 4 but only 2 minbefore crate 3 and crate 5. Sand added to thedischarge tank mixed with sand leaving the down-stream end of the test channel(Fig. 1) and travelled

through more than 15 m of recirculation pipes andpumps before entering the test channel. Thisprocess acted to damp any fluctuation in sandflux. After initiation of sand input, the sand flux tothe hydraulic jump did not cease until the run wasstopped andno abrupt change in sediment flux wasobserved within the test channel. The input sand

was well-mixed and unimodal (modal class was250 to 300 lm), with a mean grain-size of 368 lmand standard deviation of 222 lm.

Ultrasonic Doppler velocity profiler array 2 wasfixed in position at x = 610 m throughout therun. Because the jump moved slowly upstream,the UDVP recorded u and wvelocity componentsat increasing distances downstream of thehydraulic jump. The shape of the sand depositwas recorded at 23 instants and the position of thewater-free surface was recorded at 13 instants,both by tracing onto the sidewalls. The appearance

A

B

Frs = 273

Res = 282000

ds = 009 m

Fr= 024

Re = 270000

d= 0 25 m

Fig. 3. Photograph and definition diagram of thehydraulic jump. (A) Oblique downstream view onto thesurface of the hydraulic jump. Two acoustic Dopplervelocimeters are deployed into the subcritical flow.(B) Diagram showing the sense of rotation in vortices aboveand below the detached jet (indicated by the thick

black line). The general flow characteristics are givenfor the conditions on either side of the hydraulic jump.




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The submerged wall jet thinned downstream(from 009 to 006 m). At 067 m downstream ofthe toe, the submerged wall jet expanded verti-cally (maintaining contact with the flume floor)and the fastest core rose to follow the highestposition of the expanding jet, as a detached jet

(Fig. 2). The detached jet approached the freewater surface and thickened downstream to spanthe entire flow depth (Fig. 4A). This unidirec-tional flow spanning the entire flow depth down-stream of the hydraulic jump is described as thetailwater. In the volume of fluid below the lowerboundary of the detached jet, there was noobvious flow movement except when bubbles(described below) highlighted discrete eddies.

Above the submerged wall jet and detached jetwas a recirculating roller with fluid in its lowerpart travelling downstream, adjacent to the jet

and in its upper part travelling upstream, belowthe free water surface (Fig. 2 and green arrow ofFig. 4A). The thin, highly aerated upstream flowalong the top 005 m of the roller is termed thereverse flow strip (Fig. 2) and persisted through-out Run 1. Above the roller, the water surfaceoscillated with a 005 m vertical amplitude(Fig. 4A). Localized free surface peaks, typicallyspanning less than half the flow width, rose abovethis oscillation and spilled upstream in seconds(Fig. 2A and B). These are termed splashes andwere observed at 5 to 45 sec intervals throughoutRun 1. Splash height and position varied, with

maximum heights recorded in Fig. 4A. Thehydraulic jump toe oscillated in the streamwisedirection between x = 438 and 488 m (totalexcursion of 050 m) around a near-stationarymean streamwise position. The toe oscillationwas a local feature and had a frequency notsimply related to the vertical, free surface oscil-lation of the roller. Video analysis showed thatsplashes were particularly high when the toe wasin its most upstream position.

The continuous breaking of the sloping front ofthe hydraulic jump admitted air bubbles into the

flow via the toe. Incident supercritical flow wasnot aerated but bubbles constituted a consider-able fraction of the roller and the flow down-stream of it. The highest concentration of bubbleswas at the turbulent shear layer between theupper surface of the submerged wall jet andthe roller. The submerged wall jet and the core ofthe detached jet contained few bubbles comparedwith the water above and below.

Immediately downstream of the toe there was azone of vortex generation: the upper surface of thewall jet as it entered the deeper water ran under

relatively stationary fluid. The high shear in thisregion corresponded to: (i) high vorticity; and (ii)a thickening of the zone of transition from high-speed fluid below and slow fluid above. Vorticeswere generated within the shear layer and tight-ened to discrete entities 005 to 009 m in diam-

eter. Some vortices followed the upper edge of thedetaching jet. Others were deflected downwardsand brushed the flume floor, upstream of jetdetachment. Throughout Run 1, further vorticeswere shed from the lower boundary of thedetached jet and these rotated slowly withouttightening as they moved into the quiescentregion below the detached jet. These vorticesgenerally were larger than, contained more dif-fuse bubbles than and rotated in the oppositesense to those generated in the shear layer. Allvortices had axes of rotation across-stream.

Groups of bubbles surrounded by fluid withoutbubbles (bubble sets) exited the upper portion ofthe downstream edge of the roller in pulsesapproximately every 5 sec. These bubble setsfollowed a curved trajectory within the expand-ing jet and tailwater and burst at the free surfacewithin the flume length (Fig. 4A). The bubble setswere restricted to the top quarter of the flow justdownstream of the roller, extended down to threequarters of the flow depth about 1 1 m down-stream (at x = 750 m) and had all escaped by19 m.

General flow characteristics

Supercritical flow upstream of the hydraulicjump is defined by Frs (Fr > 1), where Frs is theFroude number for mean velocity Us and flowdepth ds. As the wall jet enters the jump,Frs = 273, Res = 282 000 and Ls = 591.Downstream of the jump, Frx=640m = 024 andRex=640m = 270 000. Such high Reynolds num-bers confirm that the flow was fully turbulentthroughout Run 1. Boundary layer separationfrom a wall occurs for flows of high Reynolds

numbers (Re > 100 000 for flow around a bluffbody) travelling from low to high pressure.

Velocity data

At 05 m upstream of the hydraulic jump(x = 420 m), the time-averaged streamwise veloc-ity, u, reached a maximum (274 m sec)1) atZUmax 0033 m above the flume floor (Fig. 4Binset). Supercritical flow was steady betweenupper and lower bounds and additionally hadinstances of slower flow (minimum 118 m sec)1,




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half the lower bound) of up to 0 1 sec duration,with no apparent periodicity (Fig. 5D).

As the supercritical wall jet became submerged,Umax slowed by 85% in 09 m (to 041 m sec

)1 inProfile F). ZUmax moved down over a horizontal

distance of 067 m to within 0001 m of the flumefloor and moved up to 003 m by Profile D(Fig. 4B). In Profiles A to D, u decreased smoothlyupwards, across the shear layer and becamenegative within the recirculating roller.

