Journal of Sedimentary Research, 2009, v. 79, 83–93

Research Article

DOI: 10.2110/jsr.2009.012

FINE-GRAINED VERSUS COARSE-GRAINED WAVE RIPPLES GENERATED EXPERIMENTALLY UNDERLARGE-SCALE OSCILLATORY FLOW

DON I. CUMMINGS,1* SIMONE DUMAS,1{ AND ROBERT W. DALRYMPLE1

1Department of Geological Sciences and Geological Engineering, Queen’s University, Kingston, Ontario, K7L 3N6 Canada

e-mail: dcumming@nrcan.gc.ca

ABSTRACT: Wave ripples were generated in a wave tunnel under large-scale oscillatory flow (orbital diameter 1–4.5 m) usingtwo different grain sizes, very fine sand and coarse sand. The geometry of bed configurations that were produced varied stronglyas a function of grain size: small anorbital ripples (wavelengths , 10 cm, heights , 1 cm) formed exclusively in very fine sandat low oscillatory velocities, whereas large orbital ripples (wavelengths 50–350 cm, heights 7–26 cm) formed in both very fineand coarse sand, but were subdued, sharp- to round-crested, and 2-D to 3-D in very fine sand, and steep, sharp-crested, and 2-Din coarse sand. The large ripples in fine sand, if aggraded, would deposit low-angle (5–15u) cross stratification resemblinghummocky cross stratification, whereas the large ripples in coarse sand would deposit high-angle (15–25u) cross stratificationthat might be mistaken for the deposit of a dune because of its high dip angle and large set thickness (. 5 cm). These resultssupport the hypothesis advanced by Leckie (1988) that large waves generate markedly different stratigraphic signatures in fine-grained and coarse-grained sediment.

INTRODUCTION

The back-and-forth motion of water beneath waves commonly stirssediment on the seafloor, shaping it into regularly spaced mounds termedwave ripples. Wave ripples are an invaluable tool to geologists: theirpresence indicates subaqueous deposition, and their shape, size, andstratification can be used to infer the size of the waves that depositedthem, which, in turn, provides a general idea of the size of the water bodyin which they formed. This makes them useful for interpreting ancientdepositional environments (e.g., open-ocean shoreface versus back-barrier lagoon) and for reconstructing the migration of ancientdepositional environments with time, an important component ofsequence stratigraphy.

Unfortunately, compared to bedforms generated by unidirectionalcurrents, for which robust phase diagrams have been developed (South-ard and Boguchwal 1990), our understanding of the relationship betweenthe form and generating conditions of wave ripples is still incomplete.This is particularly true for bed forms generated by large waves (e.g.,storm waves in the ocean). The reasons for this are twofold. First,instruments deployed to monitor the seafloor during storms commonlyfail or become damaged (e.g., Wright et al. 1994; cf. Traykovski et al.1999; Hanes et al. 2001). Second, it is difficult to generate high (. 2 mfrom peak to trough), long-period (. 6 s) waves like those present in theocean in the laboratory because prohibitively long, deep flumes arerequired (e.g., Williams et al. 2004). A successful solution has been the useof wave tunnels—enclosed ducts through which water is forced back andforth—to study wave ripples generated by large-scale oscillatory flow. In

previous experiments (e.g., Southard et al. 1990; Arnott and Southard1990; Dumas et al. 2005; O’Donoghue et al. 2006), a particular bedconfiguration consisting of low-relief, meter-wavelength mounds (‘‘hum-mocks’’) was reported in each case. Aggradation of these moundsproduces low-angle (, 15u), gently undulating cross stratification thatclosely resembles hummocky cross stratification (‘‘HCS’’; Harms et al.1982; Southard et al. 1990; Dumas and Arnott 2006). This observationsupports the hypothesis, advanced by field geologists in the 1960s and1970s (e.g., Cambpell 1966; Harms et al. 1975), that HCS is diagnostic ofdeposition under the influence of large waves in large water bodies.

Despite the promise of wave tunnels for understanding bed formsgenerated by large waves, few have been built because they are big andexpensive. Consequently, few experiments have been conducted, the resultbeing that the variables that control the size, shape, and stratification ofbed forms generated by large waves—namely sediment grain size (D50),oscillatory velocity (Uo), and orbital diameter (d0) (Fig. 1)—have notbeen explored comprehensively. In particular, the effects of grain size arepoorly understood, because most large-scale wave-tunnel experimentshave used very fine or fine sand, the grain size in which HCS is mostcommonly reported (Harms et al. 1982). What if coarser sand is used?Does HCS still form? Based on an analysis of modern and ancient wave-ripple data, Leckie (1988) argued that large straight-crested ripples formin place of hummocks in coarse sediment, an idea that appears to besupported by recent field and experimental data (Traykovski et al. 1999;O’Donoghue and Club 2001; Hanes et al. 2001; O’Donoghue et al. 2006).To test this hypothesis explicitly in a controlled laboratory setting, and tofurther our understanding of wave ripples in general, this studydocuments equilibrium bed forms generated under large-scale oscillatorymotion in a wave tunnel at Queen’s University, Canada, using first a bedof very fine sand, and then, under the same hydraulic conditions, a bed ofcoarse sand.

