integrative and comparative biology...understanding the influence of copepods’ behavior in...

SYMPOSIUM

Copepods’ Response to Burgers’ Vortex: DeconstructingInteractions of Copepods with TurbulenceD. R. Webster,1,* D. L. Young* and J. Yen†

*School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA; †School of

Biology, Georgia Institute of Technology, Atlanta, GA 30332, USA

From the symposium ‘‘Unsteady Aquatic Locomotion with Respect to Eco-Design and Mechanics’’ presented at the

annual meeting of the Society for Integrative and Comparative Biology, January 3–7, 2015 at West Palm Beach, Florida.

1E-mail: [email protected]

Synopsis This study examined the behavioral response of two marine copepods, Acartia tonsa and Temora longicornis, to

a Burgers’ vortex intended to mimic the characteristics of a turbulent vortex that a copepod is likely to encounter in the

coastal or near-surface zone. Behavioral assays of copepods were conducted for two vortices that correspond to turbulent

conditions with mean dissipation rates of turbulence of 0.009 and 0.096 cm2 s�3 (denoted turbulence level 2 and level 3,

respectively). In particular, the Burgers’ vortex parameters (i.e., circulation and rate of axial strain rate) were specified to

match a vortex corresponding to the median rate of dissipation due to viscosity for each target level of turbulence. Three-

dimensional trajectories were quantified for analysis of swimming kinematics and response to hydrodynamic cues. Acartia

tonsa did not significantly respond to the vortex corresponding to turbulence level 2. In contrast, A. tonsa significantly

altered their swimming behavior in the turbulence-level-3 vortex, including increased relative speed of swimming, angle

of alignment of the trajectory with the axis of the vortex, ratio of net-to-gross displacement, and acceleration during

escape, along with decreased turn frequency (relative to stagnant control conditions). Further, the location of A. tonsa

escapes was preferentially in the core of the stronger vortex, indicating that the hydrodynamic cue triggering the dis-

tinctive escape behavior was vorticity. In contrast, T. longicornis did not reveal a behavioral response to either the

turbulence level 2 or the level 3 vortex.

Introduction

The interactions between small biological organisms

and turbulence remain fascinating and mysterious to

biological oceanographers. For example, studies by

Rothschild and Osborn (1988), Saiz and Kiørboe

(1995), and Incze et al. (2001) raised puzzling

open-ended questions regarding the effect of the hy-

drodynamic forcing imposed on small organisms,

such as copepods, due to the turbulent flow field

they inhabit. It is known that copepods are of similar

size to the Kolmogorov microscale in coastal-zone

turbulence (Jimenez 1997) and that they typically

swim at speeds on the order of the fluid’s fluctuating

velocity (Yamazaki and Squires 1996). Therefore,

transport and behavior of copepods are linked by

similar scales to finescale fluctuations in velocity of

turbulence in coastal and near-surface environments.

It is likely that the effects of turbulence on copepods’

behaviors, such as feeding rate, growth rate, and

predator–prey interaction, are species-specific

(Dower et al. 1997; MacKenzie 2000; Marrase et al.

2000; Peters and Marrase 2000), which indicates that

fully understanding the interaction of zooplankters

and turbulence will prove to be an arduous task

(e.g., Jonsson and Tiselius 1990; Saiz and Alcaraz

1992; Visser et al. 2001; Saiz et al. 2003; Galbraith

et al. 2004; Lewis 2005). One observation of turbu-

lence affecting behavior was the species-specific ver-

tical distribution of copepods, seemingly in response

to the distribution of the intensity of turbulence

within the water column (Heath et al. 1988; Haury

et al. 1990; Mackas et al. 1993; Lagadeuc et al. 1997;

Incze et al. 2001; Visser et al. 2001; Manning and

Bucklin 2005). It is relatively intuitive to grasp that

the physical forcing of turbulence could mediate the

vertical distribution of copepods via advection, but,

Integrative and Comparative BiologyIntegrative and Comparative Biology, volume 55, number 4, pp. 706–718

doi:10.1093/icb/icv054 Society for Integrative and Comparative Biology

Advanced Access publication May 21, 2015

� The Author 2015. Published by Oxford University Press on behalf of the Society for Integrative and Comparative Biology. All rights reserved.