The time-averaged jet expanded downflow of

Profile D and ZUmax moved upwards, followingthe upper limit of the expanded jet. A furtherpeak in u occurred below ZUmax in Profiles F andG (at z = 009 m). Underneath the length of theroller, the upper jet edge was abrupt. The loweredge of the detached jet was less abrupt. Althoughnot material surfaces, jet edges are defined by theabrupt transition in velocity from the jet to theouter flow. The upper edge of the detached jetrose to 075 of the flow depth within 06 and,downstream of this, the jet became indistinct.

Above the time-averaged jet, there was a min-

imum in u at z = 020 m; this was negative at theupstream end of the roller ()076 m sec)1) andincreased to 003 m sec)1 downstream throughthe roller (Profiles A to F). The integrated mean uat velocity Profile A is negative, indicating nettupstream volume flux (Fig. 4B); this resulted fromthe greatly aerated state of the recirculating flowwithin the roller; the negative (up-flume) volumeflux of water (rather than water and air bubbles)was less than the down-flume volume flux of thesubmerged wall jet (that contains no bubbles).The highest magnitude of negative u in each ofProfiles A to D coincided with the stream of

vortices above the detached jet.The flow below the time-averaged detached jet

was directed downstream. Downstream of the jetdetachment point and upstream of the pointwhere the tailwater was fully developed (ProfileG), the water near the flume floor was nearly static(less than 004 m sec)1 below z = 6 mm) and thenear-floor velocities were greater both upstreamand downstream of Profile G.

In Profiles F and G, two peaks in time-averaged uwere recorded because the jet core positionchanged repeatedly between a jet-up and jet-

down state. The u time series at ZUmax (z = 027 m)shows that most data were spread uniformlyaround a steady mean (Fig. 5A) and additionallyu minima each lasting for less than 2 sec wererecorded, at times when the whole detached jetwas in the jet-down state and instantaneousZUmax was below z = 027 m. The detached jet istransient in vertical space, through time.

The time-averaged tailwater velocity is drawnabove and below an offset, as two unjoined lines(Profiles H to K; Fig. 4B). The height of offsetfollowed the trajectory of the bubble sets (which

Profile K, Z = 022 m 027 m

2000

1000

0

1000

2000

2000

1000

0

1000

2000

2000

1000

0

1000

2000

Profile G, Z = 027 m

Profile I, Z = 022 m 027 m

2000

1000

3000

Supercritical profile, Z = ZUmax

Streamwisevelocity(ms

ec1)

0 200 400 600

Time (sec)

A

B

C

D

0

Fig. 5. Time series of u at positions downstreamthrough the jet and tailwater. (A) 12000 datapoints froma single probe, at z = ZUmax of the supercritical flow.

Compare inset in Figure 4B. (B) to (D) 500 datapointsfrom array 1 at: (B) within the detached jet; (C) twopositions within the tailwater near the upstream limitof the bubble pulses; and (D) further downstreamwithin the tailwater. Note that in (D) the bubble pulsesreach down to Z = 027 m more regularly than in (C).




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highlighted pulses from an upper region of theroller). The velocity profiles below the offsetremained unchanged throughout, with a symmet-rical spread of data about a steady mean (blacklines in Fig. 5B and C). At each position above theoffset, the u time series were similar for most of

the recording period but with slightly widerbounds (grey lines in Fig. 5B and C) and thisrecorded the non-offset pattern displayed by thedashed lines of Fig. 4B. In addition, there wererepeated short periods (up to 5 sec long) whenvelocity varied by two to three times the excur-sion of the steady flow. At any point in spaceabove the offset, the large excursions were onlyabove or below the upper boundary of steady ubut not both. By Profile J, the time-averaged uprofile was approaching a complete parabola. Allbubbles had disappeared. The tailwater contin-

ued to slow downstream.

Turbulent kinetic energy and Reynolds shear

Turbulent kinetic energy, Tke, and Reynoldsshear, szx, were calculated from coincident uand w data generated by the UDVP array 2(Fig. 6). In the xzplane, turbulent kinetic energyper unit mass is defined as:

Tke 1

2u02 w02

2

where u and w are deviations from the time-

averaged velocity components. Reynolds shearper unit mass is expressed as:

szx u0w0 3

for incompressible Newtonian fluids. Localizedviscous stresses within the flow are expressed byvelocity fluctuations, mathematically describedin the turbulent acceleration term of the NavierStokes equations: the gradient of szx acceleratesthe local fluid.

At the jet detachment site, Tke was highest at the

upper and lower edges of the jet (the lower edgewas the flume floor) because of high shear fluctu-ations (Fig. 4C, Profile (i); Fig. 6). The Tke mini-mum in the middle of the detached jet wasapproximately 20% of that at the upper jet edge.Tke was low in the downstream half of the rollerand the reverse flow strip. At Profile (ii), thedetached jet had Tke maxima at the upper andlower edges and a mid-jet minimum, all higherthan at jet detachment. A Tke minimum atz$ 005 m underneath the detached jet is associ-ated with the centre of diffuse vortices, shed from

the lower jet edge at consistent locations. Wherethe pulses were nearest to the flume floor, twodistinct regions were recorded, above and belowthe height at which bubbles were seen [Profile(iii)].Below thepulses [below z = 014 m in Profile (iii)],Tke was virtually zero. Above z = 014 m, Tke

rapidly increased, peaking at the height of thefavoured path of bubble sets within the pulses(z = 030 m). The tailwater downstream of thepulses exhibits a smooth Tke curve, peaking atthe height of maximum shear which was below thebreak in the velocity profile [Profile (iv)].

A mid-jet minimum in Reynolds shear, szxcoincided with the Tke minimum [cf. Profiles(i); Fig. 4C]. Rapidly accelerating sheared flow atthe upper jet edge is associated with a strongpositive vertical gradient in szx. An abruptdecrease in stress occurred between sheared

layers and the upper flow region and this isattributed to the presence of the upward-travelling stream of vortices. The flow abovez$ 0180 m did not deviate abruptly in speed ordirection and exhibited low values of Reynoldsshear. The detached jet profile at x = 610 mhighlights the jet retardation in the negativeszx/z around z = 0150 m. The shorter negativegradient below (around z = 005 m) marked thejet-down position. At this streamwise location,the jet-up state produced a more diffuse patternin u, spanning more of the flow depth than thejet-down state. Strong positive values of szx/z

existed at the upper and lower jet edges, despitediminished direct acceleration by the retarding jetto the flow surrounding it. The region of diffusevorticity below the detached jet had compara-tively low values of szx (Fig. 4C). The szx peak,lower in the flow, marked the mean vortex centrepoint. In this case, szx/zwas negative above thevortex centre, so the upper part of the vortexcircumference is detected to have rotated down-stream, while the lower part rotated upstream.The reverse flow strip had a low value of szx,consistent with the zero-shear stress boundary

condition which exists on the free surface flowwithin this ever-present part of the flow structureand consistent with the low Tke values.