* Present address: Geological Survey of Canada, 601 Booth Street, Ottawa,

Ontario K1A 0E8, Canada{ Present address: Department of Earth Sciences, University of Ottawa, Ottawa,

Ontario K1N 6N5, Canada

Copyright E 2009, SEPM (Society for Sedimentary Geology) 1527-1404/09/079-083/$03.00

TERMINOLOGY, MATERIALS, AND METHODS

Unlike current-generated bed forms (Ashley 1990), descriptive termsfor wave ripples (e.g., steep, large) are not standardized. To facilitatedescription, therefore, an informal terminology is adopted (in part fromSouthard 1991). A bed form is defined as a distinct topographic elementon the bed, and a bed configuration is the assemblage of all topographicelements on the bed at one time. The term wave ripple is applied to allwave-generated bed forms, irrespective of shape and size (cf. Carstens etal. 1969). Following Hanes et al. (2001), small wave ripples (SWRs) aredefined as having wavelengths of , 30 cm, and large wave ripples (LWRs)are defined as having wavelengths . 30 cm (Fig. 2). Steep and subduedripples have maximum flank slopes greater and less than 15u, respectively.Two-dimensional (2-D) ripples have regular crest-to-crest spacings alongthe length of two adjacent bedforms and sinuous to straight, continuouscrests, whereas three-dimensional (3-D) ripples have irregular crest-to-crest spacings and highly sinuous to discontinuous crests. The term quasi–two-dimensional (2.5-D) is used to designate a bed configurationcharacterized by the presence of both 2-D and 3-D wave ripples. Itshould be noted that, given the limited width of the tunnel used (0.5 m),all wave ripples exceeding several meters in wavelength appeared to be 2-D even though their true shape may have been more irregular.

The wave tunnel at Queen’s University is a large, fully enclosed, race-track–shaped duct through which water is forced back and forth in asimple harmonic motion by a motor-driven piston (Fig. 3). Prior to eachseries of runs, the bed was planed flat. The orbital diameter was then setby fixing the throw of the piston, and the oscillatory velocity was varied inincrements by adjusting the angular speed of the motor that drives thepiston. In each case, the bed was allowed to reach equilibrium before

proceeding to the next increment of oscillatory velocity. An equilibriumbed was judged to have been reached when the average size and shape ofthe wave ripples stopped changing. In general, equilibrium was reachedrapidly, usually within several tens of minutes to one hour. However, inone coarse-sand run just above the threshold of sediment motion, the bedrequired almost twelve hours to reach equilibrium. Runs were terminatedrelatively rapidly (, 3 seconds), which prevented any ‘‘spin down’’modification of the equilibrium bed configuration. Once the run wasstopped, the bed was photographed and the height (h), wavelength (l),flank length, and flank slope of any wave ripples that had formed weremeasured, to a precision of 6 0.1 cm. These values are reported asaverages for each run (Table 1). When the highest possible oscillatoryvelocity was achieved for a given orbital diameter, the orbital diameterwas reset to a new value and another series of runs was performed. Afterthe full range of orbital diameters and oscillatory velocities was explored,the limits of which were dictated by the mechanical limits of the wavetunnel apparatus, the sediment was changed from very fine to coarsesand, and a similar set of experiments was conducted.

The range of hydraulic conditions explored in the experiments was9 5 c m , d 0 , 4 5 0 c m , 2 0 c m / s , U o , 1 7 0 c m / s , a n d4.5 s , T , 14 s (Table 1). Such conditions are common during stormson open continental shelves, where waves may exhibit a wide range ofperiods (, 1 to 25 s) and heights (, 1 to 15 m) but are rarelyencountered in lakes, rivers, and estuaries, where waves tend to belimited to periods of less than 4 seconds and maximum heights of 1 to2 meters because of the small fetch (Komar 1974; Young 1999; US ArmyCorps of Engineers 2002; Goda 2003). The two sediment types used in theexperiments had median grain sizes (D50) of 0.8 mm (coarse sand) and0.12 mm (very fine sand) (Fig. 4). In a very general way, they can beconsidered representative of the coarser sediment that is a commoncomponent of relict deposits (transgressive lags) on the continental shelfand finer sand commonly found in highstand deltas and highstand andtransgressive shorefaces on the inner continental shelf (Wright andNittrouer 1995; Geyer et al. 2005). The coarse-sand runs may also berelevant to carbonate shelves where coarse bioclastic material isabundant.

