JOURNAL OF SEDIMENTARY RESEARCH, VOL. 72, NO. 5, SEPTEMBER, 2002, P. 629–640Copyright q 2002, SEPM (Society for Sedimentary Geology) 1527-1404/02/072-629/$03.00

SEDIMENT SUPPLY-LIMITED BEDFORMS IN SAND–GRAVEL BED RIVERS

M.G. KLEINHANS, A.W.E. WILBERS, A. DE SWAAF, AND J.H. VAN DEN BERGUtrecht University, Netherlands Centre for Geo-ecological Research (ICG), Department of Physical Geography, P.O. Box 80115, 3508 TC Utrecht, The Netherlands

e-mail: m.kleinhans@geog.uu.nl

ABSTRACT: The stability of bedforms in mixtures of gravel and sandis not well understood. Two bedform types are characteristic: flow-parallel sand ribbons and flow-transverse barchans. Flume experi-ments and field data presented here show that gradual transitionsexist from sand ribbons to barchans, and from barchans to fully de-veloped dunes. Barchans and sand ribbons occur when not enoughtransportable sediment is available for the formation of fully devel-oped ripples or dunes. The reason is that a part of the bed sedimentis immobile, e.g., with an armor layer, which limits the sediment sup-ply and thus the volume of sediment available for the formation ofbedforms.

Bedform stability diagrams are shown to be extendable to sedi-ment supply–limited bedforms in sand–gravel sediment, if the par-ticle parameters of the diagrams are derived from the transportedsediment instead of the bed sediment. Barchans and forms transi-tional to fully developed dunes plot in the dune stability fields. Sandribbons, on the other hand, plot in the ripple, lower plane bed, anddune fields.

In the case of sediment supply limitation, bedforms are partly orcompletely related to the characteristics of the sediment supply fromupstream. The sediment underlying the bedforms may be a stablearmor and the exchange of sediment between this armor and thebedforms may be small or non-existent. Consequently, bedform char-acteristics in sand–gravel mixtures in supply–limited conditions oftenare not predictable from the local hydraulics and sediment charac-teristics.

INTRODUCTION

The stability of bedforms in sandy material is well understood. Manybedform stability diagrams for uniform sand have been proposed in thepast decennia, e.g., Simons and Richardson (1965), Allen (1984), Southardand Boguchwal (1990), and Van den Berg and Van Gelder (1993, 1998).Bedforms in sediments with both gravel and sand have received attentiononly recently. An outstanding property of (bimodal) sand and gravel mix-tures is that the larger grains become practically immobile during somecritical lower flow stage, while the smaller grains are propagating down-stream as bedforms (Wilcock 1998; Carling et al. 2000a; Carling et al.2000b). The effect of this partial mobility of sediment on bedform char-acteristics and morphology is not well known.

The objectives of this paper are (1) to describe the bedform types thatoccur in sediments with sand and gravel, (2) to test the applicability ofexisting bedform stability diagrams to sediment mixtures, and (3) to de-termine the effect of sediment supply on bedform morphology. Flume ex-periments presented herein provide bedform data for conditions rangingfrom extremely transportable sediment-supply-limited to supply-unlimited.Furthermore, new data are presented for bedform types in natural riverswith (bimodal) sand–gravel sediment. These data and data from the liter-ature are used to infer the main factors determining bedform stability andmorphology in sediment supply-limited conditions, and are applied to ex-isting bedform stability diagrams to extend their applicability.

REVIEW

Dinehart (1989, 1992) observed active gravel dunes in the North ForkToutle river, proving that dunes do exist in very coarse sediment. Super-

imposed on and migrating over these dunes, features were found thatseemed to be transitional forms between bedload sheets and small dunes.Carling (1999) presented an overview of published data on bedforms incoarse sediments and applied those to the bedform stability diagrams ofAllen (1984) and Southard and Boguchwal (1990). The stability fields ofbedforms in sand could be extended into the gravel grades. However, thedata used by Carling refer mostly to unimodal sand or gravel sediments;bimodal mixtures were not considered.

The effect of sediment sorting on bedform stability was experimentallydetermined by Chiew (1991). Lognormally distributed sediments with aD50 of 0.6 mm and a Trask sorting coefficient varying from 1.2 to 5.5 weresubjected to steady flows of 0.3 to 2 m/s in a small recirculating flume.Chiew found that differences from uniform sand were: the armoring ten-dency, the absence of antidunes, and the fact that bedform sizes at inter-mediate flows were dependent on the availability of fine sediment at thebed-surface. Chiew did not provide information on detailed bedform mor-phology and sediment transport.

Three bedform types appear in literature as typical for sand–gravel sed-iment: bedload sheets, flow-parallel sand ribbons, and flow-transverse bar-chans. Bedload sheets are thin accumulations of bedload sediment abouttwo grain diameters thick and ; 0.5–2 m long, and are recognizable mainlyby their flow-transverse sorting with the coarse grains at the leading edge.Sand ribbons are created by near-bed helical flow cells in combination withselective transport of bed sediment (e.g., Allen 1970; McLelland et al.1999). The sand is concentrated in flow-parallel ribbons and transportedover the immobile gravel. The spatial segregation of fine and coarse sed-iment enhances this flow structure, providing a positive feedback for for-mation of sand ribbons (Colombini 1993; McLean 1981; McLelland et al.1999). Barchans have a crescent shape with the horns pointing downstream,and they migrate over an immobile base. They are well known features insubaerial settings and have a stable form; here, barchans were observed topreserve their form while migrating over long distances (McKee 1979; Pyeand Tsoar 1990; Hesp and Hastings 1998). The supply of transportablesediment is limited, either because the base is wet and thus cohesive dueto a high groundwater table, or because the base is more or less immobile,in the case of a desert pavement or sabkha. Individual barchans are sepa-rated from each other by the immobile substrate. With increasing supplyof mobile sediment barchans may coalesce to barchanoid transitional formsbetween barchans and dunes.

The first mention of barchans in the fluvial literature known to the au-thors is by McCulloch and Janda (1964), who observed barchan dunesmigrating over an immobile gravel lag in an Alaskan river. They suggestthat subaqueous barchans are formed in response to a limited sand supplydue to the immobility of the coarser grains. Recently, Carling et al. (2000a)and Carling et al. (2000b) described large sandy barchans migrating overan armor layer in the river Rhine (Germany) downstream of a hydropowerdam, which limits the upstream sediment supply. In addition, researchersmention barchans migrating over armor layers in flume experiments (Klaas-sen 1986; Rosza and Jozsa 1999).

Compared to their subaqueous counterparts, subaerial dunes are not lim-ited in height because of an infinite air ‘‘depth,’’ whereas dunes in flumesor shallow rivers react strongly to changes in water depth (e.g., Southardand Boguchwal 1990). An important similarity is that the height of sub-aerial barchans is often limited by sediment supply, although the limitationof sediment supply does not necessarily mean that barchans become smaller

630 M.G. KLEINHANS ET AL.

FIG. 1.—Grain-size distribution of the initial bed sediment in the flume experi-ments. The distribution is given as the envelope of the distributions of five largesamples.

FIG. 2.—Sequence of the experiments of Blom and Kleinhans (1999) (after Klein-hans 2000).

