Unsteadiness of bivalve clam jet flow according to ...

AQUATIC BIOLOGYAquat Biol

Vol. 13: 175–191, 2011doi: 10.3354/ab00364

Published online September 6

INTRODUCTION

The predator–prey relationships between bivalveclams Mercenaria mercenaria and predators such asblue crabs Callinectes sapidus and knobbed whelksBusycon carica are influenced by the filter-feedingbehavior of clams (Smee & Weissburg 2006). As thewater passes through the filter-feeding clam, wastemetabolites are picked up and carried out throughthe excurrent siphon in a jet-like flow. The releasedmetabolites are transported downstream with theambient flow and create the chemical plume thatmay be tracked by predators. This predator–preyinteraction is mediated by 3 distinct phases: genera-tion of the chemical signal, transport of the chemical

downstream, and acquisition of the chemical infor-mation. Much of the current literature on this preda-tor–prey relationship is focused on the acquisition ofthe chemical signal and the behavioral reaction bythe predator (e.g. Weissburg & Zimmer-Faust 1993,Jackson et al. 2007, Page et al. 2011a,b). In contrast,the goal of the current study was to quantify theexcurrent siphon flow of the bivalve clam M. merce-naria. In particular, this study took an important steptoward understanding how the excurrent jet velocitybehavior was modified by environmental conditions.

We focused on the variation of the excurrent flowof hard clams in response to several environmentalparameters, including bulk mean crossflow velocity,density of clam patch, and size of the clam. The char-

© Inter-Research 2011 · www.int-res.com*Email: [email protected]

Unsteadiness of bivalve clam jet flow according toenvironmental conditions

S. K. Delavan1,2,*, D. R. Webster1

1School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0355, USA

2Present address: Department of Civil and Natural Resources Engineering, University of Canterbury, Christchurch 8140, New Zealand

ABSTRACT: To determine whether hard clams Mercenaria mercenaria alter excurrent jet velocityas a function of environmental factors, this laboratory study quantified the excurrent jet velocity asa function of bulk mean crossflow velocity, density of clam patch, and clam size. The excurrent ve-locity was measured via the non-intrusive particle image velocimetry technique. The flow and un-steady patterns in the time records of vertical velocity near the tip of the excurrent siphon were an-alyzed by calculating the mean, variance, power spectral density, fractal dimension, lacunarity,and mean jet-to-crossflow ratio. The results revealed that clams vary their excurrent flow charac-teristics according to bulk mean crossflow velocity; in particular, the texture of the time record ofvelocity varied. Further, the jet-to-crossflow velocity ratio was larger for smaller clams, and the re-sponse of clams to the density of the clam patch was dependent on the size of the animal. These ob-served behaviors may impact the predation success of blue crabs Callinectes sapidus and knobbedwhelks Busycon carica under various environmental conditions. In this context, the resultsindicated that blue crabs dominate the predator–prey system because of the dependence on clamsize and bulk mean crossflow velocity. Alternatively, the varying clam excurrent siphon velocity be -havior may provide hydrodynamic signaling of the clam patch recruitment status to settling larvae.

KEY WORDS: Predator–prey · Olfactory predation · Jets-in-crossflow · Bivalve · Non-consumptivepredator effects · Lacunarity

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Aquat Biol 13: 175–191, 2011

acteristics of the excurrent flow as a function of bulkmean crossflow velocity and clam size are of interestbecause the predators of this system, blue crabs andknobbed whelks, both consume clams and use ol -factory navigation as a means of locating prey, butthe turbulence regimes in which they are successfulare highly disparate. Blue crabs are less successfulpredators during highly turbulent hydrodynamicconditions (Jackson et al. 2007). In contrast, knobbedwhelks are successful in highly turbulent regimes(Ferner & Weissburg 2005). Also, blue crabs preferclams of a small size range despite the fact that theycan consume prey over a wide size range (Micheli1995). Therefore, as clams increase in size, they be -come less susceptible to predation by blue crabswhile maintaining their susceptibility to whelk pre-dation. Thus, there may be alternate strategies forpredator avoidance depending on the size of theclams and the turbulence regime of the environmentin which they live.

The influence of the density of the clam patch wasalso of interest because there may be predator avoid-ance strategies depending on the proximity of con-specifics. High-density patches may appear as onelarge, hard to eat prey to blue crabs, and small clamsmay have higher survival rates in these patches.Also, greater density could mean that loss of only afew clams out of the group minimally influences the overall population. Alternatively, juveniles may be atgreater risk when settling in established clam beds.Greater clam densities may release a larger flux ofodorant and, therefore, be more attractive to poten-tial predators. In this context, there may be an advan-tage to large nearest neighbor distances to decreasethe odorant release flux.

It was also relevant to consider clam excurrentflow as a jet-in-crossflow), defined as a jet of fluidexiting an orifice in a direction perpendicular to thedirection of the surrounding fluid motion that typi-cally consists of a boundary layer flow along the solidsurface containing the orifice, and to quantify the jetvelocity characteristics within the context of previousjet-in-crossflow studies. Monismith et al. (1990) andCrimaldi et al. (2007) found that clam mimic jetsaltered the momentum distribution in the bound -ary layer in a manner similar to that seen in jet-in-crossflow studies (e.g. Andreopoulos & Rodi 1984).O’Riordan (1993) and van Duren et al. (2006) foundsimilar boundary layer alterations with actual clamand mussel excurrent jets, respectively, in a labora-tory setting. Over a wide range of jet and boundarylayer Reynolds numbers, the jet-to-crossflow velocityratio was the dominant indicator of the jet/crossflow

interaction (Andreopoulos & Rodi 1984, Morton &Ibbet son 1996, Sau & Mahesh 2008). Hence, wesought to quantify the jet-to-crossflow velocity ratiofor the clam excurrent siphon as a function of envi-ronmental parameters.

The overall objective of this study was to quantifythe clam excurrent jet vertical velocity unsteadinessaccording to external environmental cues. Labora-tory flume experiments captured time records ofclam jet vertical velocity for 4 bulk mean crossflowvelocity values, 2 clam size ranges, and 2 clam near-est neighbor distances.

MATERIALS AND METHODS

Animal collection and storage

Clams that were imported from Florida were pur-chased from a local supplier near Atlanta, Georgia,USA. Clams were housed in an aquarium filled withartificial sea water with salinity between 28 and 35ppt. Sand covered the bottom of the aquarium toallow clams to acclimate to laboratory conditions andbury themselves. The aquarium temperature wasmaintained at room temperature (roughly 22°C), andthe pH was ~8.0. Clams were fed every other dayduring data collection periods with a commerciallyavailable slurry of live phytoplankton (DT’s LiveMarine Phytoplankton) purchased from local aquar-ium/pet stores.

Flow facility

The flow facility was an artificial seawater flumelocated in the Environmental Fluid Mechanics Labo-ratory at the Georgia Institute of Technology (Fig. 1).This biological-grade flume was 0.76 m wide and13.5 m long with a level bed. The bed was coveredwith a thin layer of sand with a median grain dia-meter of d50 = 1.1 mm. The side walls of the flumewere constructed of acrylic for optical transparency.A centrifugal pump recirculated artificial seawaterthrough the flume. The flow depth was controlled bythe height of a downstream sharp-edged weir, andthe flow rate was calculated via the Kindsvater-Carter equation for rectangular weirs (Kindsvater &Carter 1957). The roughness Reynolds number (Re*= ksu*/ν), where ks is the effective sand roughnessheight, u* is the wall shear velocity, and ν is the fluidviscosity, was less than 10 for each flow rate usedhere.

