pedocchi4jgrb

Ripple morphology under oscillatory flow:

2. Experiments

F. Pedocchi1,2 and M. H. Garcıa1

Received 3 March 2009; revised 28 July 2009; accepted 17 August 2009; published 11 December 2009.

[1] Recent large-scale laboratory experiments on the formation of ripples underoscillatory flow are presented. The experiments were performed in the Large OscillatoryWater-Sediment Tunnel (LOWST) at University of Illinois at Urbana-Champaign, using250 mm silica sand as sediment. The dimensions of the ripples formed under a wide rangeof flow conditions are compared with some of the existing predictors and with a newpredictor presented in a companion paper. For a given near-bed water excursion the size ofthe ripples is observed to initially decrease with the increase of the maximum orbitalvelocity, as has been suggested before. However, an abrupt change of the ripple size andthe transition to large round-crested ripples is observed when the maximum orbitalvelocity becomes larger than 0.5 m/s. Above this value the size of these round-crestedripples continuously increased with the increase of the maximum orbital velocity.Additionally, anorbital ripples were never formed despite the long water excursions usedin several of our experiments, confirming that anorbital ripples are only formed in finesands. Finally, the performance of the existing planform geometry predictors and a newlyproposed predictor is evaluated using our new experimental data. The results confirm thatthe bed planform geometry is controlled by the wave Reynolds number and theparticle size. The comparison or the new data with previous results from narrow facilitiesshows that the facility width can restrict the development of bed form three-dimensionality.

Citation: Pedocchi, F., and M. H. Garcıa (2009), Ripple morphology under oscillatory flow: 2. Experiments, J. Geophys. Res., 114,

C12015, doi:10.1029/2009JC005356.

1. Introduction

[2] When a fluid moves over an erodible sediment bed, itmay interact with the sediment particles, transporting andredistributing them along the bottom. Subject to thistransport, an initially flat bed may become unstable andgive rise to the formation of wavy features on the bed.These bed features or bed forms in turn affect the waterflow, which results in a strong coupling between the fluidmotion, the sediment transport, and the bed morphology. Incoastal and continental shelf areas the surface waves induceoscillatory water motions in the vicinity of the seabed. Inthe presence of a sandy bed these oscillatory motionsproduce bed forms, called ripples. These ripples can eitherscale with the near-bed water excursion or not, and thereforethey are known as orbital and anorbital ripples, respectively.Similarly, ripples can either present a two-dimensional orthree-dimensional planform geometry, depending if theircrests are long and straight or short and wavy.

[3] Ripples modify the seabed roughness, which affectsthe wave height as the waves propagate toward thecoast. This has a profound impact on large-scale coastalmorphodynamics. The presence of ripples also changes thenear-bed turbulence level, influencing the sedimenttransport and the exchange of substances between theseabed and the water column. On another aspect,understanding the environmental conditions that lead tothe formation of a particular bed configuration is anessential tool for interpretation of the sedimentary record.[4] Oscillatory flow ripples were first systematically

studied in the field by Inman [1957], followed by Dingler[1974] and Miller and Komar [1980b]. These early surveyswere performed by divers, limiting the observations to fairweather conditions. Recent field efforts have included thedeployment of measuring equipment for several weeks,allowing for the study of bed evolution under differentwave conditions [e.g., Traykovski et al., 1999; Hanes et al.,2001; Xu, 2005]. In spite of great advances made on thequality and quantity of data obtained in field campaigns, thecost and time involved still limit the number of conditionsthat can be actually studied. In this regard, laboratorystudies are significantly less expensive and the experimentalconditions can be fully controlled for long periods of time,allowing for a more detailed observation of the processesinvolved.

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114, C12015, doi:10.1029/2009JC005356, 2009ClickHere

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1Ven Te Chow Hydrosystems Laboratory, Department of Civil andEnvironmental Engineering, University of Illinois at Urbana-Champaign,Urbana, Illinois, USA.

2Now at Instituto de Mecanica de los Fluidos e Ingenierıa Ambiental,Faculatad de Ingenierıa, Universidad de la Republica, Montevideo,Uruguay.

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[5] In the past, most studies of ripples in the laboratorymainly produced data for short oscillation periods and waterexcursions. This was the consequence of the small size ofthe experimental facilities used at the time: oscillating bedsand small wave flumes [e.g., Bagnold, 1946; Kennedy andFalcon, 1965]. Ripples formed in oscillatory bed experi-ments have been found to significantly differ from thoseproduced in wave tanks [Miller and Komar, 1980a].Similarly, the periods of the waves that can be obtained inwave flumes are generally limited to a maximum of 6 s[Miller and Komar, 1980a], even in the case of extremelylarge facilities used more recently [Williams et al., 2004].Oscillatory water tunnels are an alternative to these labora-tory facilities in which these limitations are significantlydiminished. The water motion produced inside an oscilla-tory water tunnel is essentially a current that reverses itsdirection periodically. This is not the exact flow conditionfound under progressive waves, where the water motion at agiven time is not the same at every cross section. Despitethis difference, bed configurations generated in water tun-nels tend to be in good agreement with the ones obtained inwave flumes [Mogridge and Kamphuis, 1972], and watertunnels have been extensively used in bed morphologystudies [e.g., Carstens et al., 1969; Mogridge andKamphuis, 1972; Lofquist, 1978; Southard et al., 1990;Ribberink and Al-Salem, 1994; O’Donoghue and Clubb,2001; Dumas et al., 2005; O’Donoghue et al., 2006].[6] The size of oscillatory water tunnels and the type of

conditions that can be simulated have dramaticallyincreased since the pioneering work of Carstens et al.[1969]. Newer tunnels have allowed for the study of longoscillation periods, long water excursions, and high orbitalvelocities that mimic the conditions found in the fieldduring storms [Southard et al., 1990; Ribberink and Al-Salem, 1994; O’Donoghue and Clubb, 2001; Dumas et al.,2005; O’Donoghue et al., 2006]. However, with few excep-tions, tunnels have tended to be relatively narrow, thusconstraining the development of ripple three-dimensionalityand limiting the study of ripple planform geometry.[7] The experiments described herein were performed

in the Large Oscillatory Water-Sediment Tunnel (LOWST)at the Ven Te Chow Hydrosystems Laboratory at theUniversity of Illinois at Urbana-Champaign. The testsection of this facility is 12.5 m long, 0.8 m wide, and1.2 m high. The sediment bed is 0.60 m deep, leaving a0.60 m water column throughout the test section. Thisallows for the study of ripple morphodynamics over a widerange of flow conditions. Oscillations with long periods,high orbital velocities, and long water excursions can begenerated within the tunnel covering a wide range of field-like oscillatory flows.[8] Two main objectives were pursued with the experi-

ments presented in this article: First, to identify the con-ditions that lead to the formation of two-dimensional orthree-dimensional ripples. The planform geometry ofripples affects the near-bed hydrodynamics changing thehydraulic roughness felt by the flow. O’Donoghue et al.[2006] recognized the importance of adequately predictingthe planform geometry of ripples and noted that the existingplanform geometry predictors were unable to predict thebed configurations observed in their facility, which was0.3 m wide. Second, to study the combined effect of long

near-bed water excursions and orbital velocities on thewavelength and height of equilibrium ripples. There isgeneral agreement in the research community on theimportance of the water excursion for defining the size ofoscillatory flow ripples. And all of the commonly usedripple-size predictors [e.g., Nielsen, 1981; Mogridge et al.,1994;Wiberg and Harris, 1994] take the near-bed excursioninto account. Although it is clear that a second variable isnecessary to fully characterize a sinusoidal oscillation, therehas been significant debate on how this second variableshould be included in the predictors [O’Donoghue andClubb, 2001]. The need for a second variable to characterizethe flow becomes evident under long water excursions,where both orbital and anorbital ripples have been observed[e.g., Inman, 1957; Traykovski et al., 1999; O’Donoghueand Clubb, 2001].[9] Our experiments showed that the ripple formation

process can be extremely complex. In some tests, the bedpresented several pseudoequilibrium stages before a finalbed configuration was reached. For the weakest flows, thefinal bed configuration was sometimes achieved only aftermore than a hundred hours of running an experiment. Onthe other hand, for intense flows the bed evolved rapidlyand reached equilibrium in less than an hour. These recentexperiments are analyzed in detail using an alternativedimensionless framework presented in the companion paper[Pedocchi and Garcıa, 2009b]. The terminology andnotation used herein are the ones defined in the companionarticle.