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understanding the influence of copepods’ behavior in

response to hydrodynamic cues (associated with the

fluctuation of the velocity of turbulence) on the ver-

tical distributions of copepods is less obvious and

very challenging to quantify.

To tackle this formidable topic, one must first

appreciate how copepods collect sensory information

from the surrounding environment, specifically, how

they detect the hydrodynamic cues associated with

fluctuations in velocity. To detect hydrodynamic sig-

nals, copepods possess an array of mechanosensory

hairs, called setae, on many of their appendages

(note that copepods do not possess statocysts).

These setae are most numerous and most sensitive

along the antennae (Yen and Fields 1992; Boxshall

et al. 1997; Fields et al. 2002). Setae bend in response

to differences in velocity between the animal and the

ambient fluid. The sensitivity of copepods to hydro-

dynamic cues is truly impressive. For example, Yen

et al. (1992) reported that copepods detect displace-

ments as small as 10 nm, and Woodson et al. (2005,

2007a,2007b) reported sensitivities to strain rate as

low as 0.025 s�1. Several studies have attempted to

isolate the specific hydrodynamic cues that elicit cer-

tain responses by copepods, with the majority of

them concluding that strain rate is the cue that elicits

an escape response (Haury et al. 1980; Fields and

Yen 1997; Kiørboe et al. 1999; summarized in

Woodson et al. 2014).

The nature of turbulence presents unique chal-

lenges to researchers who wish to form a mechanistic

connection between flow and behavior. Turbulent

flows are characterized by (among other things)

their random and unpredictable nature. Further,

the fluctuations in velocity are intermittent, which

appears as infrequent, but extreme, peaks and

troughs both in the time-record of velocity of flow

and in the difference in flow velocity between neigh-

boring locations (at the same time). This presents

enormous challenges to researchers wishing to per-

form behavioral assays of organisms, such as cope-

pods, in a turbulent flow. One cannot be sure when

the organism will swim through the experimental

control volume and there is no way to anticipate

the instantaneous velocity in a turbulent flow.

Therefore, time-resolved three-dimensional data on

velocity must be constantly acquired throughout

the behavioral assay. Furthermore, many behaviors

that are of interest (such as escape jumps of cope-

pods) are relatively infrequent events, and the events

must occur within the experimental control volume

while data on velocity are being collected (such that

the hydrodynamic cues triggering the event are

quantified). Compounding this issue is the fact that

experimental techniques for imaging flows that allow

time-resolved collection of three-dimensional data on

velocity, such as tomographic particle image veloci-

metry (Tomo-PIV), have a limited range of scales

that necessitates a relatively small measurement

volume to meet resolution requirements around the

zooplankton (Murphy et al. 2012). Continuously

taking data on flow, while waiting for an animal to

swim through the necessarily small control volume

and perform an infrequent escape jump (or other

modifications of behavior) is a recipe for countless

hours of behavioral assays to acquire even a few

quantified behavioral events. Acquiring enough

data-points in this scenario to statistically test hy-

potheses is a monumental task.

The present study took an alternate approach and

employed a laboratory apparatus to create a Burgers’

vortex (Jumars et al. 2009) in order to perform be-

havioral assays of copepods swimming in and around

a turbulent-like vortex. The Burgers’ vortex was an

ideal model because the swirling and straining mo-

tions (see Fig. 1) closely match the characteristics of

turbulent vortices in the dissipative range (Webster

and Young 2015). The goal was to test the hypothesis

that the copepods Acartia tonsa and Temora long-

icornis sense hydrodynamic cues related to vortices

in turbulent flows and actively respond via changes

in swimming kinematics.