Two modes of the flow were detected atx = 750 m [Profile (iii); Fig. 4C]; a low-szx tail-water, below a region where szx had increasedthree-fold. The transition between these regionswas at the base of the observed favoured path ofbubble sets, between z = 0120 and 0180 m. Thedistribution of szx/z within the transition waspositive: a nett acceleration of the immediatelysurrounding water by the lowest reaching pulses




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which were still travelling downstream. Abovez = 0180 m in Profile (iii), a strong negativegradient in szx was observed because the fluidhad comparable values of u and w. Because oftheir buoyancy, the w of bubbles may be greaterthan that of water. The tailwater further down-stream [Profile (iv)] exhibited low negative shearof slowing steady flow except for the marked peakaround z = 018 m, consistent with the data forTke and velocity.

Turbulent velocity fluctuations

Instantaneous u and w of necessity have a meanof zero and the data scatter indicates the predom-inance of horizontal or vertical fluctuations,shedding light on the time-transient flow charac-ter (Fig. 6). u and w both generally decreased asthe flow slowed downstream. Jet flow generatedhigh instantaneous velocity fluctuations. The jetthickness was 012 to 023 m as it rose from the

Fig. 6. Plots of the instantaneousdeviation from mean streamwisevelocity, u, against the correspond-ing instantaneous deviation frommean vertical velocity component,w, for Run 1 at Profiles (i) to (iv)(Fig. 4C). u > 0 denotes down-stream and w > 0 denotes awayfrom the flume floor. These plotsgive a visual impression of thevariation in turbulence structure inspace.




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flume floor [Profiles (i) and (ii); Fig. 6] (ds was009 m). The detached-jet centre was less spreadin u and w than the jet-up edges (Fig. 6). Inaddition, there was less spread in u and w at thelower edge of the jet while it was in the jet-downstate and still less spread between the two states.

x = 580 m was the location of the widest spreadin u and w and was along the path on whichvortices passed downstream. w in the recirculat-ing roller (at z = 0186 m) was twice as widelyspread as u. Close to the bed at x = 580 m, wherethe wall jet was thinnest, a few outlying valuesnegative in u and positive in w indicatedslowing, rising bursts when the jet began todetach from the flume floor. Downstream of jetdetachment, turbulence was reduced at the flumefloor but increased within the water column.Transport of suspended sediment and bedload

would be promoted by turbulence because of thejet edges at jet-up and jet-down conditions. Theslowly rotating vortices which spanned the flowcolumn below the detached jet at x = 610 maccord with a small spread in u and w comparedwith the surrounding fluid.

Throughout the profile at x = 840 m and thelower region at x = 750 m, u and w wereclustered particularly close to the origin. u andw were more spread above z = 0186 m and lessspread below this, in accordance with the mini-mum height that pulses reached down to. Atz = 0246 m, data were more spread in u than in

w because the pulses which travel deeper alsotravel further downstream before rising towardsthe free surface. The additional turbulence whichthe pulses caused within the downstream watercolumn could cause suspended sediment totravel further downstream before settling, than ifthe vortices had not passed to downstream of theroller.

DISCUSSION OF SEDIMENT-FREEHYDRAULIC JUMP

Flow patterns

Despite the high Froude number in most pub-lished experimental studies, there are similaritiesin the Run 1 flow pattern. The shape of thehydraulic jump is consistent with the Murzynet al. (2005) photograph for Frs = 30, as well asthe sketch by Chanson & Brattberg (2000) ofhydraulic jumps of Frs 633 and 848 and wasonly marginally steeper than the free surfaceprofiles measured by Sarma & Newnham (1973)

for Frs 110 to 379 with fully developed inflowdownstream of an undershot sluice gate.

Oscillation of the streamwise position of the toeof the hydraulic jump, on or over the supercriticaljet, is thought to result from competition betweenthe upstream pressure gradient force from

the thicker subcritical flow to the thinner super-critical flow and the viscous drag on the rollerbecause of the incident wall jet.

The jet slowed exponentially with distancedownstream from the toe of the hydraulic jump,unlike that observed by Chanson & Brattberg(2000) and this may be due to their thin inflowfrom an undershot sluice gate. It simultaneouslythinned because the stream of upward anddownward travelling vortices widened down-stream. Contrary to the suggestion of Chanson &Brattberg (2000), the turbulent shear layer

between the submerged wall jet and the rollerdid not display triangular u profiles with avelocity peak at the layer interface. Here, uprofiles approached triangular further down-stream within the detached jet (Fig. 4B; ProfilesF and G).

In Profiles A to E (Fig. 4B) above the jet, thereis a velocity profile of the flow, that is increasedby the downstream rotation of the lower half ofthe vortices and decreased above the vortexcentre (making possibly negative) by the up-stream rotation of the upper half of the vortices,for the time that a vortex exists at a particular

point in space. For the time-averaged velocity toshow a negative peak, a constant stream ofvortices would need to pass along a consistentpath, as was observed in this particular hydrau-lic jump. The Chanson & Brattberg (2000) time-averaged u profiles also showed a decrease invelocity above an increase in velocity comparedwith the general trend above the jet. Thisdecrease was not prominent in their Frs = 848case but was prominent for the Frs = 633 casewhere u approached becoming negative. Thisobservation suggests that the presence of vortices

could be the sole cause of the negative velocitypeak in natural situations of low Frs. The asso-ciated increase in velocity over the lower half ofthe vortex courses in Run 1 was magnified andthe decrease over the lower half decreased,where the jet had slowed (by up to 85%) andflow immediately above the submerged wall jetmay have more downstream momentum thanthat within the jet. Khan & Johnston (2000) noteda streamwise velocity deficit within vortex coresand this may contribute to the negative velocitywithin the roller.