2. Preliminary Considerations

2.1. Dimensionless Framework

[10] Previous studies have addressed the need for adimensionless set of variables to characterize the sedimenttransport under oscillatory flows [Yalin and Russell, 1963;Carstens et al., 1969; Mogridge and Kamphuis, 1972;Dingler, 1974]. An extended revision was given in thecompanion paper, and just a brief summary is includedherein. A sediment transport phenomenon x (e.g., ripplewavelength) under oscillatory flow should be completelydefined by the sediment and fluid properties, the flowcondition, and the external forces. For the experimentsdescribed here the sediment was quartz sand with a densityof rs = 2650 kg/m3. Its size distribution is given in Figure 1from whichD50 = 250 mm, D10 = 185 mm, andD90 = 373 mmwere estimated. As usual with natural sands, its submergedangle of repose was 8 = 32�. The fluid was fresh water, withdensity r and kinematic viscosity n, both functions of themeasured temperature. The imposed flows were sinusoidaloscillations, defined by a period T and a maximum orbitalvelocity Umax. Note that for a sinusoidal flow, the near-bedwater excursion d verifies d = 2A = UmaxT/p. Finally, theacceleration of gravity g must be included.[11] Applying the Buckingham Pi Theorem, and defining

the submerged specific gravity R = rs/r�1, the followingexpression for the dimensionless form Px of x can bederived:

Px ¼ fTnD2

50

;UmaxD50

n;

ffiffiffiffiffiffiffiffiffiffiffiffiffigRD50

pD50

n;R;8

� �: ð1Þ

C12015 PEDOCCHI AND GARCIA: RIPPLE MORPHOLOGY UNDER OSCILLATORY FLOW, 2

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In our experiments both R and 8 were constants. Thethird parameter on the right-hand side ofequation (1)


pD50/n is called Rep [Garcıa, 2008],

and for our experiments its variation was associated withthe change in water viscosity with the temperature. Sincethe temperature range in our experiments was limited, therange of variation of Rep was also fairly small. Thereforeour experiments can be properly presented and analyzedusing just two variables Tn/D50

2 and UmaxD50/n [Pedocchiand Garcıa, 2009b].[12] The dimensionless numbers Tn/D50

2 and UmaxD50/ncan be considered as a dimensionless period and maximumorbital velocity, respectively. Combining them, the dimen-sionless water excursion A/D50 and the wave Reynoldsnumber Rew = UmaxA/n are obtained. For oscillatory bound-ary layer flows over a flat surface covered with particlesof size D50, the hydraulic roughness k can be approxi-mated as k = 2.5D50 [Jensen, 1989]. The wave frictionfactor fw = 2(u*max/Umax)

2 relates the maximum shearvelocity at the bed over the cycle u*max with the maxi-mum orbital velocity Umax and is a function of A/D50 andRew. The friction factor expression used here is the oneby Pedocchi and Garcıa [2009a] for smooth, transition,and rough flow conditions (a summary is included inAppendix A). Once the wall shear velocity is known, the wallshear velocity Reynolds number Re* = u*maxD50/n can bedefined, which controls the boundary layer hydraulic regimeand defines smooth or rough flow conditions. In summary,the oscillatory flow hydraulics over a flat sediment bed can befully characterized on a plane with Tn/D50

2 and UmaxD50/n asmain dimensionless variables. Furthermore, if thethird dimensionless number Rep is known, the Shieldsdimensionless parameter q = u*max

2 /(gRD50) can becomputed.2.1.1. Initiation of Motion[13] As an example of the possible use of the described

dimensionless framework and to evaluate the performance

of the proposed expression for the friction factor, initiationof motion experiments were performed. The resultsobtained at three different water temperatures, 16�C,17�C, and 26�C are summarized on Table 1. The methodologyused to define the initiation of motion in these experimentswas naked-eye observation, which was highly subjectivebut still fulfilled the objective of obtaining an approximatedvalue of the critical shear stress for our experiments. It alsoallowed to observe the effect of the oscillation period on thecritical velocity that would initiate sediment motion.Starting from a flat bed for each oscillation period, thevelocity was gradually increased until particle motion wasobserved. This was done for a sequence of increasingoscillation periods and then for a sequence of decreasingoscillation periods. No significant difference between thevalues obtained both ways was found, and the valuesreported in Table 1 correspond to the average of both.[14] The results are shown in Figure 2, where they are

plotted on the (Tn/D502 , UmaxD50/n) plane. Since the changes

in viscosity (temperature) affect the value of the thirddimensionless parameter Rep, not included in the planerepresentation, data from the different experiments do notcollapse. At 16�C, the water kinematic viscosity is n =1.11*10�6 m2/s and Rep = 14.34; the critical Shields stressthat best approximates the experimental data is qc � 0.063.At 17�C, n = 1.08*10�6 m2/s, Rep = 14.72, and the criticalShields that approximates the experimental data best is qc �0.070. For 26�C, n = 0.87*10�6 m2/s, Rep = 18.25, andqc � 0.072. The trends in the experimental data follow theconstant Shields stress contours very well, showing the slopechange when the boundary layer transitions from smooth-turbulent to laminar at Rew � 6.6*104 [Pedocchi andGarcıa, 2009a].[15] Several modifications to the traditional Shields

diagram have been proposed in the literature, both forunidirectional and oscillatory flows. For oscillatory flowssome authors [e.g., Soulsby and Whitehouse, 1997; Hansonand Camenen, 2007] suggest that the critical Shieldparameter does not increase for small values of Rep butinstead tends to a constant value. In particular, [Hanson andCamenen, 2007] suggest values of qc very close to 0.07,which are in good agreement with our results. It is importantto note that the oscillatory flow friction factor fw is involvedin the determination of qc. There are several expressions inthe literature for the friction factor in oscillatory flows, but

Figure 1. Size distribution of the sand used in the presentexperiments in the Large Oscillatory Water-SedimentTunnel (LOWST).

Table 1. Summary of Experiments Performed to Study Initiation

of Motion

T (s)

Umax (m/s)

16�C 17�C 26�C

2 0.13 0.12 0.173 0.16 0.19 0.224 0.22 0.20 0.265 0.21 0.23 0.256 0.23 0.27 0.297 0.24 0.25 0.298 0.25 0.30 0.309 0.27 0.30 0.3010 0.27 0.30 0.3012 0.27 0.30 0.3015 0.28 - -20 0.28 - -


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the results presented here were accurately captured with ourfriction factor expression (see Appendix A).