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The test section was located 6.2 m downstreamof the flume entrance. A 7.8 cm (deep) by 45.7 cm(wide) by 118.7 cm (long) false bottom section filledwith sand was located in the center of the test sec-tion, and the sand depth for the remainder of theflume was 2.9 cm. The false bottom section allowedfor clams to bury themselves within the sediment andfeed naturally.

Velocity measurements

PIV equipment

Particle image velocimetry (PIV) was used to quan-tify the clam excurrent velocity. PIV is a non-intru-sive means of determining planar velocity fields inmoving fluids. This method uses a laser sheet to illu-minate tiny seeding particles in a plane while a cam-era captures images of the particles (Fig. 1). Sequen-tial PIV images are used to determine the particledisplacement and velocity in the illuminated plane.Previously, the PIV technique has been used to deter-mine the flow fields around organisms and theirappendages (e.g. Mead & Koehl 2000, Catton et al.2007, Peng et al. 2007).

The laser was a double head Solo III manufac-tured by New Wave Research with a wavelength of532 nm, 50 mJ of energy per laser pulse, and anexiting beam diameter of 4 mm. The beam passedthrough a system of lenses that form a planar lasersheet (specifically, a symmetrical convex lens of0.5 m focal length and a planar-concave cylindricallens with a 19 mm focal length). The laser wasmounted above the flume, and the laser sheetpassed through the fluid surface of the flumeabove the excurrent siphons of the feeding bi -valves (Fig. 1). The water surface was smooth andtemporally constant, which led to minimal variationof light transmittance.

Particles of titanium dioxide (<5 μm diameter)were suspended in the fluid, moved with the flow,and were illuminated in the laser sheet. Many typesof seeding particles were tested to determine whichwould be most useful in these experiments. Clamsare filter feeders and remove particles from the flowof certain size ranges and organic content (Troostet al. 2009). The following types of seeding particleswere tested in this study: corn starch, kaolin, tita-nium dioxide, and several types of glass balls. Tita-nium dioxide particles resulted in a good balancebetween the number of particles passing through theclam and suitable reflection of the laser light for cam-era visualization. Titanium dioxide was also used byFrank et al. (2008) in their clam jet PIV experiments,and the particles did not appear to influence the clambehaviorally.

Images of the illuminated particles were capturedon a monochrome Kodak Megaplus camera (modelES 1.0) with a dual channel 8-bit digital output anda charged coupled device (CCD) sensor array. Thecamera used a Nikon MicroNikkor lens with a 60mm focal length. Both the laser and camera weretriggered by a precision pulse generator (BerkeleyNucleo nics model 500D). The delay between imagesin each pair was 10 ms, and image pairs were cap-tured at a frequency of 10 Hz. An individual imagerequired roughly 1 Mb of hard drive space and theimages were stored on a hard drive array usingVideo Savant software (IO Industries). A typicalimage sequence file used roughly 4.6 Gb of storagedepending on the number of images collected. Anerror propagation analysis was completed and theuncertainty in the velocity measurements was esti-mated as 1.0 mm s–1, which was roughly 2% of themeasured mean velocity values. Since velocity fluc-tuations are on the same order as the mean values,the uncertainty in the velocity measurements wasquite small.

177

Fig. 1. Schematic of the laboratory seawater flume and set-up for the particle image velocimetry (PIV) system. Clamsburied in sand sediment in a false bottom section that was7.8 cm deep, whereas the sediment in the majority of theflume bed was 2.9 cm deep. The Nd:YAG laser was locatedabove the flume and was pointed downward. The PIV cam-era was located beside the flume and viewed the measure-

ment section through the acrylic side wall. t = time

Aquat Biol 13: 175–191, 2011

PIV analysis

The PIV algorithm determined the fluid velocity atdiscrete points in the images and was written byDasi (2004) based on several earlier PIV algorithmsincluding those by Gui & Wereley (2002) and Were-ley & Meinhart (2001). Details of the algorithm areprovided by Dasi (2004) and are summarized here.First, a background image file was created for theeven and odd images of the pairs. The backgroundimage was subtracted from the individual images inorder to increase the contrast of the particles. Theimages were then spatially divided into 32 × 32 pixelinterrogation bins, and a cross-correlation analysiswas performed between the first and second imagein the pair. A Gaussian peak fit analysis was per-formed on the cross-correlation data to determine thedisplacement vector between images. In a secondpass, the interrogation bins in the first and secondimage were shifted by half of the displacement esti-mate backwards and forwards, respectively, to ‘cen-ter’ the interrogation bin region in the individualimage. The correlation analysis was repeated and anew estimate of the displacement vector was calcu-lated. The centering process was repeated until theinterrogation bin position correction was less than0.005 pixels. The displacement vectors were thendivided by the delay period between laser pulses(10 ms) to yield the velocity vector. The velocity fieldscreated by the cross-correlation analysis contained afew bad vectors associated with the edges of theimage or noise. The bad vectors were removed via atemporal filtering procedure. The filter assumes aGaussian distribution for the magnitudes of thevelocity vectors and removes samples that had adeviation greater than the threshold deviation (typi-cally 3 to 4 times the standard deviation). The filterprocedure was repeated until the stray vectors wereremoved.

Data collection procedure

Clams of the desired size range were placed on thesediment of the flume false bottom section withdesired nearest neighbor distances and allowed tobury themselves under low flow conditions. The clambehavioral response to the laser light was minimal(based on >50 h of laboratory observations), whichalso agreed with the observations of Frank et al.(2008). For an individual clam (see numbered clamsin Table 1), data were collected for 225 s for a ran-domly chosen bulk mean crossflow velocity value.

The bulk mean velocity in the flume was changed toanother randomly chosen target velocity value afterthe first data collection was complete. This wasrepeated until the organism had experienced all tar-geted bulk mean crossflow velocity values. Duringcol lection, events such as siphon movement and or -ganism interference were noted so that those events

178

Clam Length U v (mm s–1)(cm) (cm s–1) NND = 3 cm NND = 9 cm

ndNND = 0.62 ndNND = 1.85

1 4.7 0.55 3.19 ± 3.49 3.11±2.331.20 4.50±8.27 3.57±3.951.98 5.65±3.67 8.20±8.452.86 2.15±3.65 2.83±2.03

2 5.2 0.55 4.15±3.78 10.46±5.481.20 0.89±0.93 4.48±7.011.98 0.79±1.33 4.62±2.692.86 1.68±5.46 3.30±7.53

3 4.9 0.55 1.99±2.15 5.23±5.361.20 4.39±2.81 1.62±2.641.98 1.79±1.35 0.64±4.752.86 1.62±2.09 1.31±2.55

4 4.6 0.55 4.88±2.73 3.65±4.441.20 6.97±2.94 8.05±11.351.98 2.56±1.92 4.11±6.552.86 2.55±2.22 0.36±1.81

5 4.9 0.55 7.65±3.78 3.26±1.751.20 2.45±4.19 3.08±4.411.98 2.04±2.74 2.98±2.122.86 0.52±1.84 2.63±2.09