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Detachment of the jet

Although jet separation from the bed has beendescribed in sites with positive lee-side ramps(McCorquodale & Khalifa, 1980; Mossa & Tolve,1998; Balachandar et al., 2000; Liu et al., 2004;

Yuksel et al., 2004) and at sharp negative stepssuch as at a headcut (Bennett & Casali, 2001;Alonso et al., 2002), wall jets entering hydraulicjumps above flat surfaces have, until recently,been assumed to expand into the tailwater with-out any separation from the floor. Run 1 confirmsthat wall jets in hydraulic jumps do separate froma solid floor rather than simply diffuse into aparabolic tailwater (cf. evidence in the figures ofAlhamid, 2004; Lennon & Hill, 2006; Dey &Sarkar, 2007). There has been little publisheddiscussion of the cause of separation or of the

implications of coherent vortices shed from thelower edge of a detached jet and no discussion ofthe implications for sediment movement. Fromupstream to downstream through the hydraulicjump, the viscous boundary layer (of sub-milli-metre thickness) moves from a region of relativelylow pressure to a region of relatively highpressure and it is probable that, in Run 1, theviscous boundary layer in high Re conditionsseparated from the flume floor. If the boundarylayer did not separate, then the flow throughoutthe tailwater would necessarily have been lami-nar. Local separation of the viscous boundary

layer from the boundary can induce a large-scalechange of the direction of the jet as observed inRun 1.

Vortex dynamics

Distribution of vorticityWith boundary separation from the flume floor, ingeneral there will be a migration of vorticity awayfrom the flume floor and this concentration ofvorticity became noticeable as the vortices belowthe detached jet. The comparatively lower vortic-

ity below the detached jet caused lower-magni-tude turbulent fluctuations than were due to thevorticity within the roller.

Vorticity which enters at the toe, can make itsway into the shear layer between the submergedwall jet and the roller by convection as the freesurface of the roller overturns and falls onto thesupercritical free surface (Hornung et al., 1995).Reconnection of the surface at the streamwise-oscillating toe and spilling splashes occurredrepeatedly throughout Run 1.

Vortex motion from the rollerVortex escape from the roller is thought to causethe periodic pulses observed within the upperpart of the tailwater. When a pulse was notpresent, the upper jet edge approached the freewater surface (the jet up state), isolating the

roller from the tailwater; vortices circulatedwithin the roller and became diffuse adjacent tothe reverse flow strip. When a pulse occurred(caused by vortex escape from the roller), thediffuse tip of the jet was lower in the flow and thevortices moved downstream into the tailwatercausing the change in mean velocity profiles (theoffsets to profile patterns in Fig. 4B).

There are three possible mechanisms for peri-odic release of vortices from the roller: (i) tightlyrolled vortices may have had strong-enough cir-culation and streamwise velocity to escape the

roller, pushing the upper jet edge downward asthey travelled downstream, close to the freesurface. Those vortices which maintained out-lying positive values in u (u ) 0; Fig. 6) mayescape the roller. (ii) The detached jet tip, a shortdistance upstream of the tailwater, could moveback and forth along the path of its core of highestvelocity, hypothetically fixed in space. As the tipmoved upstream and downstream along the path,the vertical distance, H, between the tip and thefree surface fluctuated and H changed around itstime-averaged position at 075 of the total waterdepth. Vortices were more or less likely to pass to

downstream of the jet, depending on the magni-tude of H. (iii) At splash condition (Fig. 2A), afree surface peak exists over the roller and, withit, an additional short-lived downstream pressuregradient. It is possible that this pressure gradientforced downward the downstream parts of thedetached jet from its usual jet-up state to the jet-down state where its path was lower within theflow. In doing this, a vortex may have been let outof the roller because, in the jet-down state, Hwould be increased without the path of the jetbeing shortened. Subsequent upstream spill of

the hydraulic jump collapses the free surfacepeak and so allows the jet to return to the jet-upposition.

The first mechanism is least likely to release thevortices which caused the offset to tailwater flowbecause no vortex was observed to leave the rolleras a result of its own force, despite the fact thatroller vortices were tightly rolled compared withthose observed by Long et al. (1991), were alwaysin motion and did not coalesce. The secondmechanism could be effected during the repeated




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short periods when the supercritical wall jet wasslower than the lower bound of the steady flow(Fig. 5A), so shortening the path to the jet tip andincreasing H. These periods could be due to theflume pumps (although there is no regular period)or due to the supercritical inflow being only

partially developed. The third mechanism is alsoconsidered likely to produce some of the periodicreleases observed: if the constant air intake at thetoe and unsteady roller free surface exceedsthe bubble flux out of the roller free surface, thevolume of the rollers increases; the level of theroller free surface may be raised periodicallyabove the level of the tailwater free surface. Therapid up-flume spill of the splash would rapidlyallow the jet to return to jet-up, bound the rollerdownstream extent, and the cycle restart. Thesub-second duration that splashes took to appear

and then collapse compares with the durationsthat the jet was in the jet-down state. The meanfrequency of the jet moving into the jet-downstate does not account for pulses every 5 sec. Theslowing to the supercritical wall jet is much morefrequent and the three mechanisms may alloperate, resulting in a complex periodicity tothe flow within the hydraulic jump.

RUN 2: HYDRAULIC JUMP WITH SANDFLUX

Run 1 demonstrated the complex internal flowpatterns and Run 2 was designed to test: (i) howsediment addition to the flow influenced the flowbehaviour; and (ii) how the flow behaviourcreated deposits. Starting with flow conditionsidentical to Run 1, the flow was monitored assand was added. Upon cessation of the sedimentinput and flow, the resulting deposits wereexamined in detail.

Comparison of hydraulic jump behaviour withand without sediment

Flow patternIn Run 2, the hydraulic jump moved 272 mupstream in response to sand accumulatingdownstream of it. The position of the toe of thehydraulic jump in Run 2 oscillated to the samedegree as the sediment-free jump. The sameinternal fluid processes were observed, in thesame geometry as Run 1: The jet detached fromthe flume floor with a similar angle, from thesame streamwise position relative to the toe of thehydraulic jump and rose to a similar flow depth

downstream; vortices were generated at locationsconsistent with Run 1, with a similar scale andfrequency and passed downstream along similarpaths. Fewer bubbles were observed in Run 2than in Run 1 and none observably persisteddownstream of the roller (Fig. 7A and B), makingflow components (e.g. vortices) more difficult tosee.

A

B

C

Fig. 7. Photographs of Run 2 showing: (A) the rollerand the jet beneath, taken 7 min after the sedimentaddition started. Flow structure was similar to Run 1(compare Fig. 2). (B) The first hydraulic-jump unit barwhich was prograding over the fine sand sheet, at13 min. (C) The slip face of the youngest hydraulic-

jump unit bar prograding downstream over the finesand sheet at 24 min, after upstream progradation ofthe upstream part of the bar has ceased. Some slip faces

contained distinctly finer sediment than others. Silverbolts are 015 m apart.