TABLE 1.—Experimental conditions (Blom and Kleinhans 1999; Kleinhans 2000).

Experiment ConditionWater Depth*

(m)Discharge*

(m3/s)

FlowVelocity**

(m/s)(Q/A)

WaterSurfaceSlope(10-4)

u9Trans-port

Thickness ofTransp.Layer(m)

D50Transport* Final Bed State

Bed was mixed and bed slope installedT0 incipient motionT1 transitional flowT2 armoringT3a fast gradual flow rise

0.20–0.200.20–0.370.37–0.370.37–0.46

0.13–0.130.13–0.330.33–0.330.33–0.50

0.40–0.440.42–0.590.59–0.600.59–0.73

24.4824.4825.2224.53

0.0730.1020.056

0.0010.0010.0000.001

0.620.621.33

flat bed, flow-parallel sand ribbonsflat bed, flow-parallel sand ribbonsflat armored bedflat armored bed

T3b fast gradual flow riseT4a top speedT4b incipient motion

bed was remixed and new bed slope installedT5 incipient motion

0.49–0.610.49–0.520.38–0.35

0.21–0.25

0.60–0.780.60–0.600.33–0.33

0.22–0.26

0.78–0.870.77–0.820.59–0.64

0.68–0.73

27.0626.3824.88

214.72

0.1930.134

0.170

0.0020.0080.008

0.008

0.650.61

0.72

small barchans over armor layersmall barchans over armor layersmall dunes over armor layer

small barchans over armor layerT6 transitional flowT7 top speedT8 transitional flowT9 lower flow

bed was remixed and new bed slope installedT10 incipient motion

0.24–0.330.34–0.360.35–0.270.25–0.27

0.14–0.19

0.26–0.380.41–0.430.42–0.300.26–0.28

0.14–0.19

0.70–0.790.77–0.810.79–0.700.68–0.72

0.49–0.60

214.62215.20215.71216.94

211.06

0.2170.241

0.204

0.126

0.0170.0280.0290.027

0.002

0.610.59

0.60

0.73

dunes over armor layerlarge dunes over armor layerlarge dunes over armor layerlarge dunes over buried armor layer

small barchans over armor layer

Notes: Water temperature in all experiments: 148C.* To obtain constant flow velocities during an equilibrium test, both the water depth and discharge were adapted. Therefore these parameters are given as a range.** The flow velocity in the equilibrium experiments was constant, the given range is twice the standard error. The average velocity was used in the graphs.*** The water-surface slope approximates the average bed slope.

as the sediment supply diminishes. Instead, the number of barchans simplydeclines because of the declining availability of mobile sediment for bed-form formation. This agrees with the observation of Rubin and Topping(2001) that in case of extreme winnowing, coarsening of the bed may beaccompanied by reduction in surface area of transportable sediment patcheson the river bed. Thus, subaerial dunes can be limited in height only bysediment supply, whereas subaqueous dunes can be limited in addition bywater depth.

The phrase ‘‘supply-limited’’ here refers to a limitation of available,transportable sediment from which the bedforms are molded. With a fullymixed bed as the initial condition, this could also be seen as a flow limi-tation. The critical shear stress for the larger grains in the bed is not ex-ceeded by the flow, which leads to coarsening of the bed, and less sedimentin transport than would have been the case in fully mobile bed conditions.Thus the limit on entrainment is strongly related to the critical shear stressof all grain-size fractions. This effect is different for different sedimentmixtures. In bimodal sediment the finer grades are much more mobile thanin unimodal sediment, whereas in both cases the mobility of the finer gradesis less than in uniform sand (Wilcock 1998). In the case of an armor layerformed during a previous discharge wave or period of low flow, however,

sediment-supply limitation is not seen as a flow limitation, because thatcondition does not relate to the present flow. Such an armor layer (historyeffect) inhibits the entrainment of finer sediment from the underlying bed,which otherwise would have been entrained in the present flow.

An important question is how the supply limit relates to the stability andmorphology of subaqueous bedforms. Belderson et al. (1982) observed mi-grating sand ribbons, sand barchans, and dunes over a clay substrate onthe continental shelf. They presented a semiquantitative model of bedformmorphology with the availability of sediment for bedload transport as themain factor. Likewise, McKee (1979) presents a qualitative model to il-lustrate the continuous sequence of subaerial transverse dunes to transi-tional forms to barchans with unidirectional wind and diminishing sandsupply. No model is available for bedforms in rivers.

In the case of supply limitation, bedforms apparently are related partlyor completely to the characteristics of the sediment supply from upstream.Therefore, in contrast to the unimodal case, bedform characteristics in (bi-modal) mixtures at supply-limited conditions may therefore be unpredict-able from the local hydraulic and sediment characteristics. This hypothesisis tested herein.

631SEDIMENT SUPPLY-LIMITED BEDFORMS

FIG. 3.—Bedform types observed in the flume experiments. Arrows denote flow direction, and scale bars are 0.5 m. Stippled areas are sand and dots are gravel.

FIG. 4.—Bedform types and height as a function of depth-averaged flow velocityin the flume experiments. Labels refer to the flume experiments. The key to bedformtype is shown in Figure 3. The arrows indicate the order of the experiments.

FIG. 5.—Location of the field measurements in the river Allier (arrow) and theriver Waal (box). The area in the box in the Netherlands is enlarged in Figure 7.

FLUME EXPERIMENTS

Description of the Experiments

The experiments were done with slightly bimodal sediment (Fig. 1) fromthe uppermost reach of the river Waal, a distributary of the Rhine in theNetherlands. Herein, only the results with respect to bedform morphologyare given. Kleinhans (2000) presents an overview of all results. The ex-periments were started with a mixed bed, installed at a bed slope equal tothe water-surface slope. The flow was started slowly (over 15 minutes) toprevent bed damage and was maintained until the system was in equilib-rium (Fig. 2). The equilibrium phase was pragmatically defined as the timeat which changes in flow roughness, bedform dimensions, and sedimenttransport became smaller than the measurement variability. After drainingthe flume, the bed was photographed and sampled, and the sampling pitswere repaired with original sediment. Next, a different bed shear stress wasapplied until equilibrium was again reached (Fig. 2) (Blom and Kleinhans1999; Kleinhans 2000). The rising and waning flow stages between theequilibrium experiments are referred to as transitional experiments. Theconditions of most experiments were near incipient motion for most di-ameters, but some experiments had shear stresses well above critical formost diameters (Table 1). Sediment transport in suspension was negligible.

It is assumed that the bedload transport depends on the grain-related bed

shear stress (grain shear stress) (Van Rijn 1984; Van den Berg and VanGelder 1993). The grain bed shear stress is herein defined as t9 5 rg(u /C9)2, in which r 5 density of water (1000 kg/m3), g 5 gravitationalacceleration (9.81 m/s2), u 5 depth-averaged flow velocity (m/s), and C95 Chezy (m0.5/s) roughness related to grain friction (explained later). Itwas assumed that the roughness coefficient related to grains C9 (skin fric-tion) remained constant in the experiments. On the basis of this assumption,Kleinhans and Van Rijn (2002) successfully hindcasted the sediment trans-port with a bedload predictor for these flume experiments, which suggeststhat the assumption is reasonable.