3. Equipment

3.1. Large Oscillatory Water-Sediment Tunnel

[16] The Large Oscillatory Water-Sediment Tunnel(LOWST) was designed to study sediment transport andrelated phenomena under controlled wave current boundarylayer flows similar to those found in the continental shelf.The LOWST was built with support from the DURIPProgram of the U.S. Office of Naval Research, and it wasconstructed by Engineering Laboratory Design Inc. andMTS Systems Corporation.[17] The test section of the facility is 12.5 m long with a

0.8 m wide by 1.2 m high internal cross section (Figures 3and 4). Half of the tunnel height (0.6 m) is full of uniformsize silica sand. Before each experiment, the sediment bedcan be flattened with the help of a cart that redistributes thewet sand as it is pulled along the tunnel. The oscillatorymotion of the water is driven by three pistons that run inside0.78 m diameter cylinders with a maximum nominal strokeof 2.1 m. At the opposite end of the tunnel, a 1.0 m by 2.0 mholding tank open to the atmosphere acts as a passivereceiver for the water displaced by the pistons. Three servomotors, controlled by a computer, are in charge of impartingthe motion to the pistons through a screw gear system. Thesystem was designed for the pistons to drive the water inboth directions producing a symmetric periodic motion. Thepistons are able to displace up to 0.8 m3/s of water whichgives a maximum nominal velocity inside the tunnel of 2 m/s.Finally, the maximum nominal piston acceleration is 2.1 m/s2.During the start (stop) transients at the beginning (end) of arun, the pistons increase (decrease) their motion amplitudein about 5 to 10 oscillations to avoid potential waterhammer effects. The facility also has two centrifugal pumpsthat allow for the superposition of a unidirectional current tothe oscillatory motion. A 0.36 m diameter PVC pipe

connected to the pumps directs the water and sedimentmixture from the reception chamber and discharges it underthe pistons through a diffuser (Figure 4). Sediment trapsplaced at both ends of the test section collect the sedimentthat is transported as bed load.

3.2. Pencil Beam Sonar

[18] Surveying bed bathymetry inside a close conduit likethe LOWST is challenging when compared to performingthe same task in more conventional flumes, where thepresence of the free water surface gives an easy access for

Figure 2. Initiation of motion experiments for different water temperatures (16�C, 17�C, 26�C), shownon the (Tn/D50

2 , UmaxD50/n) plane. The constant Shield curves that best fit the data are shown, with theShields parameter value indicated. The laminar-turbulent transition Rew = 6.6*104 and smooth-roughtransition Re* = 6 are also shown. Note the break on the data trend when the boundary layer transitionsfrom laminar to turbulent. Data from Table 1.

Figure 3. Detail showing an imaginary cross section ofthe LOWST and its central part with the main window.Dimensions in meters.


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instrumentation [e.g., Catano Lopera and Garcıa, 2007].After considering several possibilities, it was decided topursue the design of our own system based on a Imagenexpencil beam sonar and a Velmex Bislide positioning system.[19] The selected sonar is an L-shaped Imagenex 881L

Digital MultiFrequency Profiling Sonar, produced byImagenex Technology Corp., Canada. The positioning sys-tem is a Velmex B4800TS Motorized Rotatory Table withVelmex VXM controller, produced by Velmex Inc., USA.We designed the mechanical system to combine both unitsand the system was built by the Civil and EnvironmentalEngineering Machine Shop at the University of Illinois atUrbana-Champaign. The necessary software to control themotion and acquisition of the backscatter data was developedin collaboration with Nils Oberg, Software Engineer workingat the Ven Te Chow Hydrosystems Laboratory. The systemhas two axes of rotation, a vertical one controlled by therotatory table and a horizontal one controlled by a steppermotor inside the sonar head. As the ultrasound beam isrotated over the horizontal axis, it covers a fan-shaped regioncontained in a vertical plane. This plane crosses the bed over aline. By rotating the vertical plane around the vertical axis,several crossing lines can be acquired to give a completesurvey of the bed over an area.

4. Experiments

4.1. General Description

[20] The final bed equilibrium configuration of theexperiments performed in the LOWST are summarized inTable 2. For most of the tests the initial bed configurationwas a flatbed in order to prevent any effect of the initial bedconditions. However, for some particular cases the bedconfiguration left by a previous experiment was used asthe initial bed condition. This is indicated in the secondcolumn of Table 2. The flow conditions were selected inorder to cover a wide range of periods and orbital velocities,

to study the two-dimensional to three-dimensional transitionof the planform geometry, and to explore the effect of theorbital velocity on the ripple size. The selection was alsobased on the conditions previously reported by otherresearchers from both filed measurements and laboratoryexperiments. As is shown in Appendix B, most of thesimulated conditions could be generated by linear wavesin 5 m of water depth.[21] The experiments were run for as long as it was

necessary to assure that the bed had reached its finalconfiguration. This was done in the following way: Oncethe bed was thought to have reached equilibrium, theexperiment was continued for a reasonable additional time.This additional time was between 10% and 20% of theoriginally run time. If the general aspect of the bed remainedunchanged, the experiment was stopped. If instead changeswhere found, the previous process was successively repeateduntil a ‘‘stable’’ configuration was obtained. The totalrunning time is reported in the last column of Table 2.When two-dimensional ripples were the final configuration,no net ripple migration was observed, indirectly showingthat the water motion inside the tunnel was completelysymmetric. For the tests producing quasi two-dimensionaland three-dimensional ripples as a final configuration, thebed never reached a truly stationary state. Instead, quasitwo-dimensional and three-dimensional ripples were foundto continuously move and rework the sediment bed, butwith their average size remaining constant. For experimentslasting more than 10 h, the experiments were stopped at theend of the day and restarted the following morning. Theoscillatory motions in the tunnel were slowly started andstopped, and no effect of these transients on the finalconfiguration of the bed was noticed.[22] The ripple development was found to be a complex

process, in some cases presenting several pseudoequilibriumstages before the final bed configuration was reached. Oncethe bed was clearly in equilibrium, the experiment was

Figure 4. General view of the LOWST showing the recirculation system.


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stopped and the general features of the bed recorded. Thisincluded taking photographs of the bed through the tunnelwindows and measuring the wavelength and height ofseveral ripples to obtain the mean ripple sizes reported inTable 2. Finally, once the sonar system was operative, thecomplete width of the tunnel over a length of 1.5 m wassurveyed.[23] The definition of a mean ripple size was not always

an easy task. Particularly, for the quasi two-dimensional andthree-dimensional bed configurations. For these cases thesediment bed presented an extremely complex pattern withseveral ripple sizes coexisting. To describe these cases, theselected approach was to summarize the mean features ofthe bed by reporting more than one ripple size whennecessary. This is indicated after the experiment numberwith the letters L, M, and S, for large, medium, and small,respectively. The ripple crests were usually sharp. However,for experiments that involved long excursions and highvelocities (Experiments 10, 11, and 13) the ripple crestswere round.[24] As noted in the companion paper, the facility width

may affect the free development of the bed planform

geometry, either constraining or triggering bed three-dimensionality. The ripple wavelength to the tunnel widthratio l/w, which can be considered as a measure of therestriction imposed by the tunnel width to the bed three-dimensionality, is displayed in Table 2. For five experiments(07, 11, 13, 21, and 23) this ratio is above 1. For experi-ments 07, 11, and 13 no significant wall effects wereobserved, other than the fact that the tunnel width couldhave limited the development of further ripple three-dimensionality. On the other hand, for experiments 21 and23, as well as for experiment 22, for which l/w = 0.56, theeffect of the wall presence was clearly noticeable on thefinal bed configuration. For these experiments the large bedforms reported in Table 2 lay alternately over the tunnelwalls, leaving a sinuous path between them. For theseexperiments the large ripple wavelength reported corre-sponds to the distance between two crests lying over thesame tunnel wall. If the ripple wavelength is defined in thisway, these ripples fall in the orbital class in agreement withtheir other geometric characteristics.[25] The water temperature was recorded during the

experiments and its mean value is reported in Table 2. In

Table 2. Summary of Experiments Performed to Study Ripple Formation and Final ‘‘Equilibrium’’ Configuration

