Brideg&Best 88

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Sedimentology (1988) 35,153-163

Flow, sediment transport and bedform dynamics over the transition from dunes toupper-stage plane beds: implications for the formation of planar laminae

J O H N S. B R I D G EDepartment of Geological Sciences, State Universityof New Yor k, Binghamton, New York 13901J A M E S L . BEST

Department o Geology, Th e University o Hull, Hull HU 6 7RX,England

ABSTRACTPreliminary results are reported from an experimental study of the interaction between turbulence,sediment transport and bedform dynamics over the transition from dunes to upper stage plane beds. Overthe transition, typical dunes changed to humpback dunes (mean velocity 0.8 ms-', depth 0.1 m, meangrain size 0 .3 mm) to nominally plane beds with low relief bed waves up to a few mm high. All bedformshad a mean length of 0.7-0.8 m. Hot film anemometry and flow visualization clearly show that horizontaland vertical turbulent motions in dune troughs decrease progressively through the transition whilehorizontal turbulence intensities increase near the bed on dune backs through to a plane bed. Averagebedload and suspended load concentrations increase progressively over the transition, and the near-bedtransport rate immediately downstream of flow reattachment increases markedly relative to that near dunecrests. This relative increase in sediment transport near reattachment appears to be due to suppression ofupward directed turbulence by increased sediment concentration, such that velocity close to the bed canincrease more quickly downstream of reattachment. Low-relief bedwaves on upper-stage plane beds areubiquitous and give rise to laterally extensive, mm-thick planar laminae; however, within such laminaeare laminae of more limited lateral extent and thickness, related to the turbulent bursting process over thedownstream depositional surface of the bedwaves.

INTRODUCTIONThe kinematics, dynamics and hydraulic stabilitylimits of bedforms developed beneath unidirectionalwater flows have important implications for flowresistance, nature of sediment transport, and thedevelopment of sedimentary structures. Numerousexperimental studies have contributed to an under-standing of the kinematics and dynamics of bedforms,mainly in steady, uniform and shallow (less than0.5 m) flows typical of laboratory flumes (summariesin Allen, 1982; Southard, 1984). As a result, thehydraulic stability limits of the various bed configu-rations are quite well known empirically. In addition,Saunderson & Lockett (1983) studied in detail thebedforms and sedimentary structures formed at thedune to upper-stage plane bed transition.

A popular theoretical approach, stability analysis,

has been reasonably successful in predicting thehydraulic stability limits of dunes, plane beds andantidunes under steady flows. In order to predict theinitial growth of bedforms on a planar surface, astability analysis must include an accurate descriptionof the way local sediment transport rate lags the bedform (Engelund & Fredsoe, 1982). In convergingflows, as on dune backs, bed friction is larger than inuniform flow because of flow acceleration, even thoughturbulence is known to be suppressed in such flows.Velocity increases due to convergence more than thedrag coefficient decreases due to turbulence suppres-sion (e.g. Chandrsuda & Bradshaw, 1981; Fredsoe,1982). The opposite is true in diverging flows,especially where flow separation occurs. The result isthat there is a negative phase shift between bed shear

153


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754 J . S. Bridge and J . L. Beststress and mean velocity (and bedform) such that thebed shear stress maximum occurs upstream of thedeveloping bedform crest. A s bedload is normallythought to respond virtually immediately to a changein bed shear stress, the highest bedload transport rateoccurs upstream of the crest of the developingbedform, which is essential for growth. However, thedeveloping upstream slope of the bedform tends todecrease bedload transport rate relative to the down-stream side which tends to reduce the above lag effect.The lag of suspended sediment behind changing bedshear stress represents a positive phase shift, promot-ing stability (plane bed). Although modern stabilityanalyses take some account of fluid friction, upstreamslopes of bedforms, and suspended sediment (Enge-lund & Fredsoe, 1974; Richards, 1980; Sumer &Bakioglu, 1984; Kobayashi & Madsen, 1985), none ofthem considers the effect of either high sedimentconcentrations or high streamwise pressure gradientson local turbulence structure and sediment transportrate. A s a result the physical significance of the lagdistance discussed above is not understood. Themechanisms that promote initial bed instability arenot necessarily those which determine continuedgrowth and existence of bedforms. In particular, theeffects of flow separation are not considered; sucheffects are critical to the distribution of bed shearstress on bedform backs (Fredsoe, 1982; McLean &Smith, 1986).