C9 was calculated using the White-Colebrook equation and assuming aNikuradse grain-related roughness k9 5 D90 (m) in which D90 5 90thpercentile of the original sediment mixture: C9 5 18log(12h /k9) in whichh 5 water depth (m). Alternative methods, which subtract bedform-relatedroughness from total roughness to obtain grain roughness, are subject to

632 M.G. KLEINHANS ET AL.

TABLE 2.—Summary of the collected bedform, flow, and sediment data in the riverAllier.

Bedform TypeWater Depth*

(m)

FlowVelocity*

(m/s)u9

Transport*

Thickness ofTransportLayer*

(m)

D50Transport*

(mm)

dunebarchansand ribbonlower plane bed

0.85–1.100.53–1.040.32–0.700.32–1.25

0.55–0.800.52–0.740.27–0.620.41–0.71

0.052–0.1180.066–0.1120.018–0.1310.032–0.088

0.030–0.1000.004–0.0090.001–0.0020.001–0.004

0.42–0.910.53–1.040.46–0.580.33–1.54

Notes: Water temperature during the whole period: 208C.* Range of data within the bedform class. In total, 32 data points were collected.

FIG. 6.—Observations of migrating waves of sand on the immobile armor in theriver Allier. A) Bedforms originating from a sand deposit in a meander pool. Bed-form crests are denoted by solid lines, and sand by stippled patches. B) Bedformsin a migrating wave of sand.

large uncertainties related to the measurement of the total roughness andthe determination of the bedform roughness.

In order to keep the grain-related shear stress for each experiment at aconstant value, the flow velocity (u 5 Q /A, with Q 5 flow discharge (m3/s) and A 5 hW is cross-sectional area (m2), W 5 width of the flume (m))had to be kept constant while bedforms developed. This cannot be estab-lished with a constant flow discharge, because the growing bedforms leadto increasing form roughness and hence to decreasing grain bed shearstress. Therefore both the water depth (controlled by a downstream weir)and discharge had to be adjusted iteratively while maintaining uniformflow. It is acknowledged that the assumption of constant C9 may not holdin changing surface compositions of sediment mixtures in different con-ditions, but the alternative of keeping the flow discharge constant wouldhave led to a much less constant t9.

The experiments were conducted in the straight sediment-recirculatingsand flume in the Delft Hydraulics Laboratory, which is 50 m long and1.5 m wide (Bakker 1984). The water temperature was kept constant at148C. Bed-surface and water-surface levels are automatically recorded atevery centimeter along the centerline of the flume with electromagneticwater-surface and bed-surface profilers. The total bed shear stress was cal-culated from the bed-surface and water-surface profiles and corrected forflume sidewall roughness with the method of Vanoni and Brooks. All bedprofiles were detrended and analyzed with the computer program Dunetrack2D (Wesseling and Wilbers 1999). The output of this program is a numberof bedform parameters: height, length, volume, and number of bedforms.

During the experiments the sediment transport rate was measured in therecirculation system. In experiment T2, the sediment was not recirculated,in order for an armor layer to develop. The sediment transport per grain-size fraction was determined from the bulk transport (kg/s). Samples fromthe transported sediment were analyzed by sieving and settling tube todetermine the grain-size distributions.

Results of the Flume Experiments

In Figures 3 and 4, the observed bedform types are given as a functionof depth-averaged flow velocity and bedform height. The flow-parallel rib-bons occurred at the lowest flow velocities (T0 and T2). Between the rib-bons the bed surface consisted mainly of gravel. The sand in the ribbonsmigrated downstream in the form of small ripples, which sometimes hadbarchanoid forms. Barchans occurred in experiments T3b, T4a, T5, andT10. Dunes occurred in experiments T4b and T6–T9. Furthermore, sheetswere observed to migrate over the dunes. The sheets had the height ofripples but were somewhat longer and sometimes showed a longitudinalsorting with the coarser grains at the leading edge. The sheets resembledboth sand ripples and bedload sheets.

The findings are interpreted as follows. During low flow, armoring al-most inhibits bedload transport and only a very small portion of the bed iscovered by bedload sediment in sand ribbons, bedload sheets, or barchans.At rising stages the armor layer remains unbroken up to a certain point.This point is determined by the threshold of motion of the imbricatedparticles and pebble clusters in the armor layer. In this case, the armor

layer was broken up by the turbulence in the bedform troughs, as was alsofound by Klaassen (1986), and mixed into the bedform sediment. Conse-quently, more sand becomes available from below the armor layer and thebedforms may eventually evolve into dunes.

The history of sorting in the bed partly determines the outcome of theexperiments. In the absence of an initial armor layer, a higher shear stressmobilizes more sediment and larger grains, leading to the observed tran-sition from sand ribbons to barchans to dunes (cf. T0, T10, T5, and T7).The outcome of T7 would have been the same for a fully mixed bed asinitial condition, because the turbulence in the troughs of barchans anddunes becomes strong enough to override the armoring tendency, as wasalso observed by Klaassen (1986). When an armor layer is allowed todevelop (as in T2) by cutting off the upstream sediment supply, however,then the critical shear stress for mobilizing the armor layer is much larger.Once the armor layer is mobilized, the same transitions from sand ribbonsto barchans and dunes occur (in T3 and T4), though at much higher shearstresses, and probably within a much narrower range of shear stresses.Consequently, although the experiments represent only a subset of all pos-sible realizations, they range from the endmembers of a strong armor layerto a fully mixed bed as initial conditions.

Summarizing, during low flow most of the sediment is immobile, leadingto strong sediment supply-limited conditions with sand ribbons. With in-creasing flow strength and sediment transport, sand ribbons evolve intobarchans, barchanoids, and finally dunes.

FIELD MEASUREMENTS

Field Measurements in the River Allier (France)

The river Allier, south of Moulins (central France) (Fig. 5), is one ofthe few meandering sand–gravel bed rivers without artificial bank protec-tion over distances of a number of meanders that still exist in Europe. Ata bankfull discharge, which is about 900 m3/s, the width of the river variesbetween 60 and 100 m. During a period of high discharge the banks inouter bends may erode several tens of meters. Point bar morphology is welldeveloped, with riffle spacings of about 600 m. The river bed is mostlyarmored during low flow, with D50 5 18 mm, D90 5 40 mm and 85%gravel in the armor layer. The underlying bed sediment is distinctly bi-modal, with modes at 0.7 and 24 mm, D50 5 7 mm, D90 5 32 mm and68% gravel.

Observations and measurements were done in summer during low flow

633SEDIMENT SUPPLY-LIMITED BEDFORMS

FIG. 7.—The location of the measurement section in the river Waal in the Neth-erlands is just downstream of the bifurcation point of the Rhine into the Panner-densch Kanaal and the Waal. The flow direction is west. The location of this mapis given in Figure 5.