Fig. 1 Sketch of fluid motion in the Burgers’ vortex. Fluid moves

radially-inward toward the axis while stretching outward in the

axial direction. Fluid is also rotating in a counterclockwise sense

around the axis. The combination of these motions creates

streamlines that resemble a three-dimensional spiral (not

illustrated).

Copepods’ response to Burgers’ vortex 707




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Materials and methods

Collection and maintenance of copepods

Acartia tonsa were collected off the coast of Maine,

USA, in July 2013 and subsequently shipped over-

night to Georgia Tech in Atlanta, GA, USA. Temora

longicornis were similarly collected off the coast of

Maine, USA, in September 2013 and shipped over-

night to Georgia Tech. Upon arrival, the copepods

were placed in a coldroom at 128C at low population

densities and fed a mixed diet of Tetraselmis spp. and

Rhodomonas lens. The buckets were aerated to main-

tain a reasonably high concentration of dissolved

oxygen.

Burgers’ vortex apparatus

Trials were conducted in the Burgers’ vortex appara-

tus described by Webster and Young (2015).

Following Jumars et al. (2009), the approach was

to reduce the stochastically varying nature of turbu-

lent flows to a simple vortex model. Direct numerical

simulation (DNS) experiments indicated that micro-

scale turbulence could be described as a writhing

tangle of vortex ‘‘worms’’ (Yokokawa et al. 2002).

Further, numerical simulations by Hatakeyama and

Kambe (1997) indicated that an ensemble of Burgers’

vortices under the right conditions could accurately

mimic flow characteristics of isotropic turbulence.

Combining these concepts, Jumars et al. (2009) pre-

sented a method for mimicking a single turbulence

vortex ‘‘worm’’ with a Burgers’ vortex. Such an ap-

proach had the advantage of eliminating the

temporally variable and random nature of the flow,

and the approach facilitated examination of the

mechanistic aspects of the interaction of plankton

with a turbulent-like vortex.

The apparatus consisted of a clear acrylic tank

with outer dimensions of 20.64 cm (W)� 20.64 cm

(L)� 27.31 cm (H). A mimic of a Burgers’ vortex

was created in the tank via two co-rotating discs

with a hollow driveshaft through which fluid was

drawn out of the tank (Webster and Young 2015).

Specific conditions of vortex flow were targeted

based on previous observations of behavior of

copepods. Yen et al. (2008) observed a significant

behavioral transition for Acartia hudsonica and

T. longicornis between their turbulence-level-2

(h"i¼ 0.009 cm2 s�3) and turbulence-level-3

(h"i¼ 0.096 cm2 s�3) treatments in an isotropic-

turbulence generator. In particular, the motility

number, which is the ratio of copepod transport

speed over r.m.s. of the fluctuations in velocity of

turbulent fluid, was significantly different between

the level-2 and level-3 treatments. The motility

number provided a measure of the zooplankton’s

ability to swim against, rather than be advected by,

the motion of the fluid. Gallager et al. (2004) re-

ported a critical value of 3 for the motility

number: for values more than 3 copepods were

able to aggregate, whereas for values less than 3 co-

pepods did not aggregate, which suggests that they

were unable to swim and orient effectively against

the motion of the fluid. Further, Yen et al. (2008)

observed a transition across the critical value of the

motility number of 3 for the conditions of level-2

and level-3 turbulence. As a result, we targeted

these turbulence conditions during the design of

the Burgers’ vortex apparatus. Webster and Young

(2015) described the procedure for defining the pa-

rameters associated with a typical dissipative vortex

for the target conditions and fully described the flow

fields via Tomo-PIV. The targeted conditions of tur-

bulence and the corresponding characteristics of

the vortex are summarized in Table 1. Note that

the fluctuating velocities, urms, were comparable to

the range reported by Yamazaki and Squires (1996).