It is our view that progress towards a generalizedbedform theory can only come with detailed knowl-edge of the interaction between turbulent flow,sediment transport and bedforms gained from experi-mental studies over real, moving bedforms undercontrolled conditions. Experimental conditions closeto the stability limits of particular bedforms areexpected to yield crucial information. Some of ourpreliminary (therefore incomplete) experimental re-sults concerning the transition from dunes to upperstage plane beds are considered interesting enough topresent in this paper.

THEORETICAL BACKGROUND TOTHE PROBLEMTo help understand the transition from dunes to aplane bed, consider the 1-D sediment continuityequation for steady flows

where qs is near-bed volumetric sediment transport

rate, x is downstream distance, C,, is volume concen-tration of sediment in the bed, h is local bed elevation,and t is time. From equation ( l ) , development of abed undulation (ah/ 0 locally) requires qs to varylocally in the streamwise direction. If a dune can beconsidered to migrate downstream for a finite lengthof time at rate a , without changing its form then

-6h /6 t=a 6h16x . (2)Combining equations (1) and (2) and integrating gives

9 s=Coa(h- o), (3)where ho is the local bed elevation where q,=0 (i.e. atthe flow reattachment point). Therefore, local equilib-rium bed elevation above the dune trough is linearlyrelated to local sediment transport rate. The basicproblems concerning the transition from dunes toupper-stage plane bed are therefore : (1) what controlsthe periodic streamwise variation in qs that allowsdunes to exist; ( 2 )what causes qs to increase in thedune trough relative to the crest as dunes change toupper-stage plane beds.

According to Jackson (1976) and Yalin (1977) thedownstream variation in qs is associated with theturbulence structure of the outer zone of the boundarylayer. Periodic macroturbulent ejections from regionsof adverse pressure gradient in dune trough areas arepostulated to mix with large outer-zone eddies whichsubsequently induce further strong ejections (henceerosion) downstream, in accordance with the well-known scaling law U , Tld % 7 (where U , is the surfaceflow velocity, d is depth and T is period of ejections).Others (e.g. Smith, 1970; Costello, 1974; Fredsoe,1982; McLean & Smith, 1986) have appealed to thebed shear stress maximum that occurs on the order oftens of bedform heights downstream of the separationline near dune crests. Erosion should occur upstreamof this maximum and deposition downstream, therebyproducing another dune, and so on further down-stream. Wave theory can also explain the formationof maximum steepness dunes (Kennedy, 1963, 1969;Hammond & Heathershaw, 1981; Allen, 1985);however, the occurrence of ripples and dunes in closedconduits as well as in cases where no distinct upperboundary exists indicates that a wavy free surface isno t essential for their formation (Yalin, 1977). Noattempts have been made to reconcile these differenttheories, even though the intensity and length scalesof turbulent bursting are known to be related tostreamwise variations in flow velocity and pressure.

The transition from dunes (or ripples) to upper-stage plane beds seems to be intimately involved with


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Implications o r planar laminae formation 755increasing near-bed sediment concentrations, but theexact mechanics are not understood. Bagnold (1966)reasoned that turbulence could not cause local erosionand flow separation (hence a plane bed is stable) ifone complete grain layer was involved in bedloadtransport, leading to the following criterion for theexistence of upper stage plane beds

QrC , ana, (4)where 0 is dimensionless bed shear stress, and tan a isdynamic friction coefficient. Although the physicalmechanisms involved are only vaguely stated, Bag-nolds criterion works reasonably well if the transitionis approached from the plane bed side (Allen &Leeder, 1980). However, ripples and dunes can existfor values of 0 well above those predicted by equation(4) (Allen, 1982; Bridge, 1981). Allen & Leeders(1980) explanation of the transition is that turbulenceproduction in the separated flow zone of dunes issuppressed by high sediment concentrations, so thaterosion at reattachment is reduced. Engelund &Fredsoes (1974) explanation is that suspended sedi-ment transport lags behind bed shear stress, such thatqs in dune trough areas is increased, while qs at dunecrests is lower than expected. This question isaddressed below.