FIG. 8.—A) Flow discharge and dune height inthe river Waal in October–November 1998, aswell as a planform echo-sounding map of theriver bed in the Waal just downstream of thebifurcation point with the Pannerdensche Kanaal.B) Two examples of dune profiles are givenwith large and with small dunes.

with discharges of 20–40 m3/s. Bedforms consisting of sand with a D50 of0.5 mm migrated over the armored bed. Bedform dimensions (height,width, length) and the surface area covered by the bedforms were measured.Vertical velocity profiles and water depths were obtained at several loca-tions above and near the bedforms with an electromagnetic flow device(EMF) mounted on a portable frame. The flow velocity was measured atthe following levels above the bed: 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.40,0.50 and 0.70 m. From these values, data on depth-averaged flow velocities,bed shear stress, and roughness length were obtained at the location of the

bedforms. The bed and bedforms at the measuring location were sampledafter the measurements and sieved for grain-size analysis.

Several types of bedforms were observed (Table 2): sand ribbons, bar-chans, and dunes, often concurrent in the same stretch of the river. Barchansvaried in height between 0.01 and 0.05 m, and dune heights were between0.05 and 0.25 m. The sand coverage of the bed varied from 0 to 100%.Relict gravel dunes were found on the surface of bars above the low-flowwater surface.

Meander pools often contained fine sand fills between 0.1 and 1 m thick.These are probably waning-flow or low-flow deposits as described by Lisleand Hilton (1999). During the fieldwork period, a small peak in the dis-charge occurred, which allowed a wave of sand to detach from the sanddeposit in the pool (Fig. 6). The wave of sand provided a spatially varyingsediment supply for bedforms in equal flow conditions. Near the pool,dunes with sinuous crests occurred, and these gradually changed into bar-chanoid features downstream. Farther downstream barchans occurred con-currently with sand ribbons, and only sand ribbons occurred even fartherdownstream. At the front end of the wave of sand the armor was fullyexposed. In time the volume of sand in the wave decreased, as the down-stream-propagating sand infiltrated into the armor layer.

At other locations, downstream migrating waves of sand of a few squaremeters to a few hundred square meters in area were found with the samepattern and order of bedform types, originating from the sand deposits inpools or from bank failures. In the surveyed sand wave (Fig. 6), the bed-form pattern was mirrored in both the upstream and the downstream di-rection. For all locations and bedform types the flow conditions were moreor less equal and the armor layer was stable.

Summarizing, a large range of bedform types were found in the riverAllier at flow conditions in which the gravel was immobile. These bedformtypes were the same as found in the flume experiments. In contrast with

634 M.G. KLEINHANS ET AL.

TABLE 3.—Summary of the collected bedform, flow, and sediment data in the river Waal.

Date Bedform TypeDischarge

(m3/s)Water Temp.

(8C)Water Depth

(m) u9 TransportDune Height

(m)Dune Length

(m)Dune Volume

(m2)

Thicknessof Transp.

Layer(m)

D50Transport*

(mm)

31-Oct-9802-Nov-9803-Nov-9805-Nov-9805-Nov-98

small dunessmall dunesdunesdunesdunes

39935032574160975891

1212111111

9.29.7

10.210.710.5

0.3130.3610.4890.5210.577

0.090.190.390.470.50

3.227.028.69

10.9312.37

0.200.831.872.863.41

0.0630.1180.2150.2610.276

0.940.920.740.740.61

07-Nov-9809-Nov-9810-Nov-9812-Nov-9812-Nov-98

dunessmall dunessmall dunessmall dunessmall dunes

51144198389934073372

101010

99

10.19.49.28.78.6

0.3160.2870.3440.3920.390

0.460.280.280.280.28

18.866.536.536.196.08

4.680.980.980.950.92

0.2480.1500.1500.1540.152

0.860.890.700.560.56

* D50 of transported sediment determined from Helley-Smith bedload trap samples, averaged over the width of the river.

TABLE 4.—Summary of flume and field data of flow, sediment, and bedform types from literature.

Author Condition Bedform Type

Approx. WaterTemperature

(8C)Water Depth

(m) u9 Transport

Thickness ofTransport Layer

(m)D50 Transport

(mm)

Bennett and Bridge (1995)

Blom et al. (2000)

Carling et al. (2000)**

flume

flume

field

bedload sheetslow-relief bars (small dunes)*barchansdunesbarchans

25251818unknown

0.074–0.0760.074–0.076

0.1550.320

2.7–6.65

0.103–0.1160.103–0.1160.093–0.094

0.1260.078–0.211

0.004–0.0050.006–0.0080.008–0.009

0.0340.051–0.099

2.18–2.322.18–2.321.34–1.36

1.340.9–0.9

Chiew (1991) flume dunesrippleslower plane bed

unknownunknownunknown

0.170.170.17

Chiew does not give these parameters,only bed sediment and stream power.

Dinehart (1992)Horton et al. (2000)

field****flume

dunesripplesbedload sheetslow-relief bedforms (small dunes)*ripples

8–1025252525

1.40–2.240.172–0.1810.173–0.1810.176–0.1780.138–0.15

0.105–0.2450.168–0.2640.217–0.2640.247–0.2640.119–0.221

0.079–0.2260.002–0.0020.004–0.0060.007–0.0080.002–0.003

22–360.55–0.880.55–0.880.73–0.880.54–2.78

Hirano and Ohmoto (1988)***McLelland et al. (1999)

flumeflume

bedload sheetslow-relief bedforms (small dunes)*sand ribbonssand ribbons

2525unknownunknown

0.139–0.150.139–0.142

0.0500.100

0.119–0.2210.119–0.221

0.0770.044

0.004–0.0070.004–0.006

0.0020.0005

0.57–2.780.78–2.78

0.700.87

* Low-relief bedforms and bars are here interpreted as small dunes.** For additional data, Carling and Goelz (1993) was used.*** In McLelland et al. (1999).**** North Fork Toutle river.

the experiments, the flow conditions were about the same for all bedformtypes, and the armor layer was not broken up. The main factor causing thedifferences in bedform type was the availability of mobile sand for theformation of the bedforms.

Field Measurements in the River Waal (The Netherlands)

The measurement location was the upstream section of the river Waal(Fig. 7). For navigation purposes and bank protection, both sides of theriver have a system of groins. The average width of the river (between thegroins) is 240 m. Here, the water depth varies between 3 and 12 m. Themean discharge of the Waal is 1350 m3/s with peaks up to 8000 m3/s. Athigh discharges bedforms develop with lengths over 10 to 20 m and heightsover 0.5 m over the full width of the river (Wilbers 1999).

The measurements (Kleinhans 1999, 2000) were done during a floodwave with a peak discharge of 6400 m3/s. At the measurement locationthe bed consists of a bimodal sand–gravel mixture with a median diameterof 2.8 mm, with the two modes at 0.5 mm and 10 mm. The D90 of sus-pended sediment is about 300 mm, and the mesh bag of the Helley-Smithtype bedload sampler (samples used here for grain-size analysis) had amesh size of 250 mm.

Three-dimensional mapping of the bed was done twice a day over 1 kmalong the river with a multibeam echo sounder. Dunetrack 2D (Wesselingand Wilbers 1999) software was used to calculate bedform dimensions andstatistics. The observed bedform type was straight-crested transverse (two-dimensional) dunes. The bedforms attained their maximum height one dayafter the discharge peak (Fig. 8, Table 3). After the peak discharge, smaller

dunes emerged that propagated over the immobile and gradually disap-pearing large dunes. Allen and Collinson (1974) attribute this superpositionof small active bedforms on inactive large dunes to the fast change indischarge.