Clam Length U v (mm s–1)(cm) (cm s–1) NND = 3 cm NND = 9 cm

ndNND = 0.41 ndNND = 1.23

6 7.3 0.55 2.33±1.22 1.58±1.671.20 0.80±1.16 1.66±2.131.98 1.47±2.08 2.12±3.392.86 0.90±2.01 4.70±6.19

7 7.5 0.55 3.83±3.69 2.61±3.541.20 3.33±2.36 2.34±3.151.98 4.20±7.43 0.99±2.202.86 3.17±10.64 2.06±3.66

8 6.9 0.55 3.26±2.81 1.83±9.691.20 4.95±11.63 2.61±2.521.98 5.83±2.14 1.90±10.852.86 6.19±7.13 5.40±5.60

9 8.6 0.55 1.94±2.25 5.20±2.461.20 2.09±1.84 3.24±4.231.98 3.17±1.51 1.65±3.082.86 5.17±5.27 1.12±4.16

Table 1. Mercenaria mercenaria. Mean ± SD of the verticalvelocity (v, mm s–1) in the clam excurrent jet. The table reports data for varying nearest neighbor distance(NND), non-dimensional NND (ndNND), bulk mean cross-

flow velocity (U, cm s–1), and clam size class

Delavan & Webster: Bivalve clam jet flow

could be removed from the time record analysis.Note that suspended food particles were not intro-duced into the flume because clams were ob servedto ini tiate pumping in response to a moving cross-current.

Clam size and nearest neighbor distance

The experimental parameters and the individualclams that were used are given in Table 1. PIVimages were collected for a plane that bisectedthe clam excurrent siphon for clams of 2 size ranges,4.86 ± 0.22 cm and 7.32 ± 0.32 cm, clam plots with 2nearest neighbor distances, 3 and 9 cm, and 4 bulkmean crossflow velocity values, 0.55, 1.2, 1.98, and2.86 cm s–1. The selected nearest neighbor distanceswere consistent with those observed in the field, andin addition there was evidence of differences inclam repositioning behavior for nearest neighbor dis-tances in this range (Wilson 2011). Clams may altertheir pumping behavior according to their proximityto other clams because of the potential for refiltrationof fluid or the additive predation potential with thedownstream chemical plume. Also, juvenile or smallclams have greater predation pressure from bluecrabs, which may influence their feeding behavior.Finally, since predator success is depen-dent on hydro dynamic conditions, preybehavior may also be de pendent onhydrodynamic conditions. The 4 bulkmean crossflow velocity values chosenwere within the velocity ranges experi-enced by clams in field conditions andwere small enough to allow visual loca-tion of the clam jet in the PIV images.

After time records were recorded forthe clams in this experiment, the near-est neighbor distances were alteredand the clams were allowed to reburythemselves. The velocity measure-ments were repeated for varying bulkmean crossflow velocity treatments(again in a random order).

Control data sets

Three types of control data sets werecollected in the laboratory flume forcomparison with the above data sets.For each control case, PIV measure-ments were collected for each of the 4

bulk mean crossflow velocity values reported above.First, a control data set was collected above the clamplot without clams present to quantify the effects ofthe bumps and pockets in the sediment that were cre-ated during the clam burying process. Second, PIVimages were captured above an empty clam shell tosimulate the effects of a non-pumping clam. Third, 2data sets were collected for a man-made vertical jet(diameter of 0.95 cm) with 2 jet exit flow rates, 0.467cm3 s–1 and 0.0 cm3 s–1. The mimic clam siphon (plastictubing) extended 0.75 cm into the water column,which was a similar height to many of the clamsiphons in the current study. For the case with a non-0flow, the flow rate was specified such that the jetReynolds number value for the jet mimic flow waswithin the range of those collected for the clam jets.The clam mimic case without jet flow gave the influ-ence of the physical presence of the jet siphon.

Velocity time record extraction

The sequence of velocity vectors for 1 interrogationbin was extracted to create a velocity time record fora point in the flow field. A point was chosen to corre-spond to the excurrent jet region of the flow in orderto extract a velocity time record for the clam siphon

179

Fig. 2. Mercenaria mercenaria. Example instantaneous velocity vector field fora roughly 5 cm square plane bisecting a clam excurrent jet for the case withU = 0.55 cm s–1, clam length = 4.9 cm, and a nearest neighbor distance of 9 cm(clam no. 5 listed in Table 1). The vertical excurrent jet is revealed by the red

contours on the left side of the image. U = bulk mean crossflow velocity

Aquat Biol 13: 175–191, 2011

vertical velocity (see example in Fig. 2). The pointchosen varied according to the siphon location, siphonheight, ambient velocity, and the presence of suffi-cient numbers of seeding particles, hence the extrac-tion process required considerable manual observa-tion of the images. Clams move their siphons whilefeeding by changing the height, width, and direction;they even close their siphons and open them againon a frequent basis (Tammes & Dral 1956). Also, forlarger ambient flow velocities, visually locating thesiphon jet within the flow field became increasinglydifficult. Therefore, the location of the extractionpoint depended on the individual organism and timerecord. There was little evidence that a systematic(i.e. programmable) method of determining an extrac -tion point in the flow would give consistent results forthis highly variable biological system.

The vertical velocity component of the jet velocitytime record was chosen to represent the clam excur-rent jet velocities. Employing the vertical componentof the velocity provided a consistent representation ofthe fluctuations in the total excurrent signal, helpedremove errors associated with the changes in excur-rent siphon angle, and minimized the direct influenceof the horizontal bulk flow in the measurements.

During resting periods, when the clam closed theexcurrent siphon, the velocity time record did notprovide velocities associated with the excurrent. Themeasured vertical velocity during the resting periodswas due to the ambient flow, and these segmentswere removed from the time record analysis. Further,recorded values were removed from the velocity timerecord when the researcher could not identify thelocation of the excurrent jet. This occurred moreoften during larger ambient flow treatments. In otherinstances, the presence of feces or pseudo-feces inter -fered with the seeding particle recognition by thePIV code. With all of these situations and behaviorsremoved from the time record, the remaining datawere a reliable capture of clam excurrent velocitybehavior.

Time record analyses

Spectral analysis

Spectral analysis was employed to evaluate whetherthe time records of excurrent velocity possessed periodicity. Plotting the spectrum versus frequencyrevealed the relative amount of the time record vari-ance that could have been explained by a periodicityat a particular frequency. The spectral analysis did

not reveal any dominant frequencies and will not bediscussed further, other than to conclude that thetime records of clam excurrent vertical velocitylacked a dominant periodic variation.

Fractal analysis

Fractal analysis was used to quantify the randomnature of the time record of excurrent velocity as firstproposed by Hurst et al. (1947), quantified by Man-delbrot & Van Ness (1968), and simplified by Fan etal. (1990). In the case of time record analysis, a fractalanalysis yields a fractal dimension for the record be-tween 1 and 2, with increasing values correspondingto a more space-filling record. As the value of thefractal dimension approaches 1.5 from above or be-low, the time record becomes more random as it moreclosely resembles fractional Brownian motion. Incases where the calculated fractal dimension value isbetween 1 and 1.5, the time record can be consideredcorrelated. In other words, one value of velocity is followed closely by a similar value of velocity. As thefractal dimension increases from 1 and approaches avalue of 1.5, the velocity time record values becomeless correlated and more random. On the other hand,when fractal dimension values are between 1.5 and 2,the velocity time record is considered anti-correlated.In an anti-correlated time record, one value of veloc -ity is followed by a dissimilar value of velocity. Themost highly anti-correlated time records have fractaldimension values close to 2 with more random veloc-ity values as the fractal dimension approaches 1.5.