ExperimentaInitialb

Condition T (s)dmax

(m)Umax

(m/s)l(m)

h(m) h/l l/d l/D50 2-D/3-Dc l/wd

Temperature(�C)

Duratione

(hours)

01 00 5.0 0.48 0.30 0.300 0.045 0.150 0.628 1200 3 0.13 20 0.502 01 5.0 0.32 0.20 0.200 0.035 0.175 0.628 800 2 0.25 20 18.003L 02 15.0 0.95 0.20 0.600 0.070 0.117 0.628 2400 2.5 0.75 23 18.003S 02 15.0 0.95 0.20 0.050 0.006 0.120 0.052 200 2.5 0.06 23 50.004 00 2.0 0.16 0.25 0.115 0.021 0.183 0.723 460 2 0.14 16 0.505 04 5.0 0.40 0.25 0.260 0.045 0.173 0.653 1040 2 0.33 19 19.006 05 5.0 0.40 0.25 0.260 0.045 0.173 0.653 1040 2 0.33 27 5.007L 00 25.0 1.99 0.25 1.130 0.170 0.150 0.568 4520 2 1.41 27 150.007S 00 25.0 1.99 0.25 0.106 0.014 0.132 0.053 424 2.5 0.13 27 150.008 00 8.0 1.53 0.60 0.600 0.100 0.167 0.393 2400 3 0.75 22 2.809 00 6.0 0.57 0.30 0.300 0.040 0.133 0.524 1200 3 0.38 19 1.710 09 6.0 1.34 0.70 0.400 0.130 0.325 0.299 1600 3 0.50 19 1.011 00 6.0 1.91 1.00 1.120 0.190 0.170 0.586 4480 2 1.40 21 0.612L 00 12.0 1.91 0.50 0.500 0.100 0.200 0.262 2000 3 0.63 18 15.012M 00 12.0 1.91 0.50 0.200 0.050 0.400 0.105 800 3 0.25 18 15.012S 00 12.0 1.91 0.50 0.150 0.030 0.020 0.079 600 3 0.19 18 15.013 00 8.0 1.91 0.75 0.800 0.150 0.188 0.419 3200 2.5 1.00 14 1.014 00 3.5 0.45 0.40 0.230 0.045 0.196 0.516 920 3 0.29 17 2.015 14 8.0 0.51 0.20 0.350 0.065 0.186 0.687 1400 2 0.44 20 20.016 00 8.0 1.27 0.50 0.400 0.060 0.150 0.314 1600 3 0.50 17 2.317 16 5.0 0.80 0.50 0.350 0.050 0.143 0.440 1400 3 0.44 20 1.518L 00 7.0 0.78 0.35 0.350 0.065 0.186 0.449 1400 3 0.44 18 7.018S 00 7.0 0.78 0.35 0.070 0.010 0.143 0.090 280 2.5 0.09 18 7.019 00 10.0 1.91 0.60 0.600 0.110 0.183 0.314 2400 2.5 0.75 25 3.720L 00 15.0 1.91 0.40 0.500 0.100 0.200 0.262 2000 3 0.63 21 7.620S 00 15.0 1.91 0.40 0.060 0.015 0.250 0.031 240 2.5 0.08 21 7.621L 00 15.0 1.67 0.35 1.000 0.150 0.150 0.598 4000 2.5 1.25 25 12.521S 00 15.0 1.67 0.35 0.060 0.015 0.250 0.036 240 2.5 0.08 25 12.522L 00 10.0 0.64 0.20 0.450 0.065 0.144 0.707 1800 2.5 0.56 27 70.022S 00 10.0 0.64 0.20 0.050 0.015 0.300 0.079 200 2.5 0.06 27 70.023L 00 18.0 2.86 0.50 1.800 0.150 0.083 0.628 7200 2.5 2.25 18 8.723M 00 18.0 2.86 0.50 0.250 0.040 0.160 0.087 1000 2.5 0.31 18 8.723S 00 18.0 2.86 0.50 0.080 0.010 0.125 0.028 320 2.5 0.10 18 8.7

aExperiment: L, M, and S at the end of the name indicate large, medium, and small bed forms. Small bed forms were observed superimposed on thelarger ones. Medium bed forms are used to describe complex morphologies. For the experiments in boldface at the bottom of the table, significant walleffects were observed.

bInitial condition of the sediment bed at the beginning of the experiment: 00 indicates flat bed, the other numbers indicate the number of the experimentran before, which description can be found also in this table.

cHere 2 indicates two-dimensional bed forms, 3 indicates three-dimensional bed forms, 2.5 indicates bed configurations that shown three-dimensionalbed forms together with some two-dimensional ones, or bed forms with wavy crests.

dBed form wavelength to tunnel width ratio. If the bed form is reported as 2-D but l/w is larger than 1 the bed form cannot be considered truly two-dimensional.

eDuration of the experiment. This time was longer than the necessary time for the formation of a ‘‘stable’’ bed configuration.


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all cases the variation of the water temperature for theduration of the experiment was less than 2�C. The effectof temperature on water density can be considered as minorfor the phenomenon under study. However, changes intemperature can produce significant variations in the waterviscosity. Controlling the temperature of the water inside theLOWST was not possible at this time. The room where theLOWST is located has no temperature control and the watertemperature inside the tunnel would adjust to the ambienttemperature, which varies with both weather and seasons.Experiment 05 ended during the spring and the watertemperature was 19�C, during the following weeks thesummer season started and the water temperature rose to27�C. This opportunity was used to observe possible waterviscosity effects on the particular bed configuration presentat that time. However, no significant changes whereobserved as it is reported in Experiment 06. It is possiblethat our sediment was not fine enough for viscous effects tobe easily noticeable. The role of viscosity on bed configu-ration has been repeatedly reported in the unidirectionalflow literature [e.g., Vanoni, 1974; Shen et al., 1978;Southard and Boguchwal, 1990; Garcıa, 2008]. Since thebasic process governing the sediment transport should bethe same regardless of the unidirectional or oscillatory natureof the flow, the role of viscosity on oscillatory flow bed formsdeserves further research.