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Streamwise velocity profiles were measured atx = 6100 m at eight time intervals, representingdistances increasingly downstream of the hydrau-lic jump. The progressive upstream movement ofthe hydraulic jump made it possible to measurevelocity further downstream from the hydraulic

jump in Run 2 than in Run 1. Despite the samepump settings, as soon as the sediment inputstarted, the flow in Run 2 was generally slowerthan that in Run 1. The streamwise velocity fieldat the most upstream profile within the hydraulicjump in Run 2 was similar to that at the same sitein Run 1 (Profile L in Fig. 8 compared with ProfileG in Fig. 4B). However, the velocity peak was02 m sec)1 compared with 095 m sec)1 duringRun 1. Velocity decreased more rapidly above thepeak than below it in Run 2 while the oppositewas true in Run 1. The near-bed velocity peak (injet-down conditions) was closer to the bed in

Run 2 than in Run 1. At the end of the roller the u-profile was offset at z = 026 m (Profile M; Fig. 8),above which u markedly increased beforedecreasing to the free water surface, as in Run 1.Downstream from this position, the velocity fieldin Run 2 differed from that in Run 1. No profileoffset was apparent. At the more distal sites, thevelocity increased towards the bed and was015 m sec)1 at 001 m above the bed (the lowestmeasurable height) (Profile Q; Fig. 8).

Sedimentation

All sand within the supercritical flow was trans-ported in suspension. As the sand entered thehydraulic jump, some of it moved from the jetinto the roller and some moved into the waterbelow the detached jet (Fig. 7A). Most of the sandremained in the jet as it detached from the bed.The sand distribution downstream of the distinctjet appeared uniform throughout the water col-umn, although suspension concentration patternswere not measured. Sand dropping from slowingand reversing flow in the roller was instantlyaccelerated by the jet underneath. In the jet-up

state, some sand dropped from the detached jetand through the underlying zone of separationonto the bed. When the flow pattern had switchedtowards the jet-down state, this sand waspushed downstream as a bedload sheet a fewgrains thick, to form a mound in the tailwater

about 08 m from the jet separation point (atx = 690 m). At the same time, finer sand wasdropped from suspension downstream of themound and formed a thin sheet. While the finesand sheet thickened, the mound grew andprograded downstream over it (Fig. 9A). A smallrelatively fine-grained set of upstream-inclinedlaminae formed on the upstream edge of themound as it grew upstream and a coarser-grainedavalanche set formed on the downstream edge(Fig. 9B). As the bedform grew downstream, thetopset aggraded and the avalanche face progres-sively overlapped the distal fine sand sheet

(Figs 7B and 9C). The aggradation of the topsetwas at least 10 times slower than the progradationof the foreset. The small amount of fine sandfalling onto the feature surface was transportedover the crest and incorporated with the coarsersand in the lee-side avalanche set and topset(Figs 7C and 9D). When this bed feature was fullydeveloped, the upstream growth slowed, at timesbecoming imperceptible. The fine sand sheetcontinued to thicken downstream of the ava-lanche face and a diachronous boundary formedwith the overlying set (Fig. 9E).

Sediment accumulation caused the free surfaceof the tailwater to rise, increasing the hydraulicjump free surface gradient. This change made thehydraulic jump unstable and it responded bymoving upstream. The sediment accumulationpattern moved gradually upstream in tandemwith the hydraulic jump, forcing positive feed-back. The bed feature continued to grow withslow upstream progradation, rapid downstreamavalanching and slow topset aggradation. Period-ically, a new bed feature formed above orupstream of the previous bed feature and grew

Fig. 8. Profiles of streamwise velocity component, u for Run 2, measured by UDVP and averaged over measuringintervals of 600 sec. The UDVP array was fixed at x = 610 m throughout the run. The profiles are drawn in positionsrelative to the contemporary hydraulic jump (compare line showing lowest free surface position with the same line inFig. 4A and B). Profiles Q to S are further downstream of the hydraulic jump than was measurable in Run 1.




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in a similar way to the previous feature. As a newbed feature developed, the older feature becameinactive and the new downstream-dipping ava-lanche face prograded and climbed over the top ofit (Fig. 10). When the avalanche face heightproduced a strong-enough lee separation eddy,

counter-flow ripples formed and these reached upto one-third of the height of the lee slope beforebeing met by an avalanche of downstream-travel-ling bedload. If a feature reached the downstreamend of the previous one, the avalanche facesamalgamated. At the end of Run 2, a bed featureavalanche face was still prograding downstreamand had a proto bed feature forming on itsupstream edge.

Deposit architecture

In this experiment six discrete beds developed(Fig. 11), numbered 1 to 6 upwards. Beds 2 to 6developed sequentially and displayed the samegeneral internal characteristics. The pattern ofsedimentation associated with the hydraulicjump had formed distinctive bed features with acharacteristic anatomy (Fig. 10), here termed ahydraulic-jump unit bar. In general, the hydrau-lic-jump unit bar, when fully developed, had theform of an elongated bed with a sharp lowerboundary, upstream-dipping upstream bed termi-nus, flat upper surface and steep downstream bedterminus. The cross-stream bed shape cannot be

defined, as the flume experiments were effec-tively two-dimensional. The internal architectureof each hydraulic-jump unit bar was, at theupstream end, a small wedge of gently up-stream-dipping ()9 to 7 relative to the lowerboundary) convex-up laminae with grain-sizesmaller than the bulk composition of sedimentfrom the crates; this graded downstream, througha small volume of massive deposits, into adownstream-dipping cross-set with coarsergrain-size. This foreset passed downstream intoa finer-grained foreset, which approached the

same grain-size distribution as the bulk sedimentload. The brink of the foreset was the highestpoint of each hydraulic-jump unitbar during Run2. Above both foreset types, low-angle laminaeformed a topset, which locally reached thickness-es similar to the underlying foreset. The oldest(lowest) foreset was underlain by a massive finelayer. Foresets that overrode the oldest foresetwere underlain by the fine unit at the distal end.Each hydraulic-jump unit bar had a bidirectionalcross-set pattern with greater development of thedownstream set(s).

A

B

C

D

E

Fig. 9. Model of hydraulic jump unit bar formationand growth. (A) Initial mounding on the non-erodable

bed and fine sand falling from suspension, forming asheet downstream of it. (B) Accretion of relatively finesand on the upstream side of the newly formedhydraulic-jump unit bar and formation of a coarsergrained avalanche face on the downstream side. Themassive fine sand sheet continues to thicken to form anelongate wedge. (C) The downstream avalanche face

progrades over the massive sand wedge. (D) Reductionin the rate of upstream growth corresponds with morefine sand reaching the avalanche face. As the slip facemoves further from the hydraulic jump, fine sedimentsettling from suspension (previously falling to themassive fine-grained wedge) is incorporated in theforesets. The topsets aggrade as the foreset progradesand the unit appears to climb. (E) The pattern formed in(D) continues with topset aggradation and downstreamextension. Inset boxes (i) to (iii) in (B), (C) and (D):detail of change in the shape of the front of the unit bar,explaining the blocking (and deposition) of fine-grained sand and later bypass.