It is generally believed that there is negligible spatiallag in bedload transport behind bed shear stress(Engelund & Fredsoe, 1982; Fredsoe, 1981, 1982;Allen, 1984). At high bedload transport rates typicalof upper stage plane beds the mean grain velocityUh = 0 U* (Bridge & Dominic, 1984). If a grain issettling through the bedload layer at its fall velocity,V s , he downstream (lag) distance travelled in movingfrom the top to the bottom of a bedload layer ofthickness Y h is approximately 10 U * y b / V s . As thesuspension criterion is U * / V s z , the lag distancemust be less than loyh, and is not likely to exceed afew tens of grain diameters. According to Grant &Madsen (1982) the inertial lag of a grain beingaccelerated from the bed to the top of the bedloadlayer is much less than that associated with settling tothe bed. Therefore, the assumption of negligiblebedload lag seems to be justified.

In contrast, the suspended sediment load lags bedshear stress changes by an appreciable amount.According to Fredsoe (1981, 1982) the suspendedsediment lag distance on dune backs is approximately10 U*E/V:, where ~=0 .077 * d . As U*/Vs,21 forsuspended sediment, the lag distance is on the orderof stream depth. Near-bed suspended sediment neara dune crest with a velocity of approximately 10 U*

could settle to the trough area of a dune of height H ina downstream distance not exceeding 10 U * H / V s %1OH)only if net upward directed turbulence did notinfluence the sediment paths. As the reattachmentzone is typically seven dune heights from the flowseparation line, the settling of appreciable suspendedsediment to the bed in the reattachment zone impliesturbulence suppression. Therefore, our hypothesis isthat the transition from ripples or dunes to upper stageplane beds must involve turbulence suppression in thefree shear layer. Settling lag by itself is not sufficientapparently.

All of the above theories and hypotheses requireexperimental testing. The main questions of concernare : (1) the scale and intensity of turbulence overnatural ripples, dunes, and plane beds (2) the effect ofsediment on suppression of turbulence in nonuniformflows, and, (3) the lag of sediment transport behindchanging flow conditions, both bedload and suspendedload.

EXPERIMENTAL EQUIPMENT ANDPROCEDUREExperiments were conducted in a laboratory flume(5 m long, 0.3 m wide, 0.3 m deep) which recirculateswater and sediment. The sediment used in theexperiments was well-sorted fine sand with a mediangrain diameter of 0.3 mm. Four runs were made overthe dune to upper stage plane bed transition. For eachrun uniform, equilibrium flow was established withinthe test section of the flume (i.e. away from entranceand exit effects). Uniform, equilibrium flow was takenas existing when the mean depth and velocity withinthe test section were essentially invariant for a periodof several hours. Depth was kept constant a t 0.1 m forall runs, therefore velocity was controlled with thepumped discharge. The flume slope was adjusted sothat the base of the.flume, the mean bed surface, andwater surface were parallel. For each run, measure-ments of flow and sediment transport were madealong the centreline of the test section as follows.

Mean velocity D (that occurring at 0.4 m depth)was measured using a Nixon Instruments Streamflocurrent meter, with a propellor diameter of 10 mm.Vertical profiles of the downstream component of flowvelocity were measured using a Dantec hot-filmanemometry system with a conical probe (model55R42) capable of measuring turbulent fluctuationsup to a frequency of 256Hz. At each point in thevertical profile, velocity was sampled for 64 s, with


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756 J . S. Bridge and J . L. Bestmeasuring points being concentrated in the lowest10% of the flow depth. Vertical profiles were measuredon plane beds, dune backs and troughs. Duringmeasurements over dunes, the probe was moved onan instrument carriage to maintain a constant positionrelative to the migrating dune. This procedure led toinaccuracy in determination of the distance of theprobe from the local bed level. Water temperaturewas recorded regularly in order to calibrate the hotfilm sensor, and to allow determination of viscosity.The hot film anemometry data were used to calculatevertical profiles of mean velocity, turbulence intensi-ties, and in the spectral analysis of turbulence.