4.2. Long Water Excursion Experiments

[26] Some of the experiments reported in Table 2 weredesigned to cover a wide range of oscillatory flow con-ditions in order to identify the ones leading to the formationof either two-dimensional or three-dimensional ripples. Thiswas not the only goal of our work and another set ofexperiments was specifically designed to study the maxi-mum orbital velocity effect on long water excursion experi-ments. These long excursion experiments are specificallyreported in Table 3, and for all of them the near-bed waterexcursion was kept constant at 2 m. For four of theseexperiments a detailed description supported by severalfigures and Animations 1–4 is provided.4.2.1. Experiment 07[27] For this experiment, T = 25 s,Umax = 0.25m/s, and d =

1.99 m. The experiment started from a flat bed. First,small ripples grew from the sidewalls of the tunnel andpropagated into the central part of the sediment bed,completely covering it. The wavelength of those smallripples was 0.06–0.07 m, their height was approximately0.015 m, and they were straight crested. We classified themas rolling grain ripples [Bagnold, 1946], since no significantflow separation occurred over their crests, and no suspendedsediment was observed either [Faraci and Foti, 2001]. Soon

after these ripples had covered the entire bed a doublingprocess started. The doubling process originated at thesidewalls of the tunnel and consisted in the disappearanceof every other ripple crest and the growth of the remainingones. No merging of ripples was observed and these largerripples quickly replaced the initial ones over the entire bed.After this, the doubling process started again, but this timesmall perturbations consisting of short trains of small ripplesmoving along the bed, were observed at several locations.However, aside from the presence of these perturbations, thedoubling process was the only growth mechanism observeduntil the final bed configuration was reached, whichhappened after 150 h of running the experiment. Thedoubling process is a good example of water flow bedmorphology coupling. The initial small ripples perturbed theflow generating circulation cells that induce sediment trans-port, which in turn was reflected on the growth of someripples and the depletion of others, leading to the increase ofthe overall ripple size. A fast-forward video of this processis included as Movie S1 in the auxiliary material.1

[28] The final configuration consisted of large sharpcrested ripples with l = 1.13 m and h = 0.17 m (Figure 5).These ripples were clearly orbital ripples, since l/d � 0.6and h/l � 0.15 [Clifton, 1976], despite the fact that thedimensionless excursion d/D50 � 7600 was clearly abovepreviously defined limits for the occurrence of orbitalripples [Clifton and Dingler, 1984; Wiberg and Harris,1994]. Small superimposed ripples were observed migratingon top of the larger ones. These superimposed ripplestraveled from the troughs of the large ripples toward theircrests, where they were washed out as they were exposed tohigher shear stresses. The superimposed ripples had shortsharp crests, and their wavelength and height were 0.11 and0.014 m, respectively. They looked very much likeunidirectional flow ripples, which was basically the localflow they were exposed to. At a particular phase of theoscillation cycle the local flow over the face of the largeripple facing the flow (stoss side) was a current flowingtoward the large ripple crest. On the opposite side of thelarge ripple (lee side), the flow detached and a recirculationcell formed. Therefore the local flow on the lee side wasalso toward the large ripple crest.4.2.2. Experiment 11[29] For this experiment, T = 6 s, Umax = 1.0 m/s, and d =

1.91 m. The experiment started from a flat bed. As theexperiment began, the bed was mobilized in a layer 5 to10 sand grains thick. There was no development of small-scale bed forms and no suspended sediment was observed.This remained unchanged for the first 5 min in the centralarea of the tunnel. However at the same time, long wavyperturbations were traveling from both tunnel ends towardthe central region. Once these long wave perturbations hadcovered the entire sediment bed they rapidly increased theirheight. The experiment was stopped after 35 min, whensome of the bed forms had grown enough to cover asignificant portion of the tunnel cross section. For thisexperiment the Shields parameter was q = 0.62, close tocommon criteria for the existence of sheet flow conditions[Allen and Leeder, 1980; Sumer et al., 1996]. The absence

1Auxiliary materials are available in the HTML. doi:10.1029/2009JC005356.

Table 3. Long Water Excursion Experiments Sorted by Maximum

Orbital Velocity

Experiment

07 20 12 19 13 11

d (m) 1.99 1.91 1.91 1.91 1.91 1.91Umax (m/s) 0.25 0.40 0.50 0.60 0.75 1.00l (m) 1.13 0.50 0.50 0.60 0.80 1.12h (m) 0.17 0.10 0.10 0.11 0.15 0.19q 0.04 0.11 0.16 0.22 0.35 0.62


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of initial ripples is another clear indication that sheet flowregime had been initially established. A fast-forward videoof the process is included as Movie S2 as auxiliary material.[30] The final ripple height was irregular, and the final

average ripple wavelength and height were 1.20 m and 0.19m, respectively. All the ripple crests were round (Figure 6)and the flow separation occurred over the lee side of the bedform, instead of occurring at the ripple crest, as it was thecase in experiments with milder flow conditions. At thefinal stage significant amounts of sediment were transportedin suspension but the bed load transport also seemed to beimportant, specially over the stoss side of the ripple. Nosuperimposed bed forms were observed at any time duringthe experiment.4.2.3. Experiment 12[31] For this experiment, T = 12 s, Umax = 0.5 m/s, and d =

1.91 m. For this experiment an intermediate orbital velocity,between Experiments 07 and 11, was selected. As in thecase of Experiment 07, it started from a flat bed, and smallrolling grain ripples were observed to propagate from thesidewalls rapidly covering the entire sediment bed. Thesesmall ripples had straight crests, and their wavelength andheight were approximately 0.10 m and 0.01 m, respectively.Again starting from the tunnel walls perturbations started togrow adding three-dimensionality to the bed and increasingthe average ripple size. A fast-forward video of this processis included as Movie S3 as auxiliary material, where severalperturbations can be seen traveling on top of the largerfeatures and reworking the bed. After 15 h of experiment,the final bed configuration was highly complex and three-dimensional, with the ripples continuously changing andmoving over the bed. The crests of both large and super-imposed ripples were short and sharp (Figure 7). Thewavelength and height of the larger features was estimated

to be 0.5 m and 0.1 m, respectively, putting these ripples inthe suborbital range according to the classification ofWiberg and Harris [1994].4.2.4. Experiment 13[32] For this experiment, T = 8 s, Umax = 0.75 m/s, and d =

1.91 m. Initially, it was expected that these conditionswould generate smaller ripples than Experiment 12, but thiswas not the case. The experiment started from a flat bed,and very shallow ripples spontaneously appeared over thewhole sediment bed without any observable influence of thesidewalls. The wavelength and height of these ripples were

Figure 5. Final bed configuration for Experiment 07(T = 25 s, Umax = 0.25 m/s, d = 1.99 m). (top) Sonar scan,dimensions in centimeters. (bottom) Photography showingthe general aspect of the bed, the window on the back is60 cm wide. The resolution of the sonar data was notenough to capture the small superimposed ripples. Thesonar scan and the photo correspond to two differentlocations along the bed.

Figure 6. Final bed configuration for Experiment 11(T = 6 s, Umax = 1.00 m/s, d = 1.91 m). (top) Sonar scan,dimensions in centimeters. (bottom) Photography showingthe general aspect of the bed, the window on the back is 60 cmwide. The sonar scan and the photo correspond to twodifferent locations along the bed.

Figure 7. Final bed configuration for Experiment 12(T = 12 s, Umax = 0.50 m/s, d = 1.91 m). (top) Sonar scan,dimensions in centimeters. (bottom) Photography showingthe general aspect of the bed, the window on the back is 60 cmwide. The sonar scan and the photo correspond to twodifferent locations along the bed.