In conclusion, during discharge peaks in the river Waal the bedform typeis two-dimensional dunes with no significant armor layers in the troughs.Supply-limited bedforms were not observed, but they might have been tosmall to be seen with the echo sounder.

BEDFORM STABILITY DIAGRAMS

Hereinafter the hypothesis will be tested that the boundaries betweenbedform states as provided by the stability diagrams should simply be ex-trapolated into the coarser grades (Carling 1999). A disadvantage of mostof the existing diagrams is that they require information on the energygradient of the flow, or, alternatively, the total hydraulic roughness (com-prising bedform and skin friction) in order to calculate the bed shear stress.In rivers these parameters generally are not measured with the requiredaccuracy.

The bedform stability diagram of Van den Berg and Van Gelder (1993)does not have this disadvantage, because bedforms are plotted as a functionof a grain shear stress–related dimensionless mobility number versus adimensionless grain number. The mobility, or skin friction–related Shieldsparameter, is u 5 t9[(rs 2 r)g D50], with D50 5 median diameter of thebed sediment, g 5 gravitational acceleration, rs 2 r 5 submerged densityof sediment, and t9 5 grain-related bed shear stress. The grain, or Bon-

635SEDIMENT SUPPLY-LIMITED BEDFORMS

FIG. 10.—Data on bedforms in non-uniform sediment plotted in the diagram ofChiew (1991). The D50 and D90 are determined from the bed sediment.

←

FIG. 9.—Data on bedforms in non-uniform sediment plotted in the Southard andBoguchwal (1990) bedform stability diagram for 10 C-equivalent quantities andsubcritical flow conditions: A) Flume and field data, D50 determined from bed sed-iment. B) Flume data, D50 determined from transported sediment. C) Field data, D50

determined from transported sediment. Labels for regions: I, no movement on planebed; II, ripples; III, lower-plane-bed; IV, dunes; V, upper-plane-bed.

nefille, parameter is D* 5 D50 5 [(rs 2 r)g(rn2)]1/3, with n 5 kinematicviscosity (m2/s).

A number of datasets with different types of bedforms in sand–gravelmixtures were collected from the literature (Table 4). To investigate thenature of the bedforms in all datasets (Tables 1–4), they are applied tothree bedform stability diagrams: those of Southard and Boguchwal (1990),Chiew (1991), and Van den Berg and Van Gelder (1993).

Figure 9 shows the diagrams of Southard and Boguchwal (1990). InFigure 9A, the D50 was determined from the bed sediment (if available).In uniform sediment, the bed and bedload consist of the same sediment,but in non-uniform sediment the larger grain-size fractions may be im-mobile. Bedforms then depend not only on the grain-size of the mobilesediment but also on the availability of this mobile sediment, which maydeviate considerably from the grain characteristics of the immobile bedsurface. Therefore it is hypothesized that the relevant grain-size for bedformstability is the transported sediment (bedload), because the bedforms com-prise this sediment (Figs. 9B, C).

For the diagram based on bed sediment (Fig. 9A), a considerable numberof barchans and dunes plot in the lower plane bed stability field. These arethe bedforms in the Allier (this study) and in the Niederrhein (Carling etal. 2000a; Carling et al. 2000b) (Table 4). For the diagrams based on thetransported sediment the result is much better than was expected. Barchansall plot in the dune field. Sand ribbons plot in the dune, ripple, and lower-plane-bed range.

For the Chiew (1991) diagram (Fig. 10), streampower is plotted againstthe D90/D50 of the bed sediment. For the Chiew data it is assumed that the

636 M.G. KLEINHANS ET AL.

FIG. 11.—Data on bedforms in non-uniform sediment plotted in the Van den Berg and Van Gelder (1993) bedform stability diagram. A and B are flume and field data,respectively, D50 and D90 determined from bed sediment. C and D are flume and field data respectively, D50 and D90 determined from transported sediment.

sediment was lognormally distributed and the D90 5 D50s1.3, in which sis the Trask sorting as given by Chiew. The data mostly plot in the fieldsas indicated by Chiew, confirming his conclusion that the bedform stabilityis independent of sediment sorting.

The Van den Berg and Van Gelder stability diagram is given in Figure11. Note that the D50 and D90 of the bed or transported sediment are in-corporated in the Shields parameter related to grain roughness. In Figure11A (flume) the bedform types plot in the correct stability fields, but thefield data in Figure 11B plot extremely low in the lower-plane-bed field.In Figure 11C and D, in which the D50 and D90 of the transported sedimentare used, the bedform types plot reasonably well within the correct bedformstability fields. The only exception is the Dinehart data, which apparentlyplots partly in the lower-plane-bed field. The sand ribbons plot in the lower-plane-bed field as well as in the ripple and dune fields. Again, the classi-fication is successful when size parameters of the transported sediment(instead of the bed sediment) are taken.

Note that ripples from the Horton dataset (Table 4) would have plottedin the dune range at grain-sizes larger than 0.7 mm, whereas Costello and

Southard (1981) noted that ripples do not exist for grain-sizes larger than0.7 mm. Horton (personal communication) indicates that the ripples con-sisted of sand with grain-sizes smaller than 0.7 mm, which migrated overthe other bedforms, as has often been observed in the flume experimentsand in the Allier. Data on superimposed ripples in the dune regime havetherefore been excluded from the diagrams.

There has been some discussion in literature about the nature of bedloadsheets (e.g., Whiting et al. 1988; Iseya and Ikeda 1987; Bennett and Bridge1995), particularly their relation with ripples or dunes. The bedload sheetsand low-relief bedforms in the Bennett and Horton datasets plot in the dunefields. Dinehart (1989, 1992) and Whiting et al. (1988) observed bedloadsheets that were superimposed on dunes. Just like the ripples of Horton,these sheets would also plot in the dune stability field because the bed isin the dune phase, but this does not mean that they are in the dune phaseas well. Anyhow, bedload sheets seem not to be supply-limited becausethey do not occur when the coarser grains are immobile, and thus areprobably not very relevant in the present discussion of supply-limited bed-forms.

637SEDIMENT SUPPLY-LIMITED BEDFORMS

FIG. 12.—Transition of bedform types in response to changing flow velocity andbedload transport. The arrows indicate the order of the experiments; see Figure 3for key to bedform types.

FIG. 13.—Bedforms plotted against the modified Shields parameter (related to thegrains of the transported sediment), and the ratio of predicted to measured bedloadtransport.

In conclusion, the extended bedform stability diagrams describe the ob-served bedforms in non-uniform sediment reasonably well, provided thatthe grain-size parameters are derived from the transported sediment insteadof the bed sediment, bed surface, or substrate. This proviso is the conse-quence of the sediment-supply limitation. Bedload sheets and barchans plotalmost without exception within the dune stability fields, whereas sandribbons plot within the lower-plane-bed field, as well as in the ripple anddune stability fields. Thus the bedform stability diagrams have a limitedpredictive capacity to discriminate between the different bedform types insupply-limited conditions.