In most cases, the oscillatory flow generated in the wave tunnel wasvery slightly asymmetric in magnitude (the maximum speed of theforward stroke was slightly more than that of the backward stroke) andtime (the forward stroke took less time to complete than the backwardstroke). (In all figures traced from the side-wall viewing area (e.g., Fig. 5),the shorter, faster stroke is to the right.) The asymmetry increased withincreasing oscillatory velocity (because of increasing stress on the wave-tunnel drive mechanism), but the difference between forward andbackward strokes rarely exceeded several percent. As a consequence,bed forms were almost invariably symmetric (see ripple symmetry valuesin Table 1). An exception to this occurred near the transition to plane bed

FIG. 1.— The three key controls on wave-ripple shape and size—orbitaldiameter (d0), maximum oscillatory velocity (Uo) and sediment grain size (D50).(Many authors (e.g., Clifton 1976; Southard et al. 1990) substitute wave period (T)for d0 since T 5 pd0/Uo.) Other variables may be important under certaincircumstances (Yalin and Russell 1962; Southard et al. 1990), especially in the‘‘nearshore zone’’ (water depths , 10 m; see Clifton et al. 1971; Clifton 1976;Swift and Niedoroda 1985), where strong wave-orbital asymmetry and/orunidirectional currents may generate asymmetric ripples (e.g., the lunatemegaripples of Clifton (1976) and Hay and Mudge (2005)). However, on vastexpanses of the continental shelf where near-bed oscillatory motion is nearlysymmetric and unidirectional currents negligible (i.e., less than 5–10 cm/s; seeClifton 1976; Arnott and Southard 1990; Dumas et al. 2005), d0, Uo, and D50 arethe first-order controls on wave-ripple shape and size.

FIG. 2.— Ripple properties measured in this study. Ripple steepness (height/wavelength), ripple symmetry (left-flank length/right-flank length), and maximumflank slope angles were measured from the side-wall viewing area (see Fig. 5 fortraced photos). LWRs are defined as having wavelengths . 30 cm, whereas SWRshave wavelengths , 30 cm.

84 D.I. CUMMINGS ET AL. J S R

in the very fine sand runs, where substantial stress on the drivemechanism caused flow asymmetry to reach 10–15%. (The wave ripplesgenerated in these runs were consequently slightly asymmetric; seeTable 1.) Although flow asymmetry in general had no obvious effect onbed-form symmetry, it did cause the otherwise-symmetric wave ripples to

migrate in the direction of the shorter, faster stroke, especially in runswith higher oscillatory velocities, where migration rates reached severalcentimeters per minute. Sand was therefore gradually mobilized out of theviewing area, and had to be shovelled back several times over the courseof the experiments.

FIG. 3.— Race-track–style wave tunnel at theCoastal Hydraulics Laboratory, Queen’s Uni-versity, Canada. The side-wall viewing area isrelatively large (12 m long, 1 m high, and 0.5 mwide) and has windows on both sides. SeeBrebner and Riedel (1973) for details.

TABLE 1.—Experimental conditions and results.

Run

GrainSize

(mm)

Orbitaldiameter

(cm)

OscillatoryVelocity(cm/s)

Waveperiod

(s)

Bedconfigura-

tion*

Ripplewavelength1

(cm)

Rippleheight1

(cm)

Ripplesymme-

try1Ripple

steepness1

Flankshape inprofile*1

Slope ofleft

flank1(u)

Slope ofright flank1

(u)

Crestshape inprofile*

Planformmorpho-

logy

Wavelength/ orbital di-ameter (%)

S1R2 0.12 450 170 9 Plane bed – – – – – – – – – –S1R4 0.12 450 150 10 Plane bed – – – – – – – – – –S1R1 0.12 450 120 12 LWR 347 15 1.25 0.05 CV 5 6 R 2-D** 77S1R3 0.12 450 115 14 LWR 208 14 1.08 0.07 6 10 R 2-D** 46S2R5 0.12 250 130 6.5 Plane bed – – – – – – – – – –S2R4 0.12 250 110 8 LWR 155 9.4 1.25 0.06 CV 7 8 R 2.5-D 62S2R2 0.12 250 67 12 LWR and

SWRt91 8 1.01 0.1 CV, CC 15 11 R,S 3-D 36

9 0.75 1.28 0.08 – 9 11 – – 4S2R1 0.12 250 60 14 LWR and

SWR147 12 1 0.08 CC, CV 10 9 R,S 3-D 59

8 0.7 1.1 0.08 – 10 10 – 2-D 3S3R4 0.12 160 80 6.5 LWR 94 9 1.1 0.09 11 11 R,S 2.5-D 59S3R3 0.12 160 64 8 LWR and

SWRt97 9 1.67 0.06 CV, CC 9 12 S,R 2.5-D 60

8 0.4 1 0.05 – 5 5 – – 5S3R2 0.12 160 57 10 LWR and

SWR121 7 1.01 0.06 7 6 2.5-D 7610 0.8 1.1 0.07 – 9 8.6 – 2.5-D 6

S3R1 0.12 160 37 14 SWR 8 0.9 1.11 0.1 CV, CC 12 12 – 2.5-D 5S4R2 0.12 95 80 4.5 LWR 53 7 0.92 0.14 CV, CC 15 15 S 2.5-D 66S4R1 0.12 95 75 5.5 LWR and