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0.15 m and less than 0.01 m, respectively. Their straightcrests moved half a wavelength during the oscillation cycle,and as they increased their size their crests became morewavy, but without any noticeable influence of the tunnelwalls. The ripples continued to grow until they reached theirfinal size, l = 0.8 m and h = 0.15 m. A fast-forward video ofthis process is included as Movie S4 in the auxiliarymaterial. Smaller perturbations moving over the bed werenot observed during the experiment. The crest of the finalripples appeared rounded similarly to Experiment 11(Figure 8). For this case the tunnel entrances were notfound to play any role on the ripple formation.[33] Given the heights of some of the ripples formed

under long water excursions, particularly the round-crestedripples generated in Experiment 11, a note should be madeon the possible restrictions imposed by the cross-sectionheight of the LOWST to the free development of bed forms.For example, in Experiment 11 the heights of the ripplessignificantly reduced the available cross section for thewater to flow, therefore increasing the velocities over theripple crests and reducing them over the ripple troughs.These changes in the water velocity have the potential toinduce variations on the shear stresses over the bed andaffect the resulting bed morphology. Similarly, the spatialvariation of the velocity could have induced groundwaterflows from the trough to the crest of the ripple, where thepressures were lower, eventually helping to destabilize thesediment at the crest of the ripple. Despite all theseundesired effects, which are unavoidable even in a largefacility like the LOWST, the consistency on the trendsdisplayed by the resulting morphology suggests that theyrole was limited. First, ripples with round crests wereobserved in early stages of the bed evolution before theripples had time to grow to their final hight. Second, thetransition to round-crested ripples can be observed for all

the experiment with velocities above 0.5 m/s, with the sizeof the round-crested ripples increasing, not decreasing, asthe velocity increases. Third, the size of round-crestedripples was very irregular along the tunnel, but all the crestswhere round even the smallest ones for which the flowrestriction was minimum. Finally, bed forms with similarcharacteristics have been observed by other researchers inthe laboratory [e.g., Southard et al., 1990; Arnott andSouthard, 1990; Ribberink and Al-Salem, 1994; Dumas etal., 2005; Cummings et al., 2009] and in the field [e.g., Yanget al., 2006], suggesting that our observations were notartificially generated by our laboratory setup.

5. Ripple Size and Cross-Section Geometry

5.1. Performance of Existing Predictors

[34] The performance of some of the most popular ripplesize predictors [Nielsen, 1981; Mogridge et al., 1994;Wiberg and Harris, 1994] is discussed in this section. Thesepredictors were presented in a companion paper, and thecomplete details of each formulation can be found in theoriginal articles.[35] Our new experimental data is shown in Figures 9 and

10 in terms of the dimensionless variables used by each ofthe three predictors. In Figures 9a–9c and 10a–10c thecorresponding predictor equation and our experimentalresults are shown. Also, the compiled literature data,discussed in the companion paper, are shown in the back-ground as a guide for the overall performance of eachpredictor and to allow the comparison of our observationswith the ones of other researchers. Of the three predictors,the Nielsen [1981] laboratory equation is clearly the one thatbest captures the overall trend of our experiments. However,a clear deviation from the laboratory equation is observedfor the round-crested ripples formed at high velocities. Themobility number used by Nielsen [1981] predictor is definedas y = Umax

2 /(gRD50).[36] Regarding Mogridge et al. [1994] predictor, the

constant dimensionless ripple wavelength l/l0 predictedby Mogridge et al. [1994] for large values of thedimensionless water excursion d/dl0

is only followed bysome of our experiments, while other experiments stillfollow the ‘‘orbital’’ trend. Similarly, the overall trend of theripple height is to continuously increase as the dimensionlesswater excursion increases, contrary to the decay predictedby Mogridge et al. [1994]. Therefore the predictor tends tounderpredict the size of the observed ripples, specially forlong water excursions. The characteristic ripple dimensionsand near-bed water excursions (l0 and dl0

, h0, and dh0)used by Mogridge et al. [1994] are functions of thedimensionless period parameter c = D50/(gRT

2).[37] For the case of Wiberg and Harris [1994] predictor,

the deviations are particularly dramatic, since the rippledimensionless wavelength and height (l/D50 and h/D50)remain close to the orbital trend instead of following thesuborbital-anorbital trend as the predictor suggests. Similardeviations have been reported by Traykovski et al. [1999]and O’Donoghue and Clubb [2001] for field and laboratoryexperiments, respectively. Furthermore, for the samedimensionless water excursion d/D50 � 8000 the ripplewavelength was between l/D50 � 2000 and l/D50 � 5000,depending on the water maximum orbital velocity.

Figure 8. Final bed configuration for Experiment 13(T = 8 s, Umax = 0.75 m/s, d = 1.99 m). (top) Sonar scan,dimensions in centimeters. (bottom) Photography showingthe general aspect of the bed, thewindow on the back is 60 cmwide. The sonar scan and the photo correspond to twodifferent locations along the bed.


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Figure 10. Performance of existing ripple heightpredictors with the experimental data (Table 2). The datadisplayed in gray corresponds to the data compiled fromthe literature. (a) Nielsen [1981], (b) Mogridge et al. [1994],(c) Wiberg and Harris [1994]. The symbols used are asindicated in Figure 10a.

Figure 9. Performance of existing ripple wavelengthpredictors with the experimental data (Table 2). The datadisplayed in gray corresponds to the data compiled fromthe literature. (a) Nielsen [1981], (b) Mogridge et al. [1994],(c) Wiberg and Harris [1994]. The symbols used are asindicated in Figure 9a.


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5.2. Performance of the New Predictor

[38] The new predictor proposed in the companion paperis compared here with our experimental data. The newpredictors emphasize the existence of local and globalsediment transport mechanisms over a ripple bed. Thesetwo mechanism are represented by the dimensionlessparticle size Rep =


pD50/n and the ratio of the

maximum orbital velocity to the particle settling velocityUmax/ws. For the sediment size and water temperatures inthe current experiments the value of Rep falls in the uppersediment size range of the predictor (i.e., Rep > 13). Thepredictive equations proposed for this sediment size rangeare shown in Figure 11. For the ripple wavelength theequations are

ld¼ 0:65 0:050 Umax=wsð Þ2 þ 1

h i�1; ð2Þ

and l/d = 0.65 for the horizontal line in Figure 11a. For theripple height the equations are

hd¼ 0:1 0:055 Umax=wsð Þ3þ1

h i�1; ð3Þ

and h/d = 0.1 for the horizontal line in Figure 11b.[39] The agreement between the new predictor and the

observations is clearly better than the agreement ofMogridge et al. [1994] and Wiberg and Harris [1994]predictors. It is also better that the agreement with Nielsen[1981] laboratory equation. It should be emphasized thatdespite being inspired by the trends found in our experi-mental data, the new predictor was calibrated using thecomplete data set compiled from the literature, which isdisplayed in light gray on the background of Figure 11.

5.3. Discussion

[40] The long water excursion experiments showed theimportance of including a second variable, other than thewater excursion, to describe the water oscillation. If atten-tion is directed to experiments 07, 20, 12, 19, 13, and 11 inTable 2, it can be noted that all of them had approximatelythe same water excursion, d � 1.9 m, but increasingmaximum orbital velocity, going from 0.25 m/s to 1 m/s.In Table 3 a summary of these experiments sorted bymaximum orbital velocity is given. From Table 3 animportant observation can be made; initially, both ripplewavelength and height decreased as the maximum orbitalvelocity increased, but once orbital velocities exceed 0.5 m/sthe ripples began to increase their size again. The ripplesformed at velocities above 0.5 m/s had round crests and areindicated in Figures 9, 10, and 11. As observed in thecompanion paper the transition occurred at Umax/ws � 25.This corresponds to a value of the Shield’s parameter q� 0.3.Above this threshold the dimensionless ripple wavelengthl/d increased continuously as the dimensionless orbitalvelocity Umax/ws increased. Instead, for the ripple height amuch more abrupt transition was found and the dimensionlessheight jumped from h/d = 0.05 to h/d = 0.1.[41] A first consequence of this observation is that

anorbital ripples were never observed in our experiments.The lower limit of d/D50 for the occurrence of anorbitalripples defined by Clifton and Dingler [1984] and Wibergand Harris [1994] are 5000 and 5600, respectively. Thedimensionless water excursion in the experiments discussedhere was d/D50 � 7600, well above these limits. Although areduction on the ripple size for increasing orbital velocitieswas initially observed, this reduction stopped well beforeripples could be considered anorbital, and the ripple sizestarted to increase again. The absence of anorbital ripples isin agreement with the observations from other researchersshown in the background of Figure 11 and discussed in thecompanion paper. According to the analysis in the companionpaper anorbital ripples would form in fine sands (Rep < 9),which is not the case of the sand studied here.[42] A second consequence of the above observation is

that the assumption that under high enough velocities theripple dimensions will decrease until the transition to flatbedoccurs is not universally valid. Nevertheless, a minimumripple size for a given water excursion and sediment stillexists. For the case of our experiments with d � 1.9 m,

Figure 11. Performance of the new ripple size predictor[Pedocchi and Garcıa, 2009b] with the experimental data(Table 2). The data displayed in gray corresponds to the datacompiled from the literature with Rep > 13. The symbolsused are as indicated in Figure 11a.