Collection of data on behavioral assays

Behavioral assays were conducted with a mixed-sex

population of 250 A. tonsa (length¼ 0.9 mm) and a

separate mixed-sex population of 150 T. longicornis

(length¼ 1.6 mm). Note that the sizes of the organ-

isms were very similar to the Kolmogorov microscale

for each level of turbulence (Table 1). Each behav-

ioral assay included four stages. Stage 1 consisted of

a 30-min period to allow the animals to become ac-

climated to the tank. Stage 2 was a 55-min period of

Table 1 Summary and comparison of flow parameters

Parameter Turbulence level 2 Turbulence level 3

Target Measured Target Measured

h"i (cm2 s�3) 0.009 — 0.096 —

TKE (cm2 s�2) 0.12 — 0.82 —

� (mm) 1.0 — 0.57 —

urms (mm s�1) 2.8 — 7.5 —

rB (mm) 8.1 7.5 4.6 4.9

a (s�1) 3.2� 10�2 4.2� 10�2 9.9� 10�2 10.0� 10�2

� (cm2 s�1) 1.4 1.5 2.2 1.7

Notes: Target values for mean dissipation rate h"i, turbulent kinetic

energy TKE, Kolmogorov microscale �, and r.m.s. of the fluctuations in

velocity urms are from the isotropic turbulence generator described

by Webster et al. (2004). The characteristic vortex radius rB, axial

strain rate parameter a, and circulation parameter � compare favor-

ably between the target turbulent vortex and the flow generated in

the Burgers’ vortex apparatus. Data adopted from Webster and

Young (2015).

708 D. R. Webster et al.




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recording under conditions of stagnant flow to ob-

serve the copepods’ behavior in the absence of hy-

drodynamic stimuli—hereinafter referred to as the

‘‘control’’. Stage 3 was a 30-min period for the es-

tablishment of Burgers’ vortex flow to allow the

Burgers’ vortex to reach the prescribed steady-state

conditions. The fourth stage consisted of a 55-min

period of recording the behavior of the copepods in

the presence of the Burgers’ vortex—hereinafter re-

ferred to as the ‘‘treatment’’. This procedure was

repeated twice for each strength of Burgers’ vortex,

for a total of four runs for each species (since each

run consists of collecting data for one control and

one treatment).

Pulnix cameras (JIA Inc.), with a resolution of

720� 480 pixels, recorded the copepods’ positions

from the front and bottom perspectives (Fig. 2).

The front camera was equipped with a 60-mm

Nikon lens and the bottom camera was equipped

with a 24-mm Nikon lens. Each camera recorded

images at 30 Hz via a Digital Video Cassette

Recorder (Sony model GV-D900 NTSC) that re-

corded the footage on 60-min miniature digital

video cassettes (Mini-DVs). The cameras were fo-

cused on the region surrounding the rotating discs

within the Burgers’ vortex apparatus, with roughly

equivalent viewing windows of 9 cm� 7 cm.

Illumination of the tank was provided by two near-

infrared fiber-coupled diodes (CVI Melles Griot

model 57PNL054/P4/S, 660 nm, 22 mW) (Fig. 2).

Processing of data on behavioral assays

All recordings were converted to digital files (down-

sampled to 15 Hz). As a first step, the copepods in

the recording from the front camera were tracked

manually in DLTdv5, a Matlab particle tracking soft-

ware developed by Hedrick (2008). Second, using the

common spatial coordinate and time-stamp, trajec-

tories in the bottom camera were matched to those

from the front camera. Matches were considered

‘‘high-quality’’ if the trajectories exceed 70 frames

in length and the match was quite certain. The tra-

jectories from the front and bottom perspectives

were combined to form a fully three-dimensional

time-resolved track (examples shown in Fig. 3). To

obtain the velocity and acceleration of the copepod

at each instant in time, calculations of finite differ-

ence (i.e., central-difference method) were performed

on the data on copepods’ positions.

For the treatments, the copepods’ trajectories and

experimental data on velocity (Webster and Young

2015) were aligned in a common frame of reference.

At each time-step, the flow velocity at the copepod’s

position was calculated via a trilinear interpolation

function by weighting the contributions from the

eight neighboring data-points on velocity.