Spatially averaged bed shear stress was calculatedusing T~=p g R S , where p is fluid density,R is hydraulicradius, S is slope [corrected for sidewall effects usingWilliams (1970) method], and g is gravitationalacceleration. Local bed shear stress over plane bedswas calculated using the law of the wall withmodifications to account for high suspended sedimentconcentrations, i.e.

, Rf


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758 J . S . Bridge and J . L . Best1983). The wavelength is also tolerably close to thetheoretical value of 2nd, in support of the wave modelfor subcritical bedforms. However, the present datacannot resolve whether water surface waves force thebedforms or vice versa.

Flow conditionsThe transition from dunes to upper stage planebeds occurs at a mean velocity of a little more than0.8 ms- which is in agreement with other experimen-tal studies (e.g. Southard, 1984, Fig. 7:22). However,bed shear stresses and friction coefficients calculatedusing the slope and hydraulic radius (Table 1) forplane beds are approximately twice their expectedvalues (c.f. Guy, Simons& Richardson, 1966).Furtherexperimental data are required to determine if thisanomaly is associated with the low relief bedwaves,depth-scale helical circulation, or non-uniform flow inthe flume.Vertical velocity profiles over upper stage planeTable 1.Measured and calculated data .

beds (Log y plotted against U) how an upwardincrease in slope within the logarithmic zone b / d 0.1 ms- ') or reduced apparentK associated with high sediment concentrations (seealso Gust & Southard, 1983). However, equation (5)could not be applied confidently in this zone tocalculate U* because near-bed suspended sedimentconcentrations could not be estimated and measure-ment of the distance of the hot-film probe from thebed in this zone was very difficult, especially in thepresence of low-relief bed waves. Equation (5) was,however, used to calculate bed shear stress usingmeasurements from the upper part of the logarithmiczone (0.1< y / d < 0 . 2 ) . These results (Table 1) givereasonable values of the friction coefficient.

Vertical variations in turbulence intensity( R M S ( u ' ) / U )n dune troughs show peaks in intensityat 10-25 mm from the bed and again very close to thebed (Fig. 3). These distributions and magnitudes of

Run number 1 2 3 4Depth (m) 0.1 0.1 0.1 0.1Hydraulic radius (m ) 0.06 0.06 0.06 0.06Slope 0,0071 0.0077 0.0077 0.0083Mea n velocity (ms- I ) 0.6 0.8 0.9 0.98Froude number 0.61 0.81 0.91 0.98t ,=pgRS(Pa)+sidewall correct ion 3.9 4.3 4.3 4.6U ,= ,AjG (ms- '1 0.062 0.066 0.066 0.068f= To/pu2 0.087 0.054 0.042 0.038O = ' d ( ~ - P ) g D 0.86 0.92 0.86 0.79T~ (law of the wall) - - 1.9 2.7U. (law of the wall) - - 0.044 0.052Water temperature ("C) 22.5 19.5 18 22

f = 8 T o / p u 2 - - 0.019 0,022Bed configuration Dune s Hum pback Plane PlaneDunes (+ low (+ lowwaves) waves)out-of-phase with bed wav esater surfaceMean Bedform length, L (m ) 0.76 0.75 0.7 0.8- -ange 04-0.9 0.4-1.0Bedform height, H ( m ) 0.025-0.04Downstream M igration rate (mm s - ' ) 1-3 2-4 10 10+HIL