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they are l � 0.50 m and h � 0.10 m, which is observed forUmax = 0.5 m/s. Similarly, an upper limit is given by theorbital scale, l � 0.65d � 1.2 m and h � 0.1d � 0.19 m,which was observed for both Umax = 0.25 m/s and Umax =1.0 m/s. For a given water excursion the ripple size will bebetween these minimum and maximum size limits depend-ing of the maximum orbital velocity.[43] Third, it should be noted that the increase in the size

of the bed forms, for velocities above 0.5 m/s, was associ-ated with changes in the ripple crest shape, which becamerounder as the orbital velocity increased. This change in thecrest shape resulted in the migration of the detachment pointfrom the ripple crest to the lee side (see section 4.2.2). Alsoas expected the increase in velocity produced an increase inthe sediment transport. All these characteristics, togetherwith the abrupt change in size observed in Figure 11 give astrong indication that round-crested ripples are a differentclass of bed forms. And probably they should be studiedseparately from the more commonly observed sharp crestedripples. At this point, our understanding of the bed responsein the transition from sharp crested ripples to round-crestedripples is limited, and further experiments are needed tofully understand how this transition occurs.

6. Planform Geometry

6.1. Performance of Existing Predictors

[44] In this section the planform geometry predictorsdiscussed in the companion paper are contrasted with ourexperimental observations. The predictors considered wereCarstens et al. [1969], Lofquist [1978], Sato [1987], andVongvisessomjai [1984]. The results are displayed inFigure 12.[45] The Carstens et al. [1969] criterion predicts three-

dimensional ripples for d/D50 > 1550, which is not verified

by our observations as shown in Figure 12. On the otherhand, the Lofquist [1978] criterion predicts two-dimensionalripples for y < 21.3. This would be verified only if somequasi two-dimensional ripples are considered as two-dimensional. Similarly, the Sato [1987] criterion, whichcan be approximated to the upper right quadrant ofFigure 12, is also verified if these quasi two-dimensionalripples are grouped with the two-dimensional ones. Finally,Vongvisessomjai [1984] predicts ripples to be three-dimensional if AUmax/(


pD50) > 5500, correctly

discriminating the planform configuration of ourexperiments.

6.2. Performance of the New Predictor and Discussion

[46] The planform geometry predictor proposed in thecompanion paper is based on the observation that bothlonger excursions and larger velocities tend to increase thethree-dimensionality of the ripples. Additionally, ripplesformed in fine sediments tend to present more three-dimensionality than ripples formed in coarse ones. Ournew predictor takes these elements into account, givingthe following criterion for the occurrence of two-dimensional ripples:

Rep > 0:06 Rew0:5: ð4Þ

Owing to variations in the water temperature betweenexperiments, the sediment used in our experiments did notcorrespond to a unique value of Rep but rather fell into anarrow range of Rep values, between 14 and 19. If acharacteristic Rep � 16 is selected, the upper limit forthe occurrence of two-dimensional ripples is givenapproximately by

Rew � 7 � 104: ð5Þ

The narrow range of Rep values involved allowed torepresent our experimental data in the (Tn/D50

2 , UmaxD50/n)plane. This is done in Figure 13, where the laminar-turbulenttransition Rew = 6.6*104 and the smooth-rough transitionRe* = 6 are indicated. Our predictor, indicated by theRew = 7*104 line, correctly discriminates between two-dimensional and three-dimensional ripples. From theconstant A/D50 lines, also shown in Figure 13, it can beobserved that the Carstens et al. [1969] criterion is unableto capture the two-dimensional to three-dimensionaltransition. Lofquist [1978] criterion for Rep � 16,translates to UmaxD50/n = 74, which does not seem tohold, either. Finally, Vongvisessomjai [1984] criteriontranslates to Rew = 8.8*104, which is very close to thevalue given by our predictor for this particular value ofRep. The relations used, in these transformations amongdimensionless variables, are given in section 3.2 of thecompanion paper.[47] Further insight into the performance of the new

predictor can be gained if experimental data with similarvalues of Rep obtained by other researchers are also plottedin the (Tn/D50

2 , UmaxD50/n) plane. In Figure 14 experimentsreporting planform geometry from Carstens et al. [1969],Southard et al. [1990], O’Donoghue and Clubb [2001],Williams et al. [2004], and O’Donoghue et al. [2006] are

Figure 12. Performance of existing ripple planformpredictors with the experimental data (Table 2). The datadisplayed in gray corresponds to the data compiled fromthe literature. The cross indicates the results for which thel/w ratio is larger than 1. Solid line Vongvisessomjai[1984], dashed line Lofquist [1978], dash-dot line Carstenset al. [1969].


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included. They are for Rep values between 13 and 24, closeto the ones in our experiments. Kennedy and Falcon [1965]and Mogridge and Kamphuis [1972] also reported observa-tions inside the range of Rep analyzed here. However,their experiments involved lightweight, large-diametersediments, and the observations fall out of the rangedisplayed in Figure 14. Nevertheless, all of their rippleswere two-dimensional in agreement with the criterion givenby equation (5).[48] The agreement between the literature data and our

own observations and the new criterion is excellent, and thesmall deviations are due to differences in Rep, which cannotbe considered in the (Tn/D50

2 , UmaxD50/n) plane. Experi-ments for which the ratio between the ripple wavelength andthe facility width were larger than 1 are highlighted inFigure 14. Three-dimensional ripples observed in widefacilities coexist with two-dimensional ripples found innarrow facilities. A clear indication of the importance of theconstraint imposed by the facility width on the development ofbed form three-dimensionality.