SWRt63 8 0.94 0.12 F, CC 13 14 S 2.5-D 66

9 0.5 1.02 0.05 – 7 7 – – 9S4R3 0.12 95 60 6.5S5R1* 0.8 220 58 14S5R2 0.8 220 65 12 LWR 98 17 1.06 0.17 CC 19u 19 S 2-D 45S5R3 0.8 220 75 10 LWR 108 19 1.2 0.17 CC 19u 20 S 2-D 49S5R4 0.8 220 95 8 LWR 101 16 1.13 0.16 F, CC 17u 18 S, one R 2-D 46S5R5* 0.8 220 122 6.5S6R1 0.8 410 80 14 LWR 166 26 0.94 0.16 F 18u 17 S, one R 2-D 40S6R2 0.8 410 97 12 LWR 165 23 1.16 0.14 F, CV 15u 17 S 2-D 40S6R3 0.8 410 122 10 LWR 163 24 1.18 0.15 F, CV 15u 18 R 2-D 40S7R1 0.8 400 95 14 LWR 142 22 1.06 0.15 CV, CC 16u 17 S,R 2-D 36S7R2 0.8 400 125 8 Motor broke – – – – – – – – – –S8R1 0.8 150 20 14 NM – – – – – – – – – –S8R2 0.8 150 24 12 NM – – – – – – – – – –S8R3 0.8 150 37 9 LWR 56 10 1.18 0.18 CC 19u 21 S 2-D 37S8R4 0.8 150 70 5.5 LWR 53 8 1.16 0.16 CC 17u 18 S 2-D 35

* Key to acronyms: LWR, large wave ripples (wavelength . 30 cm); SWR, small wave ripples (wavelength , 15 cm); SWRt, small, superimposed wave ripples introughs of LWRs only; NM, no movement; CV, convex-up flanks; CC, concave-up flanks; F, flat flanks; R, rounded crests; S, sharp crests. Ripple symmetry wasmeasured by dividing the length of the left flank by that of the right flank, as measured from the sidewall viewing area. The shorter, faster stroke of the oscillation wasinvariably towards the right.

1 Average value for the given run.** Given the size of these ripples relative to the width of the wave tunnel, they appeared 2-D, but could have been 3-D.

WAVE RIPPLES AND GRAIN SIZE 85J S R

For each run, the oscillatory velocity was measured using an acousticDoppler velocimeter (ADV) positioned , 15 cm above the bed, and theorbital diameter was estimated visually by tracking neutrally buoyantparticles in the viewing area. Measurements of oscillatory velocity aretherefore believed to be accurate within several cm/s, whereas orbital-diameter estimates are less accurate, with an estimated error of up to 6 0.1d0.

BED CONFIGURATIONS

Depending on the hydraulic conditions and grain size, one of fiveequilibrium bed configurations was observed: (1) no movement, (2) smallwave ripples (SWRs), (3) small wave ripples superimposed on large waveripples (SWRs/LWRs), (4) large wave ripples (LWRs), or (5) a flat,horizontal bed (referred to here as oscillatory plane bed) (Figs. 5, 6;Table 1). The effects of Uo, d0, and D50 on SWRs and LWRs aresummarized in Figure 7.

No Movement

For coarse sand, and starting from an initially flat bed, the threshold ofsediment movement was breached somewhere between an oscillatoryvelocity of 24 cm/s (no movement) and 37 cm/s (2-D LWRs) (Fig. 5). In

very fine sand, the run with the lowest possible oscillatory velocity(37 cm/s) generated SWRs from an initially flat bed. The threshold ofsediment movement for very fine sand therefore lies somewhere below37 cm/s.

Small Wave Ripples (SWRs)

Small symmetric wave ripples (4 cm , lave , 26 cm; 0.2 cm ,

have , 3 cm) formed in very fine sand at low to moderate oscillatoryvelocities (37 cm/s , Uo , 75 cm/s) over a wide range of orbitaldiameters (95 cm , d0 , 250 cm) (Fig. 5). SWRs formed at the startof some of the coarse-sand runs at low oscillatory velocities but invariablybecame unstable with time and were replaced by LWRs (see also Lofquist1978), a transformation that may have been instigated by the progressivewinnowing of a several-millimeter thick fine-grained suspension-falloutlayer that inevitably accumulated between runs. SWRs did not form inruns with an orbital diameter of 450 cm, but this may not reflect an upperd0 limit to the occurrence of SWRs because oscillatory velocity may havebeen too high during these runs (Uo . 115 cm/s). Flow separated acrossSWRs, and flow reattachment in the lee of ripple crests was relativelygentle, with no significant upward injection of fluid and/or sediment intothe core of the flow.