0.01-0.02 0.002-0.003 0.002-0.0030.04 0.02 0.0036 0.0031

Bedload transport rate ( N m -' s - ' ) - -ear reat tachment 0.015 0.086dune back 0.086 0.23spatial average - - 0.22 0.43near reattachment 0.22 0.24dune back 0.28 0.29spatial average - __ 0.3 0.36

- -Bedload mean grain size (mm) - -- -Suspended sediment conce ntration 1.6x 1 0 - ~ 2.1 x 10-4 3.2x 10-4 2.8 1 0 - ~


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Implicationsfor planar laminae ormation

90-100-

759

RUN 3. .. . . . . . . ... . . . . . . . . . . . :

l l c - ' . ~ . . ;( m m )

70-80 -90-

measured after stopping the flow.

RUN 4

. . . . ... .. . . .. . . . . .. . . . . . . . _

turbulence intensity are comparable with those inother experimental studies of separated flows (sum-mary in Allen, 1982, pp. 126-127). Turbulenceintensities in dune troughs also decrease as dunesbecome humpbacked and transitional to plane beds.On dune backs, turbulence intensities in the lowest25% of the flow increase from steep dunes to humpbackdunes, and then generally continue to increase onupper stage plane beds. Flow visualization clearlyshows intense upward-directed turbulent motionsfrom the reattachment region in dune troughs, andthat this upward-moving fluid can approach the watersurface (Fig. 18). Such vertical turbulent motionsbecome progressively diminished through the transi-tion to upper stage plane beds. It appears, then, thatboth horizontal and vertical turbulent velocity fluctua-tions decrease in magnitude in the separated boundarylayers of dune troughs and horizontal intensitiesincrease in magnitude near the bed on dune backsthrough the transit ion to plane beds.Sediment transportBedload transport rates and suspended sedimentconcentrations increase from dunes to upper stageplane beds (Table l), in a similar way to otherexperimental studies (e.g. Guy, Simons& Richardson,1966). With the steepest dunes (Run l), high near-bed

sediment concentrations occur immediately down-stream of the brink line, over the avalanche face.Sediment concentrations are relatively low in theseparated flow region (Fig. 1B). At the reattachmentzone, bedload grains are vigorously and intermittentlythrown upwards from the bed (Fig. lA), but bedloadtransport rates immediately downstream of reattach-ment are low and only 17% of that on the upper duneback (Table 1) . In contrast, low humpback dunes(Run 2) have higher near-bed sediment concentrationsin these trough areas (Fig. 1D) and bedload transportrate near reattachment is high and 39% of that nearthe crest.The mean grain size of bedload is larger on dunebacks than near reattachment, and that on dune backsincreases with mean flow velocity from steep dunes tohumpback dunes and then to upper stage plane beds(Table 1). Such increases in mean grain size can beexplained by increases in local values of bed shearstress.The bedload transport rates and vertical variationof velocity on humpback dune backs are similar tothose on transitional upper stage plane beds, insupport of Bridge's (198 1) suggestion. As there is noevidence for a decrease in qs on upper dune backsrelative to troughs over the transition from dunes toupper stage plane beds, the transition must beassociated with a relative increase in qs in dune trough


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760

80-

J . S . Bridge and J . L. Best

D U N E S - RU N 1

90P L A N E B E D - R U N 3 AND 4

5 0

\.3 02 010

\ .-_.R M S u ' /U

Fig. 3. Exampl es of variat ion in turbu lence intensity ( R M S ( u ' ) / U ) i th d is tance from the bed ( y ) or all runs.

regions. The observed relative increase in qs justdownstream of the reat tachment zone appears to bedue to suppression of upward directed turbulence(bursting) by increased sediment concentrations. Thisis supported by the vertical profiles of mean velocityand RMS(u ' ) /U over plane beds. Such turbulencesuppression enables the downstream velocity near thebed to increase more quickly downstream of reattach-ment (see also McLean & Smith, 1986). This isreflected in the development of humpback duneswhere the crestline has moved upstream relative tothe brinkline. It is not yet clear what is the role of thelag of suspended sediment concentration behind thelocal bed shear stress.