Here, the fractal dimension of the time series wascalculated to evaluate whether the nature of the flowunsteadiness varied under varying environmentalconditions. Estimates of the fractal dimension wereaveraged over the ensemble of time records to yieldan ensemble averaged value of fractal dimension,dfl, for each treatment case. Hurst’s rescaled rangeanalysis was employed, yielding values of the Hurstexponent, H. The H exponent is related to the fractaldimension:

dfl = 2 – H (1)

Random walk or fractional Brownian motion hastime record values with ‘jumps’ or ‘step sizes’ withmagnitudes corresponding to Gaussian white noise,and the Hurst’s rescaled range analysis is a measureof the randomness of the differences in the values ofthe time record. Let B(t) be a time record of equally-spaced data (in this case, a clam jet velocity timerecord). The time record of step sizes X(t) is defined

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Delavan & Webster: Bivalve clam jet flow

by X(0) = 0 and X(t) = [B(t) – B(t–dt)], where dt is thetime step between image pairs. c(t,u) is the cumula-tive departure of X(t + y) from the mean, �X(t)�s, forthe sub-record:

(2)

where s is the time lag, u = 1,2,. . ., s, and y is a timevalue from 1 to u. The sample range of X(t) for lag sis:

(3)

and the sample variance of X(t) is:

(4)

giving the scaling relationship (Fan et al. 1990):

(5)

In practice, H was calculated via Eq. (5) using the

slope of a least squares regression of a plot of

versus the time lag, s (on log–log axes). The fractaldimension of the time series was then determinedusing Eq. (1).

Lacunarity analysis

Lacunarity analysis was employed to quantify the‘look’ of the distribution or quantify the size and loca-tion of the ‘space’ between values of the velocity.While the fractal dimension was considered a mea-sure of how much space was filled or the amount of‘mass’ within a geometric space, lacunarity was ameasure of how the space was filled with that mass.In the current work, lacunarity analysis was em -ployed because some time records had similar fractaldimensions, while they were quite distinct visually.

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X t u X t su

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R t sS t s

sH( , )( , )

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R t sS t s

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R t s u s c t u u s c t u( , ) max ( , ) min ( , )= < ≤ − < ≤0 0

181

Fig. 3. Mercenaria mercenaria. Example velocity time records and lacunarity curves. (a) Time record of vertical velocity inthe excurrent jet, and (c) corresponding lacunarity curve, for clam with U = 0.55 cm s–1, clam length = 4.9 cm, and a nearestneighbor distance (NND) of 9 cm (clam no. 5 listed in Table 1); fractal dimension = 1.77. (b) Time record, and (d) corresponding

lacunarity curve, for the same clam and NND but with U = 1.2 cm s–1; fractal dimension = 1.78

Aquat Biol 13: 175–191, 2011

Lacunarity is a means of quantifying the ‘texture’ ofdistributions that appear very different, yet have thesame fractal dimension (Allain & Cloitre 1991). Asan example, Fig. 3a,b shows 2 time records with similar fractal dimension values that possess dif -ferent ‘textures.’

Lacunarity analysis was applied by Allain & Cloitre(1991) to describe the heterogeneity of binary data -sets, and Plotnick et al. (1996) extended the ana -lysis to quantitative data. The lacunarity analysischooses a unit box of size r and sums the values inthe box, v (i.e. the sum of the velocity values in ourcase). First, the record was shifted such that therewere no negative values in the time record, the gliding box was centered on each point in the dataset, and the (velocity) values within the box weresummed. The gliding box lacunarity is defined as(Tolle et al. 2008):

(6)

where:

(7)

(8)

and N was the sample size of the velocity time record.Lacunarity was calculated and plotted as a function

of the size of the box, r, in units of seconds (seeFig. 3c,d). The lacunarity curves shown here werenormalized by the lacunarity value at the smallestbox size for comparison purposes. The shape of thelacunarity curve revealed the deviation of an object(in this case the time record) from established geo-metric patterns (Plotnick et al. 1996). Further, theshape of the lacunarity curve indicated features ofthe velocity time record. For example, high lacunar-ity values indicated clumping or closely clusteredvalues of velocity. At a box size value that corre-sponded to the size of the clumped or clustered val-ues, the lacunarity value decreased and the curvedropped off as can be seen in the example in Fig. 4b.There is a distinct break in the slope of the lacunaritycurve at a box size of ~3 s. Another example is shownin Fig. 3c. Also, time records that have gap sizes withrandom step size values have a lacunarity curve witha concave-upward shape. For example, Fig. 4c for alarge clam with large nearest neighbor distance andthe largest bulk mean crossflow velocity matches thisdescription (see also Fig. 3d). Finally, fractals, by def-inition, have a power law relationship between geo-metric ratios and the box size, which means that on a

log-log scale, a lacunarity curve is a straight line for apure fractal. An example is shown in Fig. 4a.

We categorized the shape of the lacunarity curvesfor the time records of vertical velocity in the clamexcurrent. The lacunarity curves were assigned anominal category upon visual inspection of thecurve of either ‘Random’ for a shape similar to that ofFig. 4c, ‘Fractal’ for a shape similar to that of Fig. 4a,and ‘Size’ for a curve with a distinct break in slopesimilar to that of Fig. 4b.

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Z rN r

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1

1

1

111

=− +

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182

Fig. 4. Mercenaria mercenaria. Lacunarity as a function ofbox size (i.e. time segment) for the time record of verticaljet velocity (on log axes). (a) Clam no. 4 of Table 1 for U =2.86 cm s–1, clam length = 4.6 cm, and nearest neighbor dis-tance of 3 cm; (b) Clam no. 6 of Table 1 for U = 2.86 cm s–1,clam length = 7.30 cm, and nearest neighbor distance of3 cm; and (c) Clam no. 8 of Table 1 for U = 2.86 cm s–1, clamlength= 6.91 cm, and nearest neighbor distance of 9 cm

Delavan & Webster: Bivalve clam jet flow

Often there were several time records for eachtreatment case due to the removal of periods inwhich the clam stopped pumping, the siphonchanged location, or the researcher could not locatethe excurrent jet in the velocity field. In the caseswhere multiple velocity records existed for a treat-ment, the lacunarity curves were plotted for each ofthe time record segments. In most of the cases withmultiple velocity records, the shapes of the lacunarityplots were similar. In the few cases where there weredifferences in the lacunarity plot shapes for the mul-tiple velocity records, the dominant lacunarity shapetype was recorded for that case.

Statistical tests

To characterize the clam jet velocity time rec ords,several multi-way, repeated measures analysis ofvariance (ANOVA) and nominal ANOVA (NAN -OVA) tests were performed for the mean excurrentjet vertical velocity values, the jet-to-crossflow veloc-ity ratios, the fractal dimensions, and the lacunarityplot shape designations. The repeated measuresaspect of the ANOVA was the fact that individualclams were subjected to several treatment scenariosand could not be treated as unrelated replicates.