Seven parameters are reported here to define co-

pepods’ swimming behavior in and around the

Burgers’ vortex flow. First, relative swimming speed

quantified how fast the copepod was moving relative

to the local flow velocity. Second, turn frequency

quantified the number of times per second the co-

pepod changed its directional heading by more than

208. Third, net-to-gross displacement ratio (NGDR)

quantified the straightness of the path. For reference,

a NGDR of 1 corresponded to a perfectly straight

line, and a NGDR of 0 referred to a trajectory that

ended at the exact position as it began. When com-

paring values of NGDR, it was critical to compare

trajectories of the same length of time (or same dis-

placement) since NGDR was dependent on scale

(Tiselius 1992). Thus, to ensure unbiased results,

each copepod’s trajectory was divided into 3-s sub-

trajectories before computing the NGDR. The results

were insensitive to the selection of the period of the

sub-trajectories in the range of 1–4 s. The fourth pa-

rameter was the alignment of the trajectory with the

axis of the vortex, which corresponded to the angle

between the copepod’s heading and the axis of rota-

tion of the Burgers’ vortex. An angle of 08 indicated

the trajectory was parallel to the axis of the vortex,

whereas an angle of 908 was orthogonal. The fifth

parameter was the number of escapes per copepod

per 5 s, which provided a normalized measure of

the copepod frequency of escape. In this study, a

‘‘copepod escape’’ was systematically defined as any

instance of the copepod’s acceleration equaling or ex-

ceeding twice the mean acceleration of the copepod.

Fig. 2 Schematic of the camera and lighting arrangement (from

side perspective), as well as the region of interest (ROI) sur-

rounding the Burgers’ vortex.





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The sixth behavioral parameter was the ‘‘escape-

jump location’’, i.e., the radial distance from the

axis of the vortex to the location of an escape

jump. The seventh behavioral parameter was the

magnitude of the escape acceleration.

Statistical analysis

The copepods’ behavioral data for control-versus-

treatment cases were statistically compared using

one-way single-factor (two-level) repeat-measures

ANOVA (Zar 1999). The factor of interest was the

presence of the Burgers’ vortex or not, and the two

levels within that factor were the two replicates. The

null hypothesis, H0, was that the means of the two

datasets were equal. The replicates were nested inside

of the turbulence-level effect and tested for signifi-

cance. If there was no effect of the replicate on the

data, then the data of the two replicates were pooled.

This statistical analysis was performed on each of the

behavioral parameters introduced above. A post hoc

correction for false discovery rate was employed to

remove the potential for false significance (Type 1

error) that could result from a high number of sta-

tistical tests (Benjamini and Hochberg 1995). A two-

sample Kolmogorov–Smirnov test was performed on

each of the pairs of distributions of escape locations

(control versus treatment). To perform this analysis,

the bins of these distributions were uniformly scaled

such that they summed to one (i.e., they represented

an empirical PDF) and then converted to CDFs.

Results

Recall that the flow conditions, which were

denoted turbulence level 2 and level 3, were selected

because the behavioral data on copepods published

by Yen et al. (2008) indicated a significant change

in copepods’ motility number between their isoto-

pic turbulence-level-2 and level-3 trials. We hypoth-

esized that the change was due to a behavioral

response to the finescale structure of the turbulent

vortices.

Acartia tonsa

Turbulence-level-2 behavioral assays

Table 2 shows the behavioral parameters for A. tonsa

for the turbulence-level-2 cases: control A and B and

treatment A and B, where A and B signify the rep-

licate. Overall, the data for turbulence level 2 ap-

peared inconclusive. The relative swimming speed

and NGDR both significantly changed between con-

trol and treatment. Although the effect of the treat-

ment on these two parameters was significant, this

result was not definitive, as the replicate effect was

also significant. Neither the treatment nor the repli-

cate were significant for the escapes per copepod per

5-s period, the alignment of the trajectory with the

axis of the vortex, or the mean turn frequency. The

mean acceleration of escapes appeared to signifi-

cantly change, but only the effect of the replicate

was significant. Therefore, this statistical result was

due to the drastic difference between replicates A and

B, rather than an effect of the treatment.