I M P L I C A T I O N S FOR ORIGIN O FHORIZONTAL LAMINAEBridge (1978) summarized pre-1978 theories for theorigin of horizontal laminae in sands. The influenceof turbulence on sediment transport and depositionunder upper stage plane beds was recognized in manyof these theories. Bridge (1978) was the first toexplicitly invoke the turbulent bursting process toexplain some kinds of laminae formed under upperstage plane beds, but fully recognized that near-horizontal laminae can also be produced by low-reliefbedforms. Allen (1984) presented a similar turbulence-based model for horizontal laminae, but emphasized


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Implications for planar laminae form ation 761the role of the larger coherent structures within theouter region of the boundary layer. Of course, it isgenerally recognized that the bursting process isintimately related to such larger scale structures,possessing identical nondimensional periods. Allenstated that a critical difficulty with Bridges modelconcerns the predicted transverse scale of individuallaminae. Allen took this to be on the order of 0.01 m,which is much less than the across-flow lamina widthof decimetres tometres that he has observed. However,Bridge (p. 4) tated that . . . the regular streak patternis destroyed and re-established as a coherent structure,implying some degree of lateral continuity to burstand sweep events and (p. 9) Despite the postulatedlateral continuity of the bursting events, the lateralextent of individual laminae is expected to be muchless than stream depth. Therefore, Bridge (1978)predicted that it is possible for the across-flow extentof laminae to be greater than the width of a singleburst.

Allens model predicts that symmetrical bedwavesranging from 1.33 mm up to 12 mm in height shouldbe present on upper stage plane beds; their wave-lengths and downstream migration rates are postu-lated to be identical to that of the coherent turbulentstructures. It appears from the data presented previ-ously and the experimental da ta of Paola et al. (1989)and Cheel(l984) that roughly symmetrical bedwaveson the order of a few mm in height do occur on upper-stage plane beds; however, their downstream migra-tion rates are at least an order of magnitude less, andtheir lengths are more than twice those postulated byAllen. There seems little doubt that it is only theexperimentally observed bedwaves that can give riseto mm scale fining upward laminae that are laterallyextensive (Paola et al., 1989; Fig. IE). However, weand Paola have recognized turbulence-related varia-tion in grain motion within the bedload layer (e.g.Fig. IF). Bed height clearly varies with such motions,but on a smaller scale than the bedwaves. Paola et al.(1989) described bedload motion in clusters of highlyconcentrated grains at certain times and places on thebed. Deposition was associated with a surge of highlyconcentrated bedload, dominated by coarse grains,that decelerates and then freezes. Most of thedeposition occurred in a few tenths of a second.Subsequently, finer grained sediment accumulates inthe spaces between the uppermost coarse grains. Theresulting accumulation of a fining-upward laminawithin approximately one second is in general accordwith Bridges (1978) model.

Cheel & Middleton (1986a, b ; see also discussion

by Bridge, 1987) provided the first precise measure-ment of the textural and compositional variationswithin horizontally laminated deposits. They recog-nized fining-upwards laminae, coarsening-upwardslaminae and those showing little grading, althoughdefinition of lamina boundaries was somewhat subjec-tive. They interpreted these laminae in terms of aburst/sweep model, although this differed in detailfrom that of Bridge (1978). In their model, fining-upward laminae are postulated to form by fallout ofprogressively finer sand which had been temporarilycarried upward by a burst. Coarsening-upward lami-nae were supposed to form because of sorting bydispersive pressure in a layer of high grain concentra-tion close to the bed. This layer was produced duringa high-speed sweep and deposition occurs from thelayer as the sweep dissipates. Unfortunately, the heavyand light mineral grains in their coarsening-upwardsequences are not clearly dispersive pressure equiva-lent, and such a process was not observed by Paola etal. (1989). In Bridges (1978) model, the coarseningupward parts of laminae were postulated to occurduring bursting and before the maximum bed shearstress associated with a sweep reaching the bed.During this period, grains with relatively lower fallvelocities are dispersed upwards from the bed withinthe vigorous ejection, and the bed shear stress actingon the remaining bed grains progressively increaseswith the incoming sweep. Note that Bridge (1978) didnot address the issue of the distribution of light andheavy minerals in coarsening upward laminae, asimplied by Cheel & Middleton (1984, p. 499).Formation of fining upward laminae was postulatedto occur with the deceleration of the sweep, whenupward directed turbulent velocity fluctuations wereminimal and bed shear stress was decreasing. Thevariable thickness, lateral extent and textural charac-teristics of laminae described by Cheel & Middleton(1986) accord rather well with Bridges (1978) model.However, testing of these alternative hypothesis mustawait further experimental studies.