NANOVA is an extension of the ANOVA to datasets that are nominal rather than quantitative (Weiss2009) and was used in this study to qualitatively dif-ferentiate the nominal shape designations of thelacunarity analysis performed on the clam excurrentjet velocity time records. Without quantitative valuesfrom the lacunarity analysis, the test could onlydetermine whether the nominal values were qualita-tively different, but not necessarily how they differedquantitatively. NANOVAs were used to determinewhether the lacunarity plot shape designations werestatistically different for each treatment case. TheNANOVA in the current study revealed whether therandomness (for excurrent velocity values) was dif-ferent in the treatments and lacked the ability to con-clude whether an experimental treatment resulted inmore or less randomness (for excurrent velocity val-ues) than another treatment.

RESULTS

Example case

An example of a velocity field is shown in Fig. 2where the arrows represent the local velocity vector

and the color contours represent positive (upward)vertical velocity. This example set will be usedthroughout this section for demonstration purposes,and it is typical of the results for the entire dataset. The color contours highlight the location of theclam excurrent jet. The location of the buried clamis shown for clarity. In this particular example, theclam was not completely buried beneath the sedi-ment, and the siphons were extended in the up -stream direction with the incurrent siphon locatedupstream of the excurrent siphon. While this exam-ple should be considered typical, the specific charac-teristics may or may not occur in other cases of thisstudy.

Approximately 2250 consecutive velocity fieldswere collected for this case. The vertical velocity timerecord of 225 s duration was extracted, and the first100 s are displayed in Fig. 3a. The time record ofclam excurrent vertical velocity is highly unsteadywith a mean of v = 3.26 mm s–1 and variance of σ2 =3.07 mm2 s–2. A few negative values of vertical veloc-ity appear in the time record, which can be attributedto brief intrusions of the ambient fluid to the center-line of the jet.

For this example time record (Fig. 3a), the fractaldimension is 1.77, which, being greater than 1.5,indicates that the record is anti-correlated. Fig. 3cshows lacunarity as a function of box size for the timerecord shown in Fig. 3a. Alternatively, Fig. 3b showsthe velocity time record for the same clam with a dif-ferent bulk mean crossflow velocity regime. The timerecords have similar fractal dimension values, butappear to have differing distributions (or texture) ofthe velocity values. This differing ‘look’ is quantifiedin the lacunarity curves in Fig. 3c,d. The lacunarityplot type for the jet velocity time record for a bulkmean crossflow velocity of 0.55 cm s–1 is ‘Size’ (Fig. 3c)and for bulk mean crossflow velocity of 1.2 cm s–1 is‘Random’ (Fig. 3d).

Clam jets with varying environmental conditions

Table 1 (mean and SD of the excurrent jet verticalvelocity), Table 2 (jet-to-crossflow velocity ratio,Table 3 (fractal dimension), and Table 4 (lacunaritycurve type) summarize the time record collectionfor the controlled external factors: 4 horizontalbulk mean crossflow velocity values (0.55, 1.2, 1.98,2.86 cm s–1), 2 nearest neighbor distances (3 and9 cm), and 2 clam sizes (4.86 ± 0.22 cm and 7.32 ±0.32 cm). Non-dimensionalizing the nearest neighbordistance by the mean clam size in each case yielded

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non-dimensional nearest neighbor distances of 0.62and 1.85 for the smaller size clams and 0.41 and 1.23for the larger size clams, respectively, for the 3 and9 cm spacing distances.

Mean vertical jet velocities were determined foreach of the treatment combinations given in Table 1,and an average of all mean vertical jet velocities overall treatments results in v = 3.24 ± 2.01 mm s–1.

A multi-way, repeated measures ANOVA on the ver-tical jet velocities revealed a significant interaction(p < 0.034) for the mean jet velocities according to thelength of the clam and the bulk mean crossflowvelocity. In other words, the clam’s mean jet velocityvalues were influenced by the bulk mean crossflowvelocity, and those values were dependent on thesize of the clam. Due to the interaction, we wereunable to compare the individual means of the 2 fac-tors. Table 1 reveals no distinct patterns in the meanclam jet velocity values, and further analysis of thevelocity patterns were required to determine clambehavioral differences in the treatments. The jet-to-crossflow velocity ratio and the lacunarity analysiswere able to reveal distinct patterns in the clambehavior despite a lack of pattern in the mean values,spectral analysis, and fractal analysis.

By non-dimensionalizing the clam jet mean verticalvelocity values by the crossflow velocity, the jet-

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Fig. 5. Mercenaria mercenaria. Mean jet-to-crossflow veloc-ity ratio, v/U, (a) according to bulk mean crossflow velocityvalue (p < 0.001), and (b) according to clam size class (p <0.044). Error bars represent SE. Different letters indicate

significant difference

Clam Length U v/U(cm) (cm s–1) NND = 3 cm NND = 9 cm

ndNND = 0.62 ndNND = 1.85

1 4.7 0.55 0.58 0.571.20 0.38 0.301.98 0.29 0.412.86 0.08 0.10

2 5.2 0.55 0.76 1.91.20 0.07 0.371.98 0.04 0.232.86 0.06 0.12

3 4.9 0.55 0.36 0.951.20 0.37 0.141.98 0.09 0.032.86 0.06 0.05

4 4.6 0.55 0.89 0.631.20 0.58 0.671.98 0.13 0.212.86 0.09 0.01

5 4.9 0.55 1.39 0.591.20 0.20 0.261.98 0.10 0.152.86 0.02 0.09

Clam Length U v/U(cm) (cm s–1) NND = 3 cm NND = 9 cm

ndNND = 0.41 ndNND = 1.23

6 7.3 0.55 0.42 0.291.20 0.07 0.141.98 0.07 0.112.86 0.03 0.16

7 7.5 0.55 0.70 0.481.20 0.28 0.201.98 0.21 0.052.86 0.11 0.07

8 6.9 0.55 0.59 0.331.20 0.41 0.221.98 0.29 0.102.86 0.22 0.19

9 8.6 0.55 0.35 0.951.20 0.17 0.271.98 0.16 0.082.86 0.18 0.04

Table 2. Mercenaria mercenaria. Jet-to-crossflow velocityratio, v/U. The table reports data for varying nearest neigh-bor distance (NND), non-dimensional NND (ndNND), bulkmean crossflow velocity (U, cm s–1), and clam size class.

v = jet vertical velocity

Delavan & Webster: Bivalve clam jet flow

to-crossflow velocity ratios could be compared foreach treatment case (Table 2). If the clams weremaintaining the velocity values, as the results ofPrice & Schiebe (1978) suggest, then the mean jet-to-crossflow velocity ratio should have decreased linearly with increasing bulk mean crossflow velo -city. A multi-way, repeated measures ANOVA on theclam jet-to-crossflow velocity ratios did not find aninteraction between the factors (size of clam, nearestneighbor distance, or bulk mean crossflow velocityratio) which allowed us to compare the means of thefactors separately. There was a significant differencein the mean jet-to-crossflow velocity ratios accordingto the size of the clam (p < 0.044) and according to thebulk mean crossflow velocity (p < 0.001). The meanjet-to-crossflow velocity ratio at a bulk mean cross-flow velocity of 0.55 cm s–1 was significantly differentthan the mean jet-to-crossflow velocity ratio of the 3other bulk mean crossflow velocity values (p < 0.05;see Fig. 5a). As the jet-to-crossflow velocity ratio didnot decrease in proportion to the inverse of the bulkmean crossflow velocity (i.e. the normalization), theresults indicated that clams were altering their jetvelocity value as the bulk mean crossflow velocitychanged. Also, they were not maintaining a constantjet-to-crossflowvelocity ratio,particularly for the small-est bulk mean crossflow velocity case. Finally, themean jet-to-crossflow velocity ratio for the smallersize clams (v/U = 0.358 ± 0.01 SE) was significantlylarger than that for the larger size clams (v/U = 0.248± 0.006 SE; Fig. 5b).