Figure 4 shows the normalized histograms of

escape jump location as a function of radius. The

histograms were normalized by the effective area of

each bin: each bin represented an annulus in physical

space (hence the area was a function of radius). As

such, the histograms graphically represented the

escape jump density as a function of radial position.

Figure 4a did not show a clear preferred escape

jump location for either turbulence-level-2 control-

replicate A or B (disregarding the spike at a radius of

approximately 17.5 mm for control replicate B). This

result was to be expected; no flow was present in the

tank during the control cases; therefore there were

no hydrodynamic cues to trigger an escape jump.

Figure 4b revealed no obvious trend in the distribu-

tion of escape densities for turbulence level 2. The

results of the Kolmogorov–Smirnov tests were incon-

sistent; replicate A indicated a significant difference

(P50.05) between control and treatment and repli-

cate B showed no significant difference. Therefore,

the density of escape jumps for A. tonsa in the pres-

ence of a turbulence-level-2 vortex varied very little,

if at all, from the escape-jump density for copepods

in stationary fluid.

Fig. 3 Three examples of trajectories of Acartia tonsa swimming

in and around the turbulence-level-3 vortex. The vortex is rep-

resented by the cylinder with radius equal to the characteristic

radius of the Burgers’ vortex rB. Symbols indicate locations sep-

arated by 10 time points. Although shown on the same plot,

these trajectories were not simultaneously recorded during the

experiment. (This figure is available in black and white in print

and in color at Integrative and Comparative Biology online.)





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Turbulence-level-3 behavioral assays

The statistical analysis of A. tonsa for the behavioral

data at turbulence level 3 revealed much clearer

trends. There was a significant effect of treatment

on the relative swimming speed, turn frequency,

alignment of the trajectory with the axis of the

vortex, NGDR, and escape-acceleration parameters.

In each case, there was no significant replicate

effect (Young 2014). Neither the treatment nor the

replicate was significant for the number of escapes

Fig. 4 Normalized histograms of escape jump locations for Acartia tonsa as a function of radius for the turbulence-level-2 (a) control,

and (b) treatment, and turbulence-level-3 (c) control, and (d) treatment. The dashed line indicates the characteristic radius of the

Burgers’ vortex rB.

Table 2 Variables of swimming kinematics for Acartia tonsa for the turbulence-level-2 treatment

Parameter Control A Treatment A Control B Treatment B Treatment effect Replicate effect

F-ratio P-value F-ratio P-value

n 60 65 58 55

Relative speed [mm s�1] (SE) 4.3 (0.32) 4.7 (0.24) 2.6 (0.30) 4.1 (0.27) 11.9 0.0021* 8.8 0.0008*

Turn frequency [turn ind�1 s�1] (SE) 0.89 (0.020) 0.86 (0.015) 0.87 (0.019) 0.88 (0.017) 0.20 0.66 0.84 0.47

Alignment of the trajectory to

the axis of the vortex [8] (SE)

63.7 (1.5) 66.2 (1.1) 61.1 (1.4) 63.4 (1.2) 3.5 0.13 2.3 0.15

NGDR (SE) 0.41 (0.031) 0.65 (0.023) 0.52 (0.029) 0.62 (0.026) 38.3 0.0012* 4.2 0.039*

Number of escapes per copepod

per 5-s period (SE)

0.017 (0.00089) 0.014 (0.00086) 0.014 (0.00091) 0.014 (0.00093) 2.1 0.20 2.4 0.15

Escape acceleration [mm s�2] (SE) 206 (9.7) 180 (9.4) 149 (9.8) 191 (10.1) 0.66 0.49 8.9 0.0012*

Notes: ANOVA results are reported for the effect of treatment (i.e., treatment versus control) and replicate (i.e., A versus B). *P50.05.