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The downstream part of the deposit was a coset

of avalanche foresets with set boundaries dippingupstream to give a climbing and upward-thinningcoset (Fig. 11). The set boundaries are well-defined and grade from convex-up to concave-up. Each bed was longer than its predecessor andpinched out to the flume floor further upstream ofit. The set boundaries were less distinct in thearea of the upstream-dipping lamination. Thetransition between the upstream and downstreamdipping cross-laminae occurred progressivelyfurther upstream in successive beds and contactbetween the two component sets became sharper.

This architecture is termed a hydraulic-jump barcomplex.

Details of the depositsAfter flow stopped, the flume was drained and thedeposit examined: adjacent to the flume sidewall,in one section cut parallel to flow (03 m from theflume sidewall) and then in nine sections trans-verse to flow (Figs 12 and 13). The uppermost01 m and downstream-most 08 m of Bed 5 hadcollapsed into the discharge tank (Figs 12C and13D). Otherwise, the deposit was undisturbed. In

the stream-parallel sections the same features

were observed, and at comparable streamwiselocations, as seen forming through the flumesidewalls (described above). Bed 4, which termi-nated within the flume length, pinched out aty = 066 m, at x = 755 m and was thickest aty = 050 m. Most laminae were approximatelyhorizontal in y, or dipped at a low angle towardsthe sidewalls (Fig. 13). Towards their upstreamlimit, coarse-grained foresets occurred in threepackages a few centimetres thick at the leftsidewall (y = 0) that pinched out within 035 macross the flume, at the top of Beds 2 (Fig. 13C), 4

and 5 (Fig. 13B). Towards their downstream limitthese foresets occurred across the flume width(Bed 3; Fig. 13C).

Upstream-dipping lamination was distinct inthe proto bed feature (Fig. 12A), which had beendeveloping only for 3 min. Upstream-dippinglaminae appeared amalgamated in more devel-oped hydraulic-jump unit bars, e.g. Bed 4 inFig. 12B. The contact between the proto bedfeature and larger bed feature below was not easyto distinguish (Figs 12A and 13A). In the sectionshown in Fig. 13A, one set of upstream-dipping

Finest sand deposited from suspension

Sand coarser than the bulk load

Sand finer than the bulk loadLeading edge

(transverse)

(1) Fine upstream-dipping laminae

(3) Coarser

cross sets

(4) Finer

cross sets

Brink

(2) Massive deposit

Fig. 10. Diagrammatic representation of the architecture of the unit bars formed downstream of the hydraulic jump,with near-steady sand addition, steady pumping rate and non-erodable flume bed. The large (small) grains depict alocation where grain-size distribution is negatively (positively) skewed with respect to the bulk load. The thin linesshow the general orientation of laminae within the unit bar and the thick line depicts the suspension fallout deposits.

Fig. 11. Pattern of lamination within the deposits of Run 2 represented in a stream-parallel section. The line rep-resenting the water surface corresponds with the final position of the hydraulic jump at the end of the run. The initialposition of the toe of the hydraulic jump was at x = 468 m.




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laminae directly overlay another and the inter-set

contact appeared indistinct except adjacent to theflume sidewall. Both sets consisted of sand finerthan the bulk load which fined towards the top. Asimilar indistinct contact occurred between Beds 4and 5 (Fig. 13B). Counter-flow ripples also depos-ited upstream-dipping laminae at the bottom ofBed 5 at the downstream end of the test channeland produced distinctly coarse sets (Fig. 13D).

The volume of massive sand (the originalmound) was observed in Beds 2 to 6 (Fig. 11)and was visually discernable from the set of finelaminae upstream because of the coarse sand

fraction which it contained. It spanned up to

03 m in the streamwise direction and was pre-served with a similar shape to the hydraulic-jumpunit bar that developed from it, with upstream-dipping upstream bed terminus and low-anglearcuate upper surface (Fig. 12B; right-hand sideof Bed 4). The downstream terminus of themassive sand was arcuate and more abrupt thanthe upstream bed terminus (though not sharp)(Fig. 12B; left-hand side of Bed 5).

Immediately downstream of the massive sand,each coarse-grained foreset was thin (approxi-mately half the thickness of the adjacent massive

Fig. 12. Photographs taken through the side wall of the flume (i.e. stream-parallel sections) and corresponding linedrawings of the deposits of Run 2. The location of each photograph is indicated in Fig. 11. The coin used for scale is aBritish penny and is 20 mm in diameter. The lighting conditions were varied to highlight the lamination; this gives afalse impression of variation in sand colour. The line drawings are labelled with bed numbers as in Fig. 11. The redtriangles indicate that grain-size is coarsening-upward within the bed. The asterisk (*) was within Bed 5 before theflume was drained.




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deposit) and thickened rapidly downstream, withincreased dip angle, as the topset above itthinned. Maximum foreset angle occurred withinthe coarser foreset and the dip decreased down-

stream with grain fining. Each downstream tran-sition from coarse cross-set to cross-set withgranulometry approaching the bulk load, wasstreaky along the streamwise extent of transition.

*

Bed 6

Bed 5

Bed 6

Bed 5

Bed 4

Bed 3

Bed 2

Bed 5

Bed 3

Bed 2

Bed 1

Bed 6

Bed 5

Bed 4

Bed 3

A B

C D

Fig. 13. Photographs and corresponding interpretative line drawings of sections cut through the deposit perpen-dicular to mean flow direction (i.e. stream-transverse sections) with a 0 14 m long pen for scale. The most upstreamsection is (A) and the most downstream is (D). The positions of these sections are indicated on Fig. 11. (A) and (B)were photographed looking downstream, (C) and (D) are looking upstream. The thick line on each line drawing is the

boundary of the deposit and the flume floor and the laminae above are traced from the photographs in close-up view.Note that in section (D), Bed 5 sits in contact with Bed 3. The asterisk (*) was within Bed 5 before the flume wasdrained.