The fractal dimension values captured here weregenerally anti-correlated (Table 3). In other words,a value of velocity in the time record was followedby a dissimilar value of velocity. A multi-way, re -peated measures ANOVA found no significant dif-ferences or significant interactions in the meanfractal dimension values of the time records accord-ing to bulk mean crossflow velocity, clam nearestneighbor distance, or clam size (Table 3). Therewas a distinct lack of pattern in the fractal dimen-sion values presented in Table 3; however, the val-ues of the fractal dimension in Table 3 give a senseof the amount of randomness contained in thevelocity time record. The lack of pattern in Table 3justifies the use of the lacunarity analysis as ameans of quantifying the texture of the velocitytime record randomness.

The lacunarity curves were categorized with nomi-nal types according to the shape (Table 4). A multi-way, repeated measures NANOVA of the lacunaritynominal values in Table 4 found a significant differ-ence in the lacunarity curves according to the hori-

zontal bulk mean crossflow velocity (p < 0.001). TheNANOVA revealed that the clams were changingthe jet velocities in such a way that the lacunaritycurve shape changed with the bulk mean crossflowvelocity value. Therefore, although the amount ofrandomness in the velocity time records may be sta-tistically similar (as measured by fractal dimension),the distribution of the randomness or the texture ofthe randomness was bulk mean crossflow velocity

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Clam Length U dfl

(cm) (cm s–1) NND = 3 cm NND = 9 cmndNND = 0.62 ndNND = 1.85

1 4.7 0.55 1.80 1.741.20 1.86 1.641.98 1.83 1.732.86 1.79 1.75

2 5.2 0.55 1.66 1.721.20 1.76 1.761.98 1.79 1.672.86 1.70 1.74

3 4.9 0.55 1.74 1.691.20 1.79 1.671.98 1.72 1.812.86 1.71 1.69

4 4.6 0.55 1.75 1.821.20 1.73 1.811.98 1.70 1.722.86 1.67 1.57

5 4.9 0.55 1.61 1.771.20 1.78 1.781.98 1.70 1.802.86 1.80 1.66

Clam Length U dfl

(cm) (cm s–1) NND = 3 cm NND = 9 cmndNND = 0.41 ndNND = 1.23

6 7.3 0.55 1.75 1.821.20 1.76 1.811.98 1.73 1.762.86 1.67 1.86

7 7.5 0.55 1.76 1.741.20 1.78 1.811.98 1.78 1.842.86 1.80 1.74

8 6.9 0.55 1.72 1.831.20 1.75 1.791.98 1.58 1.512.86 1.73 1.84

9 8.6 0.55 1.80 1.701.20 1.77 1.791.98 1.63 1.732.86 1.79 1.68

Table 3. Mercenaria mercenaria. Fractal dimension (dfl) forthe time records of vertical velocity in the clam excurrent jet.The table reports data for varying nearest neighbor distance(NND), non-dimensional NND (ndNND), bulk mean cross-

flow velocity (cm s–1), and clam size class

Aquat Biol 13: 175–191, 2011

specific. A limitation of the NANOVA test is thatwhen a significant difference is found in the nominalvalues, there is no way to quantify that difference.The texture of the velocity time records were differ-ent, but we cannot report a measure of how theywere different.

The NANOVA test on the nominal values in Table 4also revealed a significant interaction between the

nearest neighbor distance and clam size (p < 0.001).The lacunarity plot shape was dependent on the sizeof the organism, and that dependence was influ-enced by the proximity of other clams. The most sig-nificant trend was that there are a large number of‘Random’ plot shapes for the larger clams (Table 4).Further, there appeared to be more ‘Random’ plotshapes for the 9 cm nearest neighbor distances(Table 4). The interaction between the nearest neigh-bor distance and the size of the organism implied thatthe reaction of clams to the density of the clam patchwas dependent on the size of that particular animal.Hence, there may be specific clam patch densitiesthat are advantageous for organisms of a specificsize.

Control cases

Table 5 summarizes the data for the control treat-ments. Two-way, repeated-measures ANOVA testsrevealed that there was no interaction between fac-tors for mean velocities and jet-to-crossflow velocityratios, which allowed a comparison of means. Therewas a significant difference in the mean verticalvelocities (p < 0.001) and in the mean jet-to-crossflowvelocity ratios (p < 0.03) according to the control type(e.g. clam shell only, clam mimic). The clam mimiccase with jet flow rate of = 0.467 cm3 s–1 had sig -nificantly larger values of the mean vertical velocityand the mean jet-to-crossflow velocity ratio.

A 2-way, repeated measures ANOVA did not findinteractions between factors or significant differ-ences in the mean fractal dimension values amongthe control cases for any of the factors (bulk meancrossflow velocity and control type). The lacunaritycurve types for the control cases are presented inTable 5, and the majority of cases are described as‘Random.’ A 2-way, repeated measures NANOVAfound no interaction between factors and significantdifference in lacunarity curve type for the controlcases according to bulk mean crossflow velocity (p <0.001).

DISCUSSION

Clam pumping behavior

Clams altered their excurrent flow behavior ac -cording to bulk mean crossflow velocity as seen inthe lacunarity analysis and the jet-to-crossflow veloc-ity ratios (Tables 2 & 4 and Fig. 5). Also, the reaction

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Clam Length U Lacunarity curve type(cm) (cm s–1) NND = 3 cm NND = 9 cm

ndNND = 0.62 ndNND = 1.85

1 4.7 0.55 Random Size1.20 Random Size1.98 Random Random2.86 Random Random

2 5.2 0.55 Size Random1.20 Size Random1.98 Random Size2.86 Random Size

3 4.9 0.55 Random Size1.20 Size Size1.98 Size Random2.86 Fractal Size

4 4.6 0.55 Size Random1.20 Size Random1.98 Random Size2.86 Fractal Size

5 4.9 0.55 Size Size1.20 Size Random1.98 Size Random2.86 Random Fractal

Clam Length U Lacunarity curve type(cm) (cm s–1) NND = 3 cm NND = 9 cm

ndNND = 0.41 ndNND = 1.23

6 7.3 0.55 Random Random1.20 Size Size1.98 Size Fractal2.86 Size Random

7 7.5 0.55 Size Random1.20 Random Random1.98 Random Random2.86 Random Random

8 6.9 0.55 Fractal Random1.20 Random Random1.98 Fractal Random2.86 Random Random

9 8.6 0.55 Random Fractal1.20 Size Random1.98 Size Random2.86 Random Random

Table 4. Mercenaria mercenaria. Lacunarity curve type fortime records of clam excurrent vertical velocity (see ‘Materi-als and methods’ for a description of the curve types). Thetable reports data for varying nearest neighbor distance(NND), non-dimensional NND (ndNND), bulk mean cross-

flow velocity (U, cm s–1), and clam size class

Delavan & Webster: Bivalve clam jet flow

of clams to the density of the clam patch was depen-dent on the size of the clam (Table 4), and the jet-to-crossflow velocity ratio was larger for smaller clams(Fig. 5b). Therefore, clams had dynamic jet behaviorsthat were influenced by external conditions, and theresult was a change in the unsteady character anddistribution of randomness in the velocity of theexcurrent jet.