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per copepod per 5-s period (Young 2014). These

findings indicated that the replicate did not signifi-

cantly affect the turbulence-level-3 dataset and there-

fore allowed pooling of the data (i.e., combining

replicates A and B).

The ANOVA results for the combined dataset are

shown in Table 3. Turbulence level 3 resulted in

clearly defined changes in copepods’ swimming kine-

matics from control to treatment. Acartia tonsa swam

substantially faster relative to the velocity of ambient

flow in the presence of the turbulence-level-3 vor-

tex (significantly greater mean relative speed of

swimming in the treatment than in the control).

They swam in a straighter path in the presence of

turbulence-level-3 vortex (significantly higher

NGDR) and turned significantly less frequently.

Further, copepods swam more orthogonally to the

axis of the vortex in the presence of the

turbulence-level-3 vortex, as seen in the increase in

mean angle of alignment of the trajectory with the

axis of the vortex. While A. tonsa did not escape

more frequently (no significant change in the

number of escapes per copepod per 5-s period),

when they did escape, they did so more powerfully,

with significantly greater escape accelerations in the

presence of the turbulence-level-3 vortex than in the

control case.

The turbulence-level-3 control case (Fig. 4c) did

not show a clear preferred escape jump location for

either replicate A or B. Again, this result was ex-

pected since no flow was present in the tank

during the control cases. Both replicates (A and B)

of the turbulence-level-3 treatment (Fig. 4d) ex-

hibited large spikes in escape jump density for

radial locations less than the vortex’s characteristic

radius, rB (i.e., closer to the core of the vortex).

The results of the Kolmogorov–Smirnov tests

revealed significant differences (P50.05) between

treatment and control for both replicates.

Temora longicornis

Behavioral assays at turbulence level 2 and level 3

Tables 4 and 5 show the behavioral parameters for

T. longicornis for turbulence level 2 and level 3, re-

spectively. The majority of the data revealed a signif-

icant replicate effect, which indicated that differences

in behavior, if any, were not repeatedly observed.

The one exception was relative swimming speed for

turbulence level 2. In that case, relative swimming

speed increased significantly from control to treat-

ment, and there was no significant replicate effect.

Figure 5 shows the normalized histograms of

escape jump locations. More variability (both spa-

tially and between replicates) was observed in the

escape density for the control cases for T. longicornis

(compared with A. tonsa). However, again no trend

was observed, as was expected, since the control case

had no flow present (Fig. 5a, c). For the turbulence-

level-2 treatment (Fig. 5b), the histogram again did

not have an obvious peak in escape density, and the

replicates showed substantial variability. The results

of the Kolmogorov–Smirnov tests revealed no signif-

icant differences between treatment and control for

both replicates for turbulence level 2. For the turbu-

lence-level-3 treatment (Fig. 5d), the largest escape

densities were observed for radial locations less than

rB, although there was substantial variability between

replicates and the peaks were not as substantial as

observed for A. tonsa (Fig. 4d). The results of the

Kolmogorov–Smirnov tests for turbulence level 3

were inconsistent; replicate B indicated a significant

difference (P50.05) between control and treatment

and replicate A showed no significant difference.

Table 3 Swimming kinematics variables for Acartia tonsa for the pooled turbulence level-3-treatment (i.e., combining replicates A

and B)

Parameter Control Treatment Treatment effect

F-ratio P-value

n 114 126

Relative speed [mm s�1] (SE) 3.4 (0.51) 6.7 (0.50) 7.8 0.0006*

Turn frequency [turn ind�1 s�1] (SE) 0.90 (0.011) 0.87 (0.011) 3.0 0.04*

Alignment of the trajectory to the axis of the vortex [8] (SE) 62.1 (0.71) 65.8 (0.69) 6.1 0.0012*

NGDR (SE) 0.42 (0.018) 0.59 (0.017) 16.0 0.0003*

Number of escapes per copepod per