Changes in orbital diameter did not obviously affect the size of SWRs.Rather, SWRs maintained average wavelengths of 10 cm (Fig. 8A) andaverage heights of 0.75 cm (Fig. 8B) irrespective of orbital diameter.However, SWRs decreased in height with increasing oscillatory velocity(Fig. 9). SWRs appeared 2-D to 2.5-D, but their crestal continuity wasnot measured systematically.

SWRs Superimposed on LWRs

SWRs coexisted with LWRs in very fine sand at moderate oscillatoryvelocities (57 cm/s , Uo , 75 cm/s) (Fig. 5). SWRs disappeared firstfrom LWR crests as oscillatory velocity was increased (Uo . 64 cm/s),then from LWR troughs when Uo . 80 cm/s.

Large Wave Ripples (LWRs)

Large symmetric wave ripples (55 cm , lave , 270 cm; 6 cm ,

have , 26 cm) formed at moderate to high oscillatory velocities (37 cm/s , Uo , 122 cm/s), in both very fine sand and coarse sand, at allorbital diameters investigated (95 cm , d0 , 450 cm).

When orbital diameter was increased, LWRs increased in size (Fig. 8)but did not obviously change in shape (Fig. 10). As a general rule, theirwavelengths scaled to roughly 50% of the orbital diameter, with slightlylower proportionalities for coarse sand (lave , 0.4d0) and slightly higherproportionalities for very fine sand (lave , 0.6d0) (Fig. 8A). LWRheights (h) scaled to roughly 5% of the orbital diameter, with lowerproportionalities for very fine sand (have 5 0.03–0.08d0) and slightlyhigher proportionalities for coarse sand (have 5 0.05–0.09d0) (Fig. 8B).

In coarse sand, LWRs were typically sharp-crested, concave-up tostraight-flanked, and steep (run-averaged flank slopes of 15–21u) andwere invariably 2-D at the scale of the tunnel. Under similar hydraulicconditions, LWRs in very fine sand had similar wavelengths, but weremuch more subdued (run-averaged flank slopes of 5–15u), were either 2-Dor 3-D, and were either sharp-crested or round-crested, commonly withconvex-up flanks (Figs. 11, 12, 13).

The effects of oscillatory velocity on LWR shape and size were not asobvious as the effects of grain size and orbital diameter. However, LWRheight did decrease with increasing oscillatory velocity (Figs. 14, 15),especially for very fine sand, with the most subdued LWRs occurring justbelow the transition to oscillatory plane bed. It is unclear whetherequivalent subdued LWRs are produced near the transition to plane bed

FIG. 4.— Grain-size distributions for the very fine sand (D50 5 0.12 mm) andcoarse sand (D50 5 0.8 mm) used in the study. The sands had the density ofstandard siliciclastic sand (2.65 g/cm3). They were obtained from aggregate pitsjust outside of Kingston that mine esker-associated subaqueous-outwash fans. Vf,f, m, c, and vc refer to very fine, fine, medium, coarse, and very coarse sand grainsizes. L and U refer to lower and upper divisions of each of thesesubclasses, respectively.

86 D.I. CUMMINGS ET AL. J S R

FIG. 5.—Phase diagrams for wave ripples generated in A) very fine sand and B) coarse sand under large orbital diameters (0.95–4.5 m) and moderately low to highoscillatory velocities (20–170 cm/s). The phase boundaries (horizontal lines) are solid where reasonably well constrained, dashed where extrapolated. The bed profilesshown are in general 12 m long and have no vertical exaggeration. They were traced from the viewing area.

WAVE RIPPLES AND GRAIN SIZE 87J S R

in coarse sand, because plane-bed conditions were not achieved in thisgrain size.

Flow separated over all LWRs. Over steep LWRs (i.e., LWRs in coarsesand and some LWRs in very fine sand at low Uo), flow-separation bubbleswere well developed, sediment-laden fluid was ejected violently up into thecore of the flow, and flow reattachment was vigorous. By contrast, oversubdued LWRs (LWRs in fine sand at high Uo), flow-separation bubbleswere flattened and flow reattachment was relatively gentle.

Oscillatory Plane Bed

Oscillatory plane bed was produced in very fine sand at high oscillatoryvelocities (Uo . 130 cm/s) (Fig. 5). The run with the next-lowestoscillatory velocity (Uo 5 120 cm/s) produced very subdued 3-D LWRs.

Oscillatory plane bed was not generated in runs that used coarse sandbecause sufficiently high oscillatory velocities could not be achieved.

DISCUSSION

The shape of LWRs generated in the experiments was stronglymodulated by grain size (Fig. 16). Fine-grained LWRs were commonlyhummocky (i.e., round crested, subdued and 3-D), whereas coarse-grained LWRs were invariably 2-D and almost always sharp crested. Thisappears to confirm Leckie’s hypothesis (1988) that fine-grained andcoarse-grained LWRs generated under large-scale oscillatory flow aremorphologically different. Whether fine-grained and coarse-grainedLWRs are genetically different is debatable, however, inasmuch as allLWRs generated in the experiments scaled strongly to orbital diameter.This suggests that they formed by a common mechanism related to thenear-bed fluid flow and sediment transport set up by the oscillatorymotion itself, an observation that has led previous authors to term similarbed forms oscillatory-current ripples (Southard et al. 1990) or orbital

ripples (Clifton 1976).