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At the downstream termination of Bed 2, a cross-set approaching bulk-load grain-size was pre-served (Fig. 12C). The hydraulic-jump unit barwhich overrode it (Bed 3) exhibited the patchytransition between the two cross-set types at thisstreamwise location (Fig. 12C), with the coarse

cross-set being interspersed with foresets withbulk load granulometry. The youngest hydraulic-jump unit bar(Bed 6) was the only one where thedownstream-most metre of the foreset containedno patches of coarser laminae, so Bed 6 displayedthe complete transition to bulk-load cross-set.

Topsets abruptly overlaid the foresets (Bed 6;Fig. 13B) and generally thinned downstream.Specifically, Bed 6 is at a more downstreamposition than the directly underlying bed (beingincepted further upstream of the bed below) andhas a thinner and finer-grained topset, thinning

downstream (Fig. 12B). The topset of Bed 2pinched out downstream, upstream of the down-stream terminus of the bed (Fig. 12C). The contactwith Bed 3 above is not erosional. Many of theindividual topset laminae could be traced fororders of metres in the streamwise direction,particularly in the more upstream portion of eachbed above the coarser-grained cross-set.

The fine sand wedge (Bed 1) gradually thick-ened downstream from its upstream limit atx = 670 m, to 018 m at the end of the testchannel. Containing sediment much finer thanthe bulk load, it made a distinct contact with the

beds which overlay it at different streamwiselocations (Fig. 12C). However, this contact wasnot distinct in stream transverse section(Fig. 13D). No length scale can be defined for thisunit as it would have continued downstream ifthe flume had been longer.

DISCUSSION OF SEDIMENTATIONUNDER A HYDRAULIC JUMP

A distinct sequence of beds was formed in the

flume under conditions of constant water recir-culation and near-constant sediment transport.There was no obvious correlation between thetiming of initiation of new unit bars and sedi-ment input rate variation. Notably, there was noobvious correlation with the short hiatuses inthe sediment addition resulting from changingcrates and, indeed, two new unit bars formedduring loading of the sand from the secondcrate.

A massive basal unit is thought typical ofdeposition downstream of a hydraulic jump

because of: (i) the ability of the turbulence withinthe hydraulic jump to maintain sediment insuspension and lift it into the downstream-expanding flow depth of the hydraulic jump;and (ii) the decline in turbulent regime down-stream of the hydraulic jump where fallout from

suspension takes place. The rapid decrease in uabove the mid-detached jet maximum within theroller and associated decreased vorticity produc-tion compared with Run 1 would lead todecreased vorticity (hence turbulence) passingdownstream into the tailwater. This effect pro-vided a hypothetical negative feedback betweensuspended sediment concentration and the pref-erential length scale of the massive basal unit.This length scale is also controlled by the segre-gation of bedload below the detached jet and thegrain-size distribution (hence settling velocity)

which remained in suspension.In Run 2, the lower jet edge in jet-up condi-tions was more distinct than that in Run 1 and thevelocity peak in jet-down conditions was closerto the flume floor; both these promoted bedloadtransport underneath the jet and a more distalinception of the initial sediment mound than wasanticipated from observations of Run 1. Theshape and length scale were different fromthe massive basal unit (which would form in theabsence of a bedload feature). Despite the uniformstreamflow in the tailwater (affected in an upperregion by vortex release from the roller), at no

time were downstream-migrating bedforms super-imposed on any hydraulic-jump unit bar surface.As each hydraulic-jump unit bardeveloped, sandwas deposited from suspension within the pro-grading system, particularly at the downstreampart of the hydraulic-jump unit bar and this maybe the cause of rare mud drapes between coarselaminae described by Massari (1996). The bulk-load foreset laminae were fully reverse-gradeddespite short avalanche face heights (up to011 m; Fig. 12B and C) which is comparablewith the observations of ancient deposits de-

scribed by Massari (1996). Breda et al. (2007)described 03 m thick cross-beds within PlioceneGilbert delta deposits, with characteristics similarto those produced in Run 2.

A foreset brink climbing a slope greater than57 raises the deposit height more than the topsetaggradation, which was an order of magnitudeslower than foresets prograded in the slopewisedirection. The upstream movement of thehydraulic jump was affected more by the brinkwhile Bed 2 was growing and more by the topsetwhile Beds 1 and 3 to 6 were growing. After Bed 2




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was deposited, each new bed made the hydraulic-jump bar complex surface shallower and topsetaggradation had increasingly more effect thanbrink progradation on the upstream movement ofthe hydraulic jump. Local increases in the depositsurface height increased tailwater levels irrespec-

tive of their proximity to the hydraulic jump,shown to be true for a change at fixed x by Videet al. (1993).

Historically, backset beds are the only faciesthat have been regularly interpreted as resultingfrom hydraulic jumps (e.g. Massari & Parea, 1990;Nemec, 1990; Breda et al., 2007). In Run 2, thedeposits did not have architecture similar toclassic backset beds described from the rockrecord. The finer-grained proximal part of thehydraulic-jump unit bar did have low-angleupstream-dipping cross-bedding and the set

boundaries between the unit bars dippedupstream at a low angle. The absence of relativelysteep upstream-dipping surfaces, as describedfrom the rock record, may relate to the absenceof bed erosion in a flume; if the bed wereerodable, scour upstream of the hydraulic jumpwould increase the amplitude of bed topographyand the deposits would form above a scouredsurface (e.g. Massari, 1996). The hydraulic-jumpunit bar anatomy and the general architecture ofthe hydraulic-jump bar complex, produced inRun 2, is considered characteristic of depositarchitecture under a hydraulic jump over a non-

eroding surface.

Grain-size segregation in a hydraulic-jumpunit bar

The bedload initially mounds on the flume floorat a position within the tailwater and this moundhas sharp upstream and downstream edges(Fig. 9A). The mound builds slowly comparedwith the flow velocity which encounters themound as if it were stationary (Needham & Hey,1991). The presence of the mound was seen to

influence flow velocity in the lower region of thetailwater close to the mound. Well upstream ofthe mound, the velocity increases rapidly withdistance above the flume floor, whereas immedi-ately upstream of the mound the rate of velocityincrease above the bed is less, up to the height ofthe mound. As the bedload approaches theupstream edge of the mound, it slows. Sand atthe finer end of the bedload grain-size distribu-tion comes to a halt on the flume floor at theupstream face (Fig. 9B). The coarser grains pro-trude higher into the flow where they are influ-

enced by greater velocities and, consequently,move over the mound. The velocity gradientblocking effect segregates the finer bedload onthe upstream face of the mound from coarserbedload downstream.