EFFECT OF THE SUPPLY LIMITATION ON BEDFORM MORPHOLOGY

Transitions between Types of Supply-Limited Bedforms

Until now the focus of this paper has been on the classification of sed-iment-supply limited bedform types. In reality, however, gradual transitionsexist between these types. Barchans and transitional forms (here calledbarchanoids) to fully developed dunes plot in the dune stability fields ofbedform stability diagrams, indicating that the sediment supply limitationdetermines the bedform morphology. It is interesting to note that barchanforms may occur in the ripple and in the dune stability fields. It suggeststhat this form is not limited to a certain bed state, but that a supply limitof sand may cause both a ripple and a dune to acquire a barchan form.

Sand ribbons are stable in both the ripple regime and the dune regime.Thus the dominant factor determining the occurrence of sand ribbons is astrong limit of the sediment supply, even more so than in the case ofbarchans.

The transitions are illustrated with the experiments. In experiment T4bthe flow velocity and the bedform height are lower than in T4a. The bed-forms in T4b became lower as a response to the lower flow velocity andwater depth (flow-depth limitation). Thus sand became available for thetransition from barchans to dunes (Fig. 12). The same principle lies behindthe difference in bedform types between T5 and T9, which have almostequal flow velocities. In T5 there was not enough sand available for dunesbecause of the armor layer, so the type was barchanoid. In T7, however,much more sand was entrained because it was winnowed from the bedbelow the armor layer. In T9 this sand was still available, so the type wastwo-dimensional dunes.

To summarize (Fig. 12), the bedform type transitions are gradual, frombarchans to barchanoids, to barchanoids with increasing slipface lengths,to dunes with barchanoid characteristics like crescentic slipfaces and tails,to dunes with irregular slipfaces, to more or less two-dimensional (trans-verse) dunes.

Prediction of Morphology of Sediment Supply-Limited Bedforms

The question now is how the bedform morphology in this continuumcan be predicted, incorporating the sediment supply. Belderson et al. (1982)presented their semiquantitative model for the continental shelf with flowvelocity as the only parameter. In decelerating flow the sand settled fromsuspension and the supply for bedload increased, leading to a developmentfrom ribbons to dunes. Thus the main factor is the sediment supply indisguise. In many riverine conditions, however, the reason for the sediment-supply limitation is not that all the sediment is suspended but that thesediment on the bed surface cannot be entrained. Therefore their qualitativemodel is not generally appropriate for rivers. The qualitative model ofMcKee (1979) illustrates the continuous sequence of subaerial transversedunes to barchanoids to barchans with unidirectional wind and diminishingsand supply, but offers no quantification.

The problem might be approached by comparison with the uniform-sediment case. The available bedload transport predictors (e.g., Meyer-Peterand Muller 1948) for uniform sediment neglect the armoring which is thecause of the supply limitation. Therefore a comparison between predictedtransport and measured transport will reveal whether the sediment is sup-ply-limited. In Figure 13 the bedforms of the flume dataset (Kleinhans2000) are plotted against the u9 (related to the grains of the transportedsediment) and the ratio of predicted and measured (dimensionless) trans-port. For perfect supply-unlimited bedload predictions, the latter ratio isunity. The bedload transport was predicted with the Meyer-Peter and Mull-er (1948) predictor, on the basis of the (measured) transport sediment pa-rameters and the u9 instead of the original u combined with the originalripple factor (Kleinhans and Van Rijn 2002). The different bedform typesare reasonably separated. So, if the sediment transport rate is predictableand the true transport has been measured, then the bedform type is pre-dictable.

This is confirmed by Van der Zwaard (1974), who followed a compa-rable approach for determining the bedform-related flow roughness in thecase of unimodal sand moving over an immobile coarse gravel layer. Whileincreasing the sand feed-rate in a flume, a transition was observed of bar-chans to fully developed dunes for which the sediment transport and flowroughness were the same as in experiments without the gravel. From themeasured sediment feed rate, Van der Zwaard was able to hindcast the flowroughness.

Unfortunately, this approach is impractical for the present purpose be-cause the true transport rate must be measured. In the field, these mea-

638 M.G. KLEINHANS ET AL.

FIG. 14.—The dimensionless transport-layerthickness against the modified Shields parameter(based on shear stress on grains of thetransported sediment) for A) flume and B) fieldconditions.

surements are difficult and expensive to do (Kleinhans and Ten Brinke2001). A cheap mapping of the bedforms with echosounders would directlyanswer the question about bedform morphology. Moreover, the predictionof the sediment transport rate provides a problem in rivers with an armorlayer, where the sediment supply is often unrelated to the local flow andbed sediment composition. Waves of sediment may propagate through thesystem, which are derived from sudden collapse of upstream river banksduring floods and other non-steady and history effects. This almost erraticsediment supply can in no way be predicted.

As an alternative to the transport rate, the availability of sediment forthe formation of bedforms could be expressed in a thickness of the transportlayer. Roughly, this is the thickness of the layer of transported sedimentthat is obtained after distributing the sediment of the bedforms evenly overthe bed. The thickness is computed by estimating the volume of sedimentin each bedform, multiplying this by the fraction of the bed that is actuallycovered by the bedforms, and dividing the result by the total area in whichthe bedform dimensions were collected. For fully developed dunes thatcover the armor layer, the volume per meter width (here equivalent tothickness of the transport layer) for regular triangular dunes is 0.5H (H 5bedform height) by definition, and up to 0.7H for more convex dunes (e.g.,

Havinga 1983). Here, 0.55H is taken, assuming nearly triangular forms(Shinohara and Tsubaki 1959; Jinchi 1992). For plane-bed conditions theD90 of the bedload sediment was taken as the thickness.

The thickness of the transport layer does not alone determine the bed-form morphology, because the water depth also was shown to have a largeeffect. A tentative approach is to rely on the relation between bedformheight and flow depth, because most predictors of dune height depend onthe flow depth in some way (Van Rijn 1993). As a first approximation thetransport-layer thickness is simply divided by the water depth to obtain adimensionless parameter for sediment availability. The flume and field da-tasets must then be considered separately, because dunes are higher influmes (30% of flow depth as a rule of thumb) than in rivers (15% of flowdepth).

A bedform-height predictor for uniform sediment might be applied tothe same flow conditions, but such predictions are even more uncertainthan the prediction of bedload transport. Furthermore, bedforms in non-uniform sediment plot correctly in bedform stability diagrams only if theparameters of the transported sediment are used instead of the bed sedi-ment. We expect that using the transported sediment is also necessary for

639SEDIMENT SUPPLY-LIMITED BEDFORMS

FIG. 15.—Conceptual explanatory (but not predictive) model for the occurrence of bedforms in sediment supply-limited conditions.

a correct prediction of bedform height, but that depends again on the un-reliable prediction of bedload transport.

A plot (Fig. 14) of the dimensionless transport layer thickness (TL* 5thickness divided by water depth) against the u9 for transported sedimentshows a reasonable division between the bedform types in flumes and inrivers. The barchans plot to the left of the dunes, and the sand ribbons areeven farther to the left. Heights of both ripples, sand ribbons, and bedloadsheets are unrelated to the water depth, which explains their scatter in theplot (Fig. 14A). The dunes of the Waal dataset plot in the barchan range(Fig. 14B), which is not correct. This deviation may have to do with thedelayed response of large dunes to changes in the flow, because the duneheight in the Waal dataset is much larger than in the other datasets.