In addition to exerting an influence on the shape of LWRs, grain sizealso appeared to modulate LWR size. The wavelengths of fine-grainedLWRs scaled on average to 0.6d0, which is close to 0.65d0, the mostcommonly reported scaling ratio for orbital ripples (Miller and Komar1980; Southard et al. 1990; Wiberg and Harris 1994). Coarse-grainedLWRs, by contrast, scaled on average to , 0.4d0. Similar scaling ratioshave been reported from recent wave-tank experiments (T 5 4–6 s;d0 5 0.32–1.96 m), where ripples in fine sand (D50 5 0.162 mm) scaledto , 0.65d0 and ripples in medium sand (D50 5 0.349 mm) scaled to0.45d0 (Williams et al. 2004). If representative, these observations suggestthat coarser-grained orbital ripples are on average more closely spacedthan finer-grained orbital ripples generated under the same hydraulicconditions. It is unclear why this occurs, although it may be related to thegreater fall velocity of coarser sediment (reduced amount of time neededfor grains to settle, increased amount of time needed for grains to besuspended), or the different style of fluid-flow and sediment-transport setup by the steeper (coarser) versus more subdued (finer) wave ripples.

The SWRs generated in the experiments reported here are believed tobe genetically distinct from the LWRs. Unlike LWRs, SWRs were stableonly in very fine sand and at relatively low oscillatory velocities. Inaddition, SWRs were always associated with flow separation but not withviolent flow reattachment or strong upward ejection of fluid into the core

FIG. 6.— Histograms showing frequency distributions of A) crest-to-crestwavelength and B) crest-to-trough height of ripples observed in the experiments.Note that two wave-ripple populations can be distinguished, small wave ripples(SWRs) with wavelengths , 30 cm and heights typically , 1 cm (present in veryfine sand only), and large wave ripples (LWRs) with wavelengths between 0.35 and2.7 m and heights between 5 and 26 cm (present in both grain sizes; allobservations combined).

FIG. 7.—Average response of large wave ripples (LWRs) and small wave ripples (SWRs) to increases in orbital diameter, oscillatory velocity, and grain size. A largearrow indicates a pronounced response, whereas a small arrow indicates a more subtle response. The responses apply only to the grain sizes and range of hydraulicconditions investigated (D50 5 0.12 or 0.8 mm; 0.95 m , d0 , 4.5 m; 0.2 m/s , Uo , 1.7 m/s).

88 D.I. CUMMINGS ET AL. J S R

of the flow, and they lacked obvious scaling relationships with the larger-scale structure of the flow (i.e., the oscillations themselves). As such, it istempting to think of them as two-sided current ripples—they appeared toowe their existence to the current that reversed, not to the oscillationsthemselves. (However, SWRs decreased in height with increasing shearstress (oscillatory velocity), whereas current ripples may exhibit theopposite trend (Baas 1999).) Previous authors have referred to similarripples as reversing-current ripples (Southard et al. 1990) or anorbitalripples (Clifton 1976).

All LWRs in the experiments were orbital ripples, whereas all SWRswere anorbital ripples. Indeed, anorbital ripples in natural settings doappear to be invariably small and fine-grained (e.g., Hanes et al. 2001).However, the size range of orbital ripples in natural settings overlaps thatof anorbital ripples, as orbital ripples range in wavelength from severalcentimeters (Evans 1941) to several meters (Cacchionne et al. 1984;Forbes and Boyd 1987; Traykovski et al. 1999; Yang et al. 2006)depending on the orbital diameter (and, as argued above, grain size)under which they form. As such, in fine-grained successions where both

FIG. 8.— Plots of orbital diameter versus A) ripple wavelength and B) height.Note that the wavelength of large wave ripples (LWRs) scale to , 50% of theorbital diameter, whereas the small wave ripples (SWRs) retained the samewavelength irrespective of orbital diameter.

FIG. 9.—Plot showing decrease in SWR steepness (i.e., height/wavelength) withincreasing oscillatory velocity. All of the runs plotted in this figure were conductedwith an orbital diameter of 1.6 meters and used very fine sand. SWR wavelengthsremained nearly constant on average (, 9 cm) in this series of runs, but theirheights decreased on average from 0.9 cm (S3R1) to 0.4 cm (S3R3) as oscillatoryvelocity was increased. Ripple-profile triangles accurately represent ripplesteepness but not ripple shape.