7. Summary and Conclusions

[49] The long water excursion experiments showed thatfor a given water excursion the ripple size initially reducesas the maximum orbital velocity increases. However, after acertain maximum orbital velocity threshold was crossed the

size of the bed forms started to increase again. These latterripples, produced by high velocities, have round crests. Thedifferent geometry and behavior of round-crested ripples area strong indication that they belong to a different bed formregime. The smallest ripples obtained in the long excursionexperiments were still too large to be considered to beanorbital, and it should be concluded that anorbital ripplesare not observed for the selected sand D50 = 250 mm undersinusoidal oscillations.[50] For the selected sediment it was found that ripples

were two-dimensional when the wave Reynolds numberwas smaller than 7*104 as predicted by our new predictor.The LOWST 0.8 m width removed some of the limitationsfound in narrower facilities for the development of bed formthree-dimensionality. The comparison with data fromnarrower facilities showed that facility width restricts thedevelopment of three-dimensional ripples, and that theplanform geometry results obtained in narrow facilitiesshould be used with care.[51] The performance of the existing size and planform

geometry predictors and our new size and planformgeometry predictors was evaluated with our own experi-mental data. The proposed new wavelength and heightpredictors were the ones performing best. Of the existingripple size predictors, the field equations of Nielsen [1981]were the ones showing the best agreement with ourobservations. Regarding the prediction of planform geometry,

Figure 13. Performance of the new ripple planform predictor with the experimental data (Table 2)showed on the (Tn/D50

2 , UmaxD50/n) plane. The limit for the transition from two-dimensional to three-dimensional ripples is given by the Rew = 7*104 line. Several dimensionless oscillation amplitude A/D50,constant wave Reynolds number Rew and constant shear Reynolds number Re* contours are shown. Thelaminar-turbulent transition Rew = 6.6*104 and smooth-rough transition Re* = 6 are also highlighted. Thenumber next to the data points is the Rep value.


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the proposed predictor showed the best performance. Thepredictor of Vongvisessomjai [1984], which for the sedimentused in our experiments gives a very similar condition toours, also performed very well. However, for other sedi-ments Vongvisessomjai [1984] and our predictor would givedifferent results.

Appendix A: Wave Friction Factor Summary

[52] In this article the friction factor for oscillatory flow fwwas computed according to Pedocchi and Garcıa [2009a].A summary of its mathematical expression follows.[53] For A/k > 30 and Rew > 6.6 * 104, the flow presents

rough to smooth turbulent transition and fw is obtained usingan iterative scheme over the following expressions:

1ffiffiffifp

w

¼ 1:9 ln1

1:5

A

k

ffiffiffiffifw

2

rLw

!; ðA1Þ

where

Lw ¼1

7:51� exp � 1

90

Rew

A=k

ffiffiffiffifw

2

r( )20@

1A

24

35þ . . .

8<:

. . .þ 1

2:1

Rew

A=k

ffiffiffiffifw

2

r !�19=;�1

: ðA2Þ

For A/k > 30 and Rew < 6.6*104, the flow is considered tobe laminar and the analytical solution is

1ffiffiffifp

w

¼ Rew1=4ffiffiffi2p : ðA3Þ

[54] For A/k < 30 the boundary layer concept brakesdown, since the roughness elements are of the order ofthe water excursion. Furthermore, for this case the flow cantransition from rough turbulent to laminar without passingtrough a smooth regime [Jonsson, 1966]. No expression isgiven for this A/k range.

Appendix B: Near-Bed Flow Generatedby Surface Waves

[55] In the LOWST arbitrary combinations of Umax and dcan be selected for the experiments. However, not everycombination would correspond to conditions that could begenerated by surface waves in the sea. Therefore it is ofinterest to know if a realistic combination of wave heightsand water depths would generate the selected near-bedoscillations. Clifton and Dingler [1984] presented a goodsummary on this problem, and here we will just restrict thediscussion to present a dimensionless diagram computedusing Airy theory.[56] The wavelength L is related to the water depth h and

period T by the dispersion equation [Dean and Dalrymple,

Figure 14. Performance of the new ripple planform predictor with the new experimental data (Table 2)and the data compiled from the literaturewith 13 <Rep< 24. The limit for the transition from two-dimensionalto three-dimensional ripples is given by the Rew = 7*104 line. The contours are the same of Figure 13, butthe labels have been omitted here. The number next to the data points is the Rep value.


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1991], which can be made dimensionless using h as a lengthscale

L

h¼ L0

htanh

2phL

� �; ðB1Þ

with L0 = gT2/(2p) the length of a wave with the same periodin deep waters. Note that L0/h = p/2 [(d/h)/(Umax/

ffiffiffiffiffighp

)]2.If Umax/

ffiffiffiffiffighp

and d/h are given, L0/h can be computedand L/h can be obtained from Equation (B1). Then thedimensionless wave height H/h can be computed using

H

h¼ d

hsinh

2phL

� �: ðB2Þ

The result of this procedure is shown in Figure B1 ingraphical form.[57] The limits under which the Airy theory is valid are

given by [see Komar, 1976]

H

h

L

h

� �2

< 32p2=3; ðB3Þ

and

H

h

L

htanh

2phL

� �� 1< 0:0625: ðB4Þ

And the H/h curves computed above are strictly valid underthese limits. To the right, for large values of d/h, cnoidalwave theory should be used. To the left, second- and higher-order Stokes wave theories should be used; the results ofapplying these other theories are not included here.[58] When waves are too tall for a given water depth or

too steep, they break. This introduces a limit for theconditions that may be found in the real world. In shallowwaters a very simple criterion, which takes neither the slopeof the beach nor the wave period into account is given by

Hb

h¼ 0:78; ðB5Þ

where Hb is the wave height at which the wave wouldbreak. In intermediate and deep waters the condition forwaver break is given by the Miche [1951] criterion

Hb

h¼ 0:142

L

htanh

2phL

� �: ðB6Þ

Figure B1. Wave height H as function of the near-bed maximum orbital velocity Umax and waterexcursion d, made dimensionless with the water depth h. The H/h lines were computed using Airy theoryover the full plane. However, they are strictly valid below the Airy Theory line. The wave breaking limitsare also shown by the H/h = 0.78 line and the Miche [1951] criterion close to it. The conditions of ourexperiments are plotted for h = 5 m, for which most of them fall under the range of validity of the AiryTheory. Note that all the possible combinations of H and h that would give a particular Umax and d paircan be found along the constant Umax/

ffiffiffiffiffigdp

lines.


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Both limits fall outside the area where the Airy theory isstrictly valid and they are shown in Figure B1 just toindicate where this limitations would fall if the Airy theorywas used.[59] The conditions of the present experiments are also

included in Figure B1, using h = 5 m as water depth for thecomputations. For this water depth most of the performedexperiments fall into the range of validity of the Airy theoryand can be considered to correspond to conditions found innature. Moving along the constant Umax/

ffiffiffiffiffigdp

linesother possible combinations of wave heights and waterdepths that would give the same near-bed conditions canbe found.

[60] Acknowledgments. The work presented in this article wassupported in part by the Ripples DRI of the Coastal Geosciences program,with Thomas Drake as Program Director, of the U.S. Office of NavalResearch, grant N00014-05-1-0083, the support is gratefully acknowl-edged. The Large Oscillating Water-Sediment Tunnel was built withsupport from the DURIP Program ONR grant N00014-01-1-0540. Thehelp of Sig Anderson Jr. (ELD, MN) and John Bushey (MTS, MN) with thedesign and construction of the tunnel and the piston system, respectively, isalso gratefully acknowledged. The authors would like to thank J. EzequielMartin for the enriching discussions during the course of this work. Thanksto David Admiraal and Yovanni Catano-Lopera for their comments, whichhelped to improve an earlier draft of this manuscript. Also thanks to BillArnott and Peter Nielsen for their suggestions which helped to improve thefinal form of the manuscript.

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��M. H. Garcıa, Ven Te Chow Hydrosystems Laboratory, Department of

Civil and Environmental Engineering, University of Illinois at Urbana-

Champaign, 205 N. Mathews Ave., Office 2535b, Urbana, IL 61801, USA.([email protected])F. Pedocchi, Instituto de Mecanica de los Fluidos e Ingenierıa Ambiental,

Faculatad de Ingenierıa, Universidad de la Republica, Julio Herrera yReissig 565, CP 11300, Montevideo, Uruguay. ([email protected])


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