Two alternative dimensionless parameters (not shown here) did not giveany consistent outcome when plotted on the horizontal axis of Figure 14.The first was the transport-layer thickness divided by the D90 of the trans-ported sediment, with the idea that the ripple and sand ribbon height mightbe related to the D90 of the sediment. The second alternative was the squareof the D90 of the transported sediment divided by the product of transport-layer thickness and water depth, with the idea that the ripples and sandribbons are related to the surface area of the grains (and the drag force thatacts on that surface), and to low water depth combined with small transport-layer thickness.

A block diagram (Fig. 15) based on the TL* against the u9 is given toillustrate the bedform morphology as derived from visual observations inthe flume experiments and the river Allier. This diagram is an explanatorybut not a predictive model, because the TL* is partly dependent on themostly unpredictable upstream sediment supply. The upper bound TL* 50.2 is given by the maximum (equilibrium) height that a dune can attainin rivers, which is about 20% of the water depth.

In flume experiments and some rivers the sediment supply may be lim-ited because of some (relatively weak) armoring, whereas with increasing

flow velocities more sediment may be entrained to counteract the sediment-supply limitation. In other rivers with stronger armor layers that cannot bebroken up, the sediment may be supplied only by upstream inputs likebank failures. Furthermore, sand stored in meander pools (and comparableareas in braided rivers) may be entrained by a small increase in discharge,forming a sand wave that provides the sediment for the local bedforms. Inconclusion, armoring, sand storage in pools, and bank erosion may playroles to some extent in one and the same river. Only if these processeswere fully understood and the boundary conditions well known, might aprediction of the sediment supply be feasible.

CONCLUSIONS

Sand ribbons and barchans are supply-limited bedforms that may occurfrequently in rivers with non-uniform sediment, i.e., in flows below thecritical threshold of motion of the coarser grains in or on the bed.

Bedform stability diagrams from the literature can be extended to coarsersediment. For bedforms in sediment mixtures, the particle parameters mustbe derived from the transported sediment instead of the bed sediment, asa consequence of the supply limitation of sediment.

The sediment-supply limitation determines the morphology of the bed-forms. Sand ribbons occur both in the ripple and in the dune regime, andare extremely sediment supply-limited in the dune regime. With increasingsediment availability, barchans emerge, and then grow together into bar-chanoid dunes up to fully developed dunes. The sediment supply dependsmostly on upstream sources and cannot be predicted from the local con-ditions of flow and bed sediment.

ACKNOWLEDGMENTS

The present research is part of a research program on sediment transport in sand-gravel bed rivers during high discharges at Utrecht University. The investigations

640 M.G. KLEINHANS ET AL.

were in part supported by the Netherlands Earth and Life sciences Foundation(ALW) with financial aid from the Netherlands Organization for Scientific Research(NWO). The National Institute for Inland Water Management and Waste WaterTreatment (RIZA) and the Directorate Eastern Netherlands of Rijkswaterstaat in theNetherlands financed and carried out the measurements in the rivers Waal and Bov-enrijn. The sand flume experiments were financed by (1) the Transport and Mobilityof Researchers III program of the European Commission and (2) the consortium ofTwente University, the Institute for Inland Water Management and Waste WaterManagement (RIZA) and WL/Delft Hydraulics. Joanne Horton (of Leeds University)is gratefully acknowledged for providing her data on bedforms in sand-gravel sed-iment and for discussions. Ward Koster, Gerrit Klaassen, Jan Alexander, John Sou-thard, and an anonymous reviewer are thanked for their useful and stimulating com-ments.

REFERENCES

ALLEN, J.R.L., 1970, Physical Processes of Sedimentation; London, Allen & Unwin Ltd., p.248 p.

ALLEN, J.R.L., 1984, Sedimentary Structures; their Character and Physical Basis, 1: Amsterdam,Elsevier, Developments in Sedimentology, 30, 593 p.

ALLEN, J.R.L., AND COLLINSON, J.D., 1974, The superposition and classification of dunes formedby unidirectional aqueous flows: Sedimentary Geology, v. 12, p. 169–178.

BAKKER, B., 1984, Straight sand flume description: The Netherlands, Delft Hydraulics, reportR657-XV.

BELDERSON, R.H., JOHNSON, M.A., AND KENYON, N.H., 1982, Bedforms, in Stride, A.H., ed.,Offshore Tidal Sands; Processes and Deposits: London, Chapman & Hall Ltd., p. 27–57.

BENNETT, S.J., AND BRIDGE, J.S., 1995, An experimental study of flow, bedload transport andbed topography under conditions of erosion and deposition and comparison with theoreticalmodels: Sedimentology, v. 42, p. 117–146.

BLOM, A., AND KLEINHANS, M.G., 1999, Non-uniform sediment in morphological equilibriumsituations; data report, sand flume experiments 97/98, Rijkswaterstaat Delft Hydraulics: TheNetherlands, University of Twente, Civil Engineering and Management, 26 p.

BLOM, A., RIBBERINK, J.S., AND VAN DER SCHEER, P., 2000, Sediment transport in flume exper-iments with a trimodal sediment mixture, in Nolan, T., and Thorne, C., eds., Special Pub-lication CD-ROM of the New Zealand Hydrological Society, Gravel Bed Rivers Conference,28 August–3 September 2000, New Zealand (http://www.geog.canterbury.ac.nz/services/carto/toc.htm).

CARLING, P.A., 1999, Subaqueous gravel dunes: Journal of Sedimentary Research, v. 69, p.534–545.

CARLING, P.A., AND GOELZ, E., 1993, Untersuchung und numerische Modellierung von suba-quatischen Dunen im Rhein bei Niederwalluf (Rheingau): Bundesanstalt fur Gewasserkundeand Institute of Freshwater Ecology, Koblenz, Germany, 48 p., (in German).

CARLING, P.A., GOELZ, E., ORR, H.G., AND RADECKI-PAWLIK, A., 2000a, The morphodynamicsof fluvial sand dunes in the river Rhine, near Mainz, Germany, I. Sedimentology and mor-phology: Sedimentology, v. 47, p. 227–252.

CARLING, P.A., WILLIAMS, J.J., GOELZ, E., AND KELSEY, A.D., 2000b, The morphodynamics offluvial sand dunes in the river Rhine, near Mainz, Germany. II. Hydrodynamics and sedimenttransport: Sedimentology, v. 47, p. 253–278.

CHIEW, Y.M., 1991, Bed features in nonuniform sediments: Journal of Hydraulic Engineering,v. 117, p. 116–120.

COLOMBINI, M., 1993, Turbulence driven secondary flows and the formation of sand ridges:Journal of Fluid Mechanics, v. 254, p. 701–719.

COSTELLO, W.R., AND SOUTHARD, J.B., 1981, Flume experiments on lower-flow-regime bed formsin coarse sand: Journal of Sedimentary Petrology, v. 51, p. 849–864.

DINEHART, R.L., 1989, Dune migration in a steep, coarse-bedded stream: Water ResourcesResearch, v. 25, p. 911–923.