FIG. 10.—Change in LWR profile with increasing orbital diameter at constantgrain size and nearly constant oscillatory velocity. A) LWRs generated in coarsesand. Note increase of LWR size with orbital diameter. LWRs in all three runs are2-D. These three runs were chosen because they had the closest oscillatoryvelocities to one another (oscillatory velocity was 70 cm/s in S8R4, 75 cm/s inS5R3, and 80 cm/s in S6R1). B) LWRs generated in very fine sand. Again, notethat an increase in orbital diameter causes LWR size to increase. The asymmetry ofripples in S1R3 is due to asymmetry in the oscillatory flow that developedinherently in the wave tunnel at higher oscillatory velocities (although thesymmetry of ripples in other high-velocity runs seems to have been less affected).As in Part A, the three runs in Part B were chosen because they had the nearestpossible oscillatory velocities (oscillatory velocity was 80 cm/s in S3R4, 110 cm/s inS2R4, and 115 cm/s in S1R3). See Table 1 for details.

WAVE RIPPLES AND GRAIN SIZE 89J S R

types of ripples may be present, only LWRs should be used to inferpaleoenvironmental information such as wave size and basin size, in thatSWRs in fine sand may be generated by both large waves (as anorbitalripples) or by small waves (as orbital ripples). By contrast, all coarse-grained wave ripples appear to scale to orbital diameter, and thereforecan be used to reconstruct wave size. Several detailed methods ofextracting paleohydraulic information from wave ripples have beenoutlined by previous authors (Komar 1974; Clifton 1976; Clifton andDingler 1984). As a simple rule of thumb, if symmetric ripples (fine- orcoarse-grained) with wavelengths in excess of , 75 cm are identified in a

FIG. 11.—Change in LWR profile with increasing grain size at nearly constantorbital diameter and nearly constant oscillatory velocity (S5R2: d0 5 2.2 m,Uo 5 65 cm/s; S2R1: d0 5 2.5 m, Uo 5 60 cm/s). Compared to the LWRsgenerated in very fine sand, LWRs generated in the coarse sand were steeper,sharper-crested, lacked superimposed SWRs, were 2-D at the scale of the tunnel,and had a shorter wavelength. See Figure 13 for photos of wave ripples from thesetwo runs.

FIG. 12.—Average slope of the flanks of the large wave ripples (LWRs) for eachrun plotted as a function of grain size. Note that the coarse-grained LWRs hadsteeper flanks (. 15u) than the fine-grained LRWs (, 15u). (It is important tonote that the LWR flank-slope values in this diagram are the averaged values foreach run. If the slope of each individual ripple generated in the experiments wasplotted, this plot would show greater variability and more overlap.) Ripple-profiletriangles accurately represent ripple steepness but not ripple shape.

FIG. 13.—Representative photos of the LWRs generated in A) very fine sand and B) coarse sand. (Note that SWRs are superimposed on LWR in Part A only.) TheLWRs in Parts A and B were generated under similar hydraulic conditions—they are from the two runs depicted in Figure 11 (S2R1: D50 5 0.12 mm, d0 5 2.5 m,Uo 5 60 cm/s, T 5 14 s; S5R2: D50 5 0.75 mm, d0 5 2.2 m, Uo 5 65 cm/s, T 5 12 s). Note that the very-fine-sand LWR in Part A is round-crested, subdued, andthree dimensional, and has superimposed SWRs, whereas the coarse-sand LWR in Part B is sharp-crested, steep and two-dimensional, and lacks superimposed SWRs.

FIG. 14.—Change in LWR profile with increasing oscillatory velocity in A) veryfine sand and B) coarse sand. Orbital diameter is held constant in both examples (itis 2.5 m in S2R2 and S2R4 and 4.1 m in S6R1 and S6R2). Note that the effects ofan increase in oscillatory velocity on LWR size and shape are more subtle thanthose caused by a change in orbital diameter (Fig. 6) and grain size (Fig. 8);however, the data suggest that LWRs do decrease slightly in steepness withincreasing oscillatory velocity (see Fig. 15).

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stratigraphic unit, one can conclude with relative confidence that theyformed in a fetch-unrestricted water body, such as an open-oceancontinental shelf, because the requisite large, symmetric near-bedoscillations tend not to occur beneath smaller waves inherent to fetch-limited settings such as estuaries, rivers and most lakes (Komar 1974;Clifton 1976; US Army Corps of Engineers 2002; Goda 2003).

Where preserved, cross stratification generated in the experiments byfine-grained and coarse-grained LWRs differed substantially (Fig. 17). Asmentioned previously, a slight flow asymmetry (less than several percent)caused LWRs to migrate slowly (several millimeters to several centimetersper minute) in one direction in most runs; similar behaviour is likelycommon for wave ripples beneath shoaling waves (e.g., Clifton 1976;Traykovski et al. 1999) and ripples generated by purely oscillatory wavemotion with a very weak superimposed unidirectional current (Arnottand Southard 1990; Dumas et al. 2005). As a result, the stratificationwithin the LWRs in very fine sand resembled anisotropic, low-angle (5–15u) hummocky cross stratification (e.g., Nottvedt and Kreisa 1987;Dumas and Arnott 2006), whereas stratification within the LWRs incoarse sand resembled dune cross stratification because the set thicknesspotentially exceeded 5 cm and the dip angle was high (15–21u). Theseresults suggest that the deposits formed by coarse-grained LWRs could bemisinterpreted as having been formed by dunes in the absence ofinformation on the external shape of the bed forms. In such cases, caremust be taken when interpreting the shallow-marine stratigraphic record:vertical trends in the type of cross stratification in a given succession maysimply reflect grain-size change, and not necessarily a change in theprevailing hydraulic conditions (e.g., Leckie 1988; Cheel and Leckie 1992;Yoshida et al. 2007).