The patterns in the lacunarity curve shapes for theclam jets (Table 4) were not present in the controlcases (Table 5). Most notable was the suggestion ofdissimilarity in the lacunarity shape patterns be -tween the lacunarity curves for the biological clamjets and the steady clam mimic jets. Steady jet clammimics or steady chemical sources may not mimic thesource characteristics for actual clam chemicalmetabolite plumes. Therefore, the information avail-able to predators in the downstream plume of asteady source may not necessarily represent theinformation available to predators in actual clamchemical plumes (see Webster & Weissburg 2001 fordiscussion of plume characteristics downstream ofsteady release sources). The data for the controlcases also indicated that there were no contributionsto the patterns seen in the lacunarity curve shapesdue to the pockets created by the burying action ofclams, the presence of the clam shell or non-pumpingclams, or the presence of the clam mimic siphon.Finally, since the clam source characteristics werehighly unsteady and have lacunarity curve shapepatterns that were not seen in steady source clammimics, studies that use steady clam mimics may be

misrepresenting the mixing/dilution of the clam jet.Further, this could impact calculations of concentra-tion boundary layers or clam refiltration rates.

Dominant predator–prey interaction

The predator–prey system of interest here wasthe relationship between bivalve clams Mercenaria mercenaria and their predators, knobbed whelksBusycon carica and blue crabs Calinectes sapidus.While both predators use olfactory tracking to locatetheir clam prey, they have specific consumptionmethods and are successful in flows possessing dif-ferent hydrodynamic characteristics. For example,blue crabs prefer to consume smaller, more easilycrushed clams, depending on availability and level ofstarvation (Micheli 1995). In contrast, whelks con-sume clams of all sizes and have predation success inhigh turbulence intensity regimes (Ferner & Weiss-burg 2005).

There were several clam jet quantities that weresignificantly different according to the size of theorganism. The jet mean vertical velocity was influ-enced by the bulk mean crossflow velocity (althougha pattern is not clear in Table 1), and that influencewas dependent on the size of the clam. It should benoted that Price & Schiebe (1978) found that mean jetvelocity values did not vary according to the size ofthe clam, in contrast to the results of our study. Also,smaller clams were found in our study to have alarger jet-to-crossflow velocity ratio than the larger

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Jet flow rate Diameter U v v/U dfl Lacunarity (cm3 s–1) (cm) (cm s–1) (mm s–1) curve type

No clam, – – 0.55 −0.08±0.50 −0.02 1.80 Sizeno jet 1.20 −0.08±0.67 −0.01 1.82 Random

1.98 −0.08±0.78 0.00 1.83 Random2.86 0.00±2.15 0.00 1.87 Random

Clam shell 0 – 0.55 0.33±0.78 0.06 1.80 Random(7.0 cm) 1.20 0.82±1.02 0.07 1.81 Random

1.98 1.42±1.61 0.07 1.76 Random2.86 2.23±3.81 0.08 1.79 Random

Clam mimic 0.467 0.95 0.55 13.59±1.25 2.47 1.52 Random1.20 12.74±0.61 1.06 1.76 Random1.98 11.00±1.51 0.56 1.57 Size2.86 4.83±5.65 0.17 1.92 Random

Clam mimic 0 0.95 0.55 −3.44±0.98 −0.63 1.73 Random1.20 −3.50±1.43 −0.29 1.83 Random1.98 −3.87±2.02 −0.20 1.86 Random2.86 −4.61±4.34 −0.16 1.90 Random

Table 5. Data for time records of vertical velocity for the laboratory control cases. U = bulk mean crossflow velocity, v = jet vertical velocity (mean ± SD), dfl = fractal dimension

Aquat Biol 13: 175–191, 2011

size clams of this experiment (see Fig. 5). Finally, thereaction of the clams to the density of the patch wasdependent on the size of the clam, according to thelacunarity curve types (Table 4). This suggests that ifthe clam behavioral modifications were related topredation, then blue crabs dominate or control thepredator–prey system. Since clams of all sizes aresusceptible to whelk predation, whelks were notlikely controlling the predator–prey relationshiphere because there was a size dependence on themeasured jet excurrent velocities.

Due to the dependence of blue crab predation onambient turbulence levels, there may be clam feed-ing strategies that are an attempt to avoid predationby blue crabs that are specific to the clam patch den-sity and the size of the individual organisms. Forexample, a large chemical plume, resulting from theinteraction of many clam excurrent jets, may attractblue crabs to the area, in which case the smallestclams are the most susceptible to predation. On theother hand, since crabs have been shown to react tomore discrete filaments of chemical cues (Jacksonet al. 2007), it may be advantageous for small clams,when individuals, to employ feeding behavior thatavoids predation by controlling the distribution oftheir jet velocity values.

Blue crabs tend to be more successful at locatingprey in regimes with smaller turbulence intensity(unless the flow rate decreases to quiescent), andtheir success decreases with increasing ambient tur-bulence (Weissburg & Zimmer-Faust 1993, Jacksonet al. 2007). If blue crab predation pressure is domi-nating the predator–prey relationship, as the den-sity/size results of this study suggest, then clambehavioral changes according to the ambient turbu-lence, or in this case, bulk mean crossflow velocity,may also increase survivorship. First, the jet-to-cross-flow velocity ratio for the smallest bulk mean cross-flow velocity was significantly larger than the ratioat the larger bulk mean crossflow velocity values(Fig. 5). Second, the textural distribution of the clamjet velocity values changed according to the ambienthorizontal bulk mean crossflow velocity (Table 4).Hence, as the ambient flow/turbulence regimechanged, clams altered the chemical plume sourcecharacteristics, which may have been a result of typ-ical predation pressure in those conditions. Weiss-burg & Zimmer-Faust (1993) suggested that theremay be certain hydrodynamic conditions that pro-vide a refuge from predation by certain predators. Akey component for study of the predator–prey sys-tem here was how the prey items may disguise theirpresence within the spatial and temporal environ-

ment (Weissburg & Dusenbery 2002), and our resultssuggest that clams were altering the randomness ofthe jet velocities according to the ambient flow andturbulence in a manner that may have contributed tothis ‘disguise.’ However, more information is clearlyneeded regarding how the behavioral changes actu-ally alter the downstream chemical plumes and thetracking success of predators.