As the upstream edge of the deposit progrades

upstream, its dip decreases (Fig. 9C) and thevelocity gradient immediately upstream steepens.As the dip decreased, increasingly finer-grainedsand is forced over the mound by the flow. Theaccumulation of relatively fine sand decreasesbed roughness and coarse grains more readilytraverse the smooth slope in a positive feedback.The blocking effect decreases with time until allbedload is forced across the feature and upstreamgrowth of the unit bar stops (Fig. 9D and E). Thiseffect contributes to the downstream-fining of theforeset (described above) as the fine bedload com-

ponent is transported to and deposited on the lee.A more significant cause of downstream foreset-fining is that as the unit bar extends downstream,more fine sand falls onto it from suspension and isincorporated in the topset and foreset.

CONCLUSIONS

1 The flow pattern within a hydraulic jumpcontrols the nature of the resulting deposits andwhen sediment was added to the system, a de-posit developed downstream of the hydraulic

jump causing the tailwater to rise and thehydraulic jump to migrate upstream.

2 Most of the fine-grained sediment wasdeposited from suspension in the slowing tail-water to form a sheet, thickening downstream. Inthe absence of a bedload, this massive basal unitwould be the only depositional record of thehydraulic jump.

3 Coarser sediment dropped to the bed from theflow structure within the hydraulic jump and waspushed downstream to a point where it accumu-lated as proto bed features which developed into

hydraulic-jump unit bars with characteristicstreamwise anatomy: passing downstream, a rela-tively fine-grained wedge of upstream-dippinglaminae, a small volume of massive sand, acoarse-grained and a finer-grained foreset. A topsetoverlaid both types of foreset. The unit bars mayprogressively override a massive fine-grained basalwedge.

4 The growing hydraulic-jump unit bar influ-ences the velocity profile of flow approaching it.Coarser grains within the bedload protruded intohigher velocity flow on the upstream face and




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were washed downstream. Finer grains wereblocked at the upstream edge. This blocking effectsegregated the finer bedload to form the set ofupstream-dipping laminae and, while this wasdeveloping, the foreset was coarser than the bulksediment load.

5 With near-steady flow and only minorfluctuations in sediment flux, a series ofhydraulic-jump unit bars developed, each above andupstream of the previous one and all above themassive basal unit, to form a fanning coset archi-tecture termed a hydraulic-jump bar complex.

6 In conditions where a hydraulic jump formsover a non-eroding bed, steep backsets (as clas-sically attributed to hydraulic jumps whenobserved in the rock record) are not formed.Rather, gently dipping upstream laminae form thestoss side of the hydraulic-jump unit bar and

upstream-dipping set boundaries occur betweenunit bars in hydraulic-jump bar complexes.

MODEL OF DEPOSITION UNDER AHYDRAULIC JUMP

A five-stage model describes the inception andgrowth of a hydraulic-jump unit bar (Fig. 10).Initially, there is no sediment in the system. Sandadded to the system is all transported in thesupercritical flow and into the hydraulic jump.Some of this sand drops to the bed underneath

the detached jet at the standard jet-up condition.This bedload is periodically pushed downstreaminto the slowing tailwater when the jet isdeflected downward to sit closer to the flumefloor in the jet-down state. A single isolatedfeature (the proto bed feature) begins to buildwhere bedload comes to rest. When the contact ofthe upper surface and lee slope of this protofeature becomes sufficiently abrupt and its heightsufficient for a lee slope separation eddy to form,this is when the transition from proto bed featureto non-equilibrium hydraulic-jump unit bar is

made.Finer sand falls out of suspension downstreamof the proto bed feature to form a wedge (Fig. 9B)with a preferential length scale at which slowingflow, decreasing in turbulence and decreasingsuspended sediment concentration combine mosteffectively (i.e. the length scale is dependent onsettling velocity). The non-equilibrium hydraulic-jump unit bar grows upstream and downstreamover the wedge. The established deposit slowsthe flow so that finer grains are preferentiallytrapped at the leading edge because of a boundary

layer-blocking effect [Fig. 9 insets (i) to (iii)].Downstream progradation continues separately.The upstream face of the hydraulic-jump unit barbecomes less steep, reducing the blocking effectand permitting increasingly finer bedload totraverse the feature. Pulses of fine sand reach

the lee avalanche face; a streaky characteristicappears within the coarse foreset (Fig. 9D). Oncethe leading edge gradient becomes sufficientlygentle, all bedload traverses the feature andupstream growth of the unit bar stops. All furtherbedload traverses the equilibrium hydraulic-jumpunit bar to the foreset. As the foreset grows, itreceives more sediment which falls out fromsuspension. Subsequently, the grain-size distri-bution deposited on the lee avalanche faceapproaches that of the bulk load. The topsetaggrades as the lee side avalanche face progrades

and the elevation of the brink point increases (theset climbs; Fig. 9D and E). The associated rise inthe tailwater free surface continues to push thejump upstream under a pressure gradient and anew unit bar may be initiated further upstream.The association of a resultant climbing andupward-thinning coset with the underlyingmassive basal wedge is defined here as one unit:a hydraulic-jump bar complex.

ACKNOWLEDGEMENTS

Thanks to Trevor Panter and Gareth Flowerdewfor help with equipment construction, Rob Uttingfor shovelling the sand and James Hodson forassistance with monitoring. Robert Macdonald isin receipt of NERC studentship NER/S/A/2006/14111. Thanks also to reviewers Suzanne Leclairand Rick Cheel for positive and stimulatingcomment on an earlier version of this paper.

NOMENCLATURE

ds Flow depth upstream of the hydraulicjumpdx=n Flow depth at streamwise location x = n mD50 The fiftieth percentile of the grain-size

distributionFrs Froude number upstream of the hydraulic

jumpFrx=n Froude number at streamwise location

x = n mg Acceleration due to gravityH Vertical thickness of flow above the

detached jet




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Ls Development length for the supercriticalparabolic velocity profile

l Dynamic viscosityq Fluid densityRes Reynolds number upstream of the hydrau-

lic jump

Rex=n Reynolds number at streamwise locationx = n m

Tke Turbulent kinetic energyu Streamwise velocity componentu Instantaneous deviation from mean stream-

wise velocityU Depth-averaged streamwise velocityv Cross-stream velocity componentw Velocity component normal to the flume

floorw Instantaneous deviation from mean vertical

velocity

x Streamwise coordinate parallel to the chan-nel axisy Stream transverse coordinate parallel to the

flume floorz Coordinate perpendicular to the flume floorZUmax Value of z at which streamwise velocity

maximum occurs

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Manuscript received 15 February 2008; revision

accepted 27 October 2008


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