FIG. 15.— Plots showing decrease in LWR steepness (i.e., height/wavelength)with increase of oscillatory velocity (and orbital diameter) for runs conducted in A)very fine sand and B) coarse sand. Although data are limited, the trend appears tobe slightly more pronounced in fine sand than in coarse sand. Ripple-profiletriangles accurately represent ripple steepness but not ripple shape.

FIG. 16.—Simplified cartoon showing succes-sion of equilibrium bed configurations generatedin very fine sand and coarse sand underincreasing oscillatory velocity, for moderate tolarge-sized waves (i.e., orbital diameter . 1 m).Note that the transition between small anorbitalripples and large orbital ripples in very fine sandis in fact gradual (not shown), with smallanorbital ripples occurring first on large orbitalripples before eventually disappearing. Thetransition from large orbital ripples to plane bed,as plotted, is completely conceptual, becauseplane-bed conditions were not achieved in thecoarse-sand runs. Further experiments are re-quired to determine the nature of this and othertransitions between equilibrium bed configura-tions (cf. fig. 3–16 in Harms et al. 1982).

FIG. 17.— Stratification traced from side-wall photos of fine-grained andcoarse-grained LWRs. Note that cross-strata produced by the ripple in very finesand are low-angle (, 5u) and convex-up, whereas those produced by the ripple incoarse sand are high-angle (, 25u) and concave-up. Unidirectional dip of cross-strata is due to slight flow asymmetry (less than a few percent), which in generalhad no obvious affect on bed-form symmetry but caused them to migrate slowly inone direction (to the right) in most runs. S1R1 and S5R2 refer to run numbers (seeTable 1 for details). In nature, a similar translation of the bed form could beproduced by the weak unidirectional currents that commonly accompany storms(Dumas et al. 2005) and might be termed anisotropic HCS (cf. Nottvedt andKreisa 1987).

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CONCLUSION

The results of our wave-tunnel experiments suggest that grain sizeexerts a first-order control on the geometry of ripples generated by largewaves. Two main differences were observed in the equilibrium bedconfigurations generated in very fine and coarse sand. First, smallanorbital ripples (wavelengths , 10 cm, heights 1–2 cm) formed andremained stable only in very fine sand, just above the threshold ofsediment movement. Second, large orbital ripples (wavelengths 50–350 cm, heights 10–25 cm) formed and remained stable in both very fineand coarse sand and exhibited similar wavelengths under similarhydraulic conditions. However, their shapes differed substantially as afunction of grain size: large ripples in coarse sand were steep, 2-D, andsharp-crested, whereas large ripples in very fine sand were subdued, 2-Dor 3-D, and round- or sharp-crested. These results appear to confirm thehypothesis advanced by previous authors that coarse- and fine-grainedlarge wave ripples have distinctly different shapes and, by extension,produce distinctly different styles of cross stratification (Leckie 1988;Cheel and Leckie 1992), at least over the range of variables investigatedhere. One possibility that the experiments did not rule out is that largehummocky ripples may form in coarse sediment at very high oscillatoryvelocities. This is because a significant amount of phase space existsbetween 125 cm/s, the highest oscillatory velocity tested in the coarse-sand runs, and , 200 cm/s, the oscillatory velocity at which ripples on acoarse-sand bed become planed off (Clifton 1976). Further experimentsare required to resolve this question. Nevertheless, given the results of thestudy, and taking into account data from modern and ancientenvironments (e.g., Cacchionne et al. 1984; Forbes and Boyd 1987;Leckie 1988; Traykovski et al. 1999; Cummings and Arnott 2005; Yang etal. 2006), it seems likely that the stratigraphic signature of large waves istypically different in fine-grained and coarse-grained sediment.

ACKNOWLEDGMENTS

The research was carried out when the first two authors were postdoctoralfellows at Queen’s University. The wave tunnel was graciously made availableto us by Kevin Hall and William Kamphuis of the Department of CivilEngineering, Queen’s University. Stuart Seabrook, the Coastal Lab manager,facilitated access to the premises and guided us through the use of the wavetunnel. Paul Thrasher coordinated several major repairs to the motor thatallowed us to complete our experiments. Constructive scientific reviews byPatricia Wiberg, Dale Leckie, and Paul Myrow and a thorough copy edit byJohn Southard helped improve the final manuscript. RWD acknowledges thecontinued support of the Natural Sciences and Engineering Research Councilof Canada (NSERC) for his research.

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Received 26 November 2007; accepted 10 August 2008.

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