In conclusion, it appears that laminae can be formedby both the migration of low-relief bedwaves and theturbulent bursting process, as recognised by Paola etal . (1989). Laminae formed by these two processesshould be interposed but will differ in lateral extentand thickness. Laminae associated with migratingbedwaves may extend downstream and laterally fordistances of many flow depths, and may be up to afew mm thick depending on the deposition raterelative to the bedwave migration rate. If the bedwaveshave an avalanche face (rheologic front) the coarsest


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762 J . S . B r i d g e and J . L. B e s tbedload grains accumulate at its base and the laminaegenerally fine upwards. In the absence of an avalancheface, the decrease in bed shear stress from the crest tothe trough of the bedform will result in coarsening-upward laminae as the bedwave migrates (exactlyopposite to Allen's, 1984, model). Unsteady sedimenttransport associated with the turbulent burstingprocess on the depositional downstream slope of thebedwaves (in the absence of an avalanche face) shouldform lenticular laminae parallel to the depositionalsurface, parts of which will be incorporated withinthe more extensive laminae resulting from bedwavemigration (see Paola e t al. , 1989). The downstreamextent of such laminae are predicted to be on the orderof flow depth (Bridge, 1978) but much less than thistransverse to flow. If burst periods are taken as l o - 'to 10" seconds and local deposition rates are on theorder of lo- ' mms-', laminae thicknesses of up toorder 10 ' mm are expected, or a few grain diametersof very fine to fine sand.

A C K N O W L E D G M E N T SThe experiments were conducted at the Departmentof Earth Sciences, University of Leeds, England. Weare especially grateful to Dr M. R. Leeder for makingthese facilities available to us , and to the technicalstaff in the Department of Earth Sciences formanufacture of various items of equipment. We arealso indebted to Mr Richard Middleton of theDepartment of Geology, University of Hull, England,for developing the software for analysis of the hot-filmanemometry data. Travel to the UK for J. S. B. wasmade possible through NSF grant no. INT8502397.

R E F E R E N C E SALLEN , .R.L . (1982)Sedimentary Structu res: Their Characterand Physical Basis, vol. I and 11.Elsevier, Am sterdam.ALL EN, .R .L. (1984) Parallel lamination developed fromupper-stage plane beds: a model based on the largercoherent structures of the turbulent boundary layer.Sediment. Geol., 39,227-242.ALLEN , .R.L. (1985) Principles of Physical Sedimentology.George Allen and Unw in, London.ALLEN, .R.L. & LEEDER,M.R. (1980) Criteria for theinstability of upper-stage plane beds. Sedimentology, 27,BAGNOLD,R.A. (1966) An approach to the sedimenttransport problem from general physics. Prof: Pap. U Sgeol. Surv., 422-1.BRIDGE,.S. (1978) Origin of horizontal lamin ation un der aturbulent boundary layer. Sediment. Geol., 20, 1-16.

209-2 18.