DINEHART, R.L., 1992, Evolution of coarse gravel bed forms: field measurements at flood stage:Water Resources Research, v. 28, p. 2667–2689.

HAVINGA, H., 1983, Discussion: bed load discharge coefficient: Journal of Hydraulic Engi-neering, v. 109, p. 157–160.

HESP, P.A., AND HASTINGS, K., 1998, Width, height and slope relationships and aerodynamicmaintenance of barchans: Geomorphology, v. 22, p. 193–204.

HORTON, J., BENNETT, S., BEST, J., AND KUHNLE, R., 2000, Morphological and textural charac-teristics of bedforms generated in a bimodal sand–gravel mixture, in Nolan, T., and Thorne,C., eds., Gravel Bed Rivers Conference, 28 August–3 September 2000, Special PublicationCD-ROM of the New Zealand Hydrological Society, New Zealand, (http://www.geog.canterbury.ac.nz/services/carto/toc.htm).

ISEYA, S., AND IKEDA, H., 1987, Pulsation in bedload transport rates induced by a longitudinal

sediment sorting: a flume study of sand and gravel mixtures: Geografiska Annaler, v. 69A,p. 15–27.

JINCHI, H., 1992, Application of sandwave measurements in calculating bedload discharge:Symposium on Erosion and Sediment Transport Monitoring Programmes in River Basins,Oslo, Wallingford, U.K., International Association of Hydrological Sciences, Publication210, p. 63–70.

KLAASSEN, G.J., 1986, Morfologie afgepleisterde beddingen: experimenten met afvoergolven(in Dutch): Delft, The Netherlands, Delft Hydraulics, Report M2061, 120 p.

KLEINHANS, M.G., 1999, Sediment transport in de Waal: hoogwater November 1998 (in Dutch):Netherlands Centre for Geo-ecological Research, Utrecht University Physical Geography,Report ICG 99/6, 100 p.

KLEINHANS, M.G., 2000, The relation between bedform type, vertical sorting in bedforms andbedload transport during subsequent discharge waves in large sand gravel bed rivers withfixed banks: Gravel Bed Rivers Conference, 28 August–3 September 2000, in Nolan, T.,and Thorne, C., eds., Special Publication CD-ROM, New Zealand Hydrological Society.(http://www.geog.canterbury.ac.nz/services/carto/toc.htm).

KLEINHANS, M.G., AND TEN BRINKE, W.B.M., 2001, Accuracy of cross-channel sampled sedimenttransport in large sand–gravel-bed rivers: Journal of Hydraulic Engineering, v. 127, p. 285–269.

KLEINHANS, M.G., AND VAN RIJN, L.C., 2002, Stochastic prediction of sediment transport insand–gravel bed rivers: Journal of Hydraulic Engineering, v. 28, p. 412–425.

LISLE, T.E., AND HILTON, S., 1999, Fine bed material in pools of natural gravel bed channels:Water Resources Research, v. 35, p. 1291–1304.

MCCULLOCH, D.S., AND JANDA, R.J., 1964, Subaqueous river channel barchan dunes: Journal ofSedimentary Petrology, v. 34, p. 694.

MCKEE, E.D., 1979, A study of global sand seas, introduction: U.S. Geological Survey, Pro-fessional Paper 1052, p. 20.

MCLEAN, S.R., 1981, The role of non-uniform roughness in the formation of sand ribbons:Marine Geology, v. 42, p. 49–74.

MCLELLAND, S.J., ASHWORTH, P.J., BEST, J.L., AND LIVESEY, J.R., 1999, Turbulence and secondaryflow over sediment stripes in weakly bimodal bed material: Journal of Hydraulic Engineer-ing, v. 125, p. 463–473.

MEYER-PETER, E., AND MULLER, R., 1948, Formulas for bed-load transport: 3rd Conference ofthe International Association of Hydraulic Research, Stockholm, Sweden, p. 39–64.

PYE, K., AND TSOAR, H., 1990, Chapter 6, in Aeolian Bedforms: Aeolian Sand and Sand Dunes:London, U.K., Unwin Hyman Ltd., p. 152–220.

ROSZA, P., AND JOZSA, J., 1999, Interaction of sandy bed-load and stable gravel bed: 28thInternational Association for Hydraulic Research Conference in Graz, Austria, proceedings,CD-ROM.

RUBIN, D.M., AND TOPPING, D.J., 2001, Quantifying the relative importance of flow regulationand grain size regulation of suspended sediment transport and tracking changes in grain sizeof bed sediment: Water Resources Research, v. 37, p. 133–146.

SHINOHARA, K., AND TSUBAKI, T., 1959, On the characteristics of sand waves formed upon thebeds of open channels and rivers: Kyushu University, Research Institute for Applied Me-chanics, report, p. 15–45.

SIMONS, D.B., AND RICHARDSON, E.V., 1965, A study of variables affecting flow characteristicsand sediment transport in alluvial channels, in Federal Inter-Agency Sediment Conference1963, Proceedings: U.S. Department of Agriculture publication 970, p. 193–207.

SOUTHARD, J.B., AND BOGUCHWAL, A.L., 1990, Bed configurations in steady unidirectional waterflows. Part 2. Synthesis of flume data: Journal of Sedimentary Petrology, v. 60, p. 658–679.

VAN DEN BERG, J.H., AND VAN GELDER, A., 1993, A new bedform stability diagram, withemphasis on the transition of ripples to plane bed in flows over fine sand and silt: Interna-tional Association of Sedimentologists, Special Publication 17, p. 11–21.

VAN DEN BERG, J.H., AND VAN GELDER, A., 1998, Discussion of: flow and sediment transportover large subaqueous dunes: Fraser River, Canada: Sedimentology, v. 45, p. 217–221.

VAN DER ZWAARD, J.J., 1974, Invloed van bodemtransport op de ruwheid van een vaste laagDelft, The Netherlands, Delft Hydraulics Report M988II, 82 p., (in Dutch).

VAN RIJN, L.C., 1984, Sediment transport, part I: bed load transport: Journal of HydraulicEngineering, v. 110, p. 1431–1456.

VAN RIJN, L.C., 1993, Principles of sediment transport in rivers, estuaries and coastal seas:Oldemarkt, The Netherlands, Aqua Publications, p. 683.

WESSELING, C., AND WILBERS, A.W.E., 1999, Manual DT2D version 2.2, Software for dune-tracking in two dimensions: Utrecht University, Department of Physical Geography, TheNetherlands, (in Dutch).

WHITING, P.J., DIETRICH, W.E., LEOPOLD, L.B., DRAKE, T.G., AND SHREVE, R.L., 1988, Bedloadsheets in heterogeneous sediment: Geology, v. 16, p. 105–108.

WILBERS, A.W.E., 1999, Bodemtransport en duinontwikkeling tijdens hoogwaters in de Rijnt-akken: bodempeilingen hoogwater november 1998: Netherlands Centre for Geo-ecologicalResearch/Utrecht University Physical Geography, Report ICG 99/10, 100 p., (in Dutch).

WILCOCK, P.R., 1998, Two-fraction model of initial sediment motion in gravel-bed rivers:Science, v. 280, p. 410–412.

Received 2 March 2001; accepted 7 March 2002.