Blue crab tracking success decreases (Keller &Weissburg 2004) and successful tracks take longer(Page et al. 2011a) when the chemical source plumehas a pulsed release rather than a continuousrelease. The clam jet velocity time records of the cur-rent study had highly unsteady velocity values (e.g.Fig. 3), and the lacunarity curves suggested thatthere were often documented gaps between re peatedvalues of velocity (i.e. ‘Size’ in Table 4). There fore,with unsteady clam excurrent jets, as observed here,crabs may have less predation success.

Patch dynamics

It may be advantageous to be part of a denselypacked clam patch when of a certain size range andto be an individual at other size ranges. The differ-ence in clam jet velocity randomness, as found in thecurrent study, was dependent on the density of clamsin the patch and the size of the organism (Table 4).There may be a critical clam plot density according tothe dominant clam size range within the plot wherethe excurrent chemical plumes interact with oneanother and become 1 large plume rather than manyindividual plumes. Coco et al. (2006) theorized thatbivalve patch dynamics were not necessarily the sumof the behaviors of individual animals. The resultshere suggest that individual clams had specificbehaviors for their size and patch density.

Alternatively to predator–prey interactions, thebehavior of clams according to the clam density andclam size found herein (Table 4) may not be directlyrelated to predation, but rather indirectly through lar-val recruitment. Hart et al. (1996) found that larvalsettlement was highly dependent on hydrodynamiccues. Adult clam feeding behavior may have con-tributed to those hydrodynamic conditions as a meansof communication to larvae as to whether the patchwas recruiting or deterring new patch members. Theresults here indicated that clams of different sizesaltered their feeding behavior depending on the den-sity within the patch. If patch recruitment is moredominant than predation pressure, as Coco et al.(2006) suggested, then the differences in feeding

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Delavan & Webster: Bivalve clam jet flow

behavior may not have been fostering a refuge frompredation but rather signaling clam larvae or promot-ing the hydrodynamic conditions that induce or deterlarvae from settling. Through this hydrodynamic sig-naling method, clams of certain sizes may control theclam patch density.

Experimental methods

The clams used in this study were pumping in amanner that appeared consistent with observationsof previous studies. The measurements of Frank et al.(2008) and the extensive testing of seeding particlesin this study indicated that titanium dioxide particlespassed through Mercenaria mercenaria with suffi-cient density to facilitate PIV measurements and didnot visibly alter the pumping behavior. Troost et al.(2009) used a PIV system to measure the incurrentvelocities and modeled the excurrent jet velocities of3 bivalves: a mussel, an oyster, and a cockle. Theywere unable to use the PIV system to determineexcurrent jet characteristics due to the filter-feedingnature of the organisms who removed the suspendedsynthetic particles. They predicted excurrent jet ve -locity values an order of magnitude larger than thosecollected for clams in the present study, althoughsimilar in magnitude to Price & Schiebe (1978). Franket al. (2008) found PIV systems to accurately charac-terize the excurrent jet flow of Mercenaria merce-naria along with an ascidian, a mussel, an oyster, anda scallop. They found similar mean jet velocity valuesas those collected in the current study without dis-turbing either the fluid or the animal in quiescentflow conditions. Further, occurrences of ‘resting peri-ods’ in our study were comparable to those observedby de Bruin & Davids (1970), which indicates that thepresence of the seeding particles and laser sheetwere not the cause of the resting periods.

Influence of siphon flow on the plume

The jet-to-crossflow velocity ratios varied accord-ing to the bulk mean crossflow velocity and the sizeof the organism (Fig. 5). Morton & Ibbetson (1996)studied jets-in-crossflow with a large range of Rey -nolds numbers (both laminar and turbulent) for thejet flow and the bulk mean crossflow, and a largerange of jet-to-crossflow velocity ratios (1 to 100).They found that the jet-to-crossflow velocity ratiowas the most influential factor in the structure of thejet/crossflow interaction. The jet-to-crossflow ratio

determined the dominance of structures such as thecounter rotating vortex pair, the horseshoe vortices,the wake vortices, and the shear layer vortices. Allflows, i.e. laminar and turbulent jets and boundarylayers, contain these structures, and the dominanceof the structures is dependent on the jet-to-crossflowvelocity value (Morton & Ibbetson 1996).

The jet-to-crossflow velocity ratios were larger forsmall clams compared to those of the larger clams.This suggested that excurrent jets for small clamswere more erect and the bulk mean crossflow hadmore of a tendency to deflect around the jet (Andreo -poulos & Rodi 1984), the wake vortices were moredominant than the shear layer vortices (Fric & Roshko1994, Meyer et al. 2007), and the counter-rotatingvortex pair was more dominant than the horseshoevortices (Jabbal & Zhong 2008, Sau & Mahesh 2008).In contrast, excurrent jets for the larger clams weremore severely bent over and the bulk mean crossflowtended to deflect over the jet (Andreopoulos & Rodi1984, Demuren 1992, 1993), the shear layer vorticeswere more dominant with respect to the wake vor-tices (Fric & Roshko 1994, Meyer et al. 2007), and thehairpin vortices were more dominant with respect tothe counter rotating vortex pair (Jabbal & Zhong2008, Sau & Mahesh 2008).

We also found that at the smallest bulk mean cross-flow velocity, the jet-to-crossflow velocity ratio waslarger than the other bulk mean crossflow velocitiesused here. In this small bulk mean crossflow velocitycase, the jet-to-crossflow velocity ratio indicateddominance of the counter rotating vortex pair (Sau &Mahesh 2008), dominance of the wake vortices (Fric& Roshko 1994, Meyer et al. 2007), and a more erectjet with bulk mean crossflow deflecting around thejet (Andreopoulos & Rodi 1984).

The clam jet velocity time records presented herewere highly unsteady (Fig. 3), and the character ofthe unsteadiness changed with horizontal crossflowvelocity and size and density of clams (Table 4).While the velocity time records of the clams did notnecessarily have specific pulsing frequencies associ-ated with them, we can compare the time records toliterature quantifying the effects of pulsed jets andpulsed jets-in-crossflow due to the unsteady natureof pulsed jet flow. Bera et al. (2001) found thatunsteady (pulsed) jets have greater rates of entrain-ment of the receiving fluid into the jet when com-pared to steady jets. The larger rates of entrainmentresulted in smaller concentrations of the jet fluid inthe plume. For clams, this may result in the dilutionof chemical metabolites, and it may be advantageousto encourage the mixing of the chemical plume.

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Plumes from laminar pulsed jets have increasedspread compared to continuous jets, and laminar vor-tex rings are more persistent due to the unsteadiness(Cater & Soria 2002). As vortex rings are more persis-tent, they are present longer and travel higher in thewater column before they are dissipated, resulting inmore entrainment of the ambient fluid.

In summary, knowledge about jets-in-crossflow pro-vided some insight to the flow structure, mixing, andentrainment characteristics of the excurrent flow. Thisinformation provided some explanation of the ob-served behavior differences. Nevertheless, questionsremain about the details of the mixing characteristics.

Acknowledgements. We thank M. J. Weissburg for helpfulsuggestions and use of his seawater flume. Thanks also tothe National Science Foundation for financial support undergrants OCE-0424673 to M. J. Weissburg and D.R.W. and foran NSF IGERT fellowship awarded to S.K.D.

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Editorial responsibility: Peter Beninger, Nantes, France

Submitted: October 5, 2010; Accepted: June 22, 2011Proofs received from author(s): August 29, 2011