BRIDGE, .S. (198 ) Bed shear stress over subaqueous dunes,and the transition to upper-stage plane beds. Sedimentol-BRIDGE,.S . (1987) Horizontal laminae formed under upperRow regime plan e bed co nditons: a discussion. J . Geol . ,95 ,28 1.BRIDGE,.S. &DOM INIC, .F. 1984) Bedloadgrainveloci t iesand sediment transport rates. Water Res. Research, 20 ,CHANDRSUDA,. & BRADSHAW , . (1981) Turb ulencestructure of a reattaching mixing layer. J . Fluid Mech.,CHE EL, .J. (1984) Heavy m ineral shadows, a new sedimen-tary structure formed under upper Row regime plane bedconditions : its directional and hydraulic significancc. J .sedim. Petrol.,54, 1173-1 180.CHEEL, .J . & MIDDLETON,.V . (1986a) Measurement ofsmall-scale laminae in sand-sized sediments. J . sedim.Petrol . ,56, 547-549.CHEEL, . J . &MIDDLETON,.V . (1986b)Horizontallaminaeformed under up per flow regime plane bed conditions. J .Geol . ,94,489-504.COSTELLO, .R. (1974) Development of bed con$guration in

coarse sands. Report 74.1, Earth and planet. Sci. Dep.,Massachusetts Institute of Technology.ENGELUND,. & FREDSOE,. (1974) Transitionfrom dunes toplane bed in alluvial channels: Institute of H ydrodynamicsand Hydraulic Engineering, Technical University ofDenm ark , Series Paper 4 ,4 6 p p .E NGE L UND,. & FREDSOE,. (1982) Sediment ripples a nddunes. Ann. Rev. Fluid M ech ., 14, 13-37.FREDSOE,. (1981) Un stead y flow in straig ht alluvial streams.Par t 2 . Transi t ion from dune to plane bed. J . Fluid Mech.,FREDSOE,. (1982) Shape and dimensionsof s tat ionary dunesin rivers. J . Hy draul. D iv . , A m . Soc. Civ. Engnrs, 108,932-947.GR ANT , W .D. & MADSEN,O.S. (1982) Moveable bed

roughness in unsteady oscillatory Row. J . geophys. Res.,GUST,G . & SOUTHARD,.B. (1983) Effects of weak bedloadon the universal law of th e wall. J . geophys. Res. , 88,5939-5952.GU Y, H.P . , SIMONS,D.B . & RICHA RDSON , .V. (1966)Sum mary of alluvial channel d ata fro m flume experiments,1956-1961. Prof: Pap. USg eol . Surv . ,4621.HAM M OND,.D.C. & HEATHERSHAW,.D. (1981) A wavetheory for sand wave s in shelf seas. Nature, 293,208-210.JACKSON, .G. (1976) Sedimentological and fluid dynam icimplications of the turbulent bursting phenomenon ingeophy sical flows. J . Fluid Mech. 11, 31-560.JOPLING,A.V. (1964) Interpreting the concept of thesedimentation unit. J . sedim. Perrol., 34, 165-172.KE NNE DY,.F. (1963)The mechan icsofdun esand ant idunesin erodible-bed channels. J . Fluid Mech., 16,521-544.K E N N E D Y ,.F. (1969) The formation of sediment ripples,dunes and antidunes. Ann. Rev. Fluid Mech ., 16, 521-544.KOBAYASHI,. & MADSEN, 3.1985) Formation of ripplesin erodible channels. J . geophys. Res ., 90,7332-8340.MCLEAN, .R. & SMITH, .D. (1986) A model for flow overtwo-dimensional bedforms: J . Hydraul . Eng., 112, 300-317.PAOLA, ., WIELE, .M . & REINHART, .A. (1989) Upper-

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I m p l ic a t io n s o r p l a n a r laminae o r m a t i o n 763regime parallel lamination as the result of turbulentsediment transport and low amplitude bedforms. Sedimen-tology, 36, in proof.RICHARDS,. J . (1980) The formation of ripples and duneson an erodible bed. J . Fluid Mech., 99, 597-618.SAUNDERSON, .C . & LOCKETT,.P . (1983) Flume experi-ments on bedforms and structures at the dune-plane bedtransition. Spec. Publ. Int. A ss . Sediment. , 6,49-58.

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(Manuscript received I8 Augu st 198 7: recision received 8 February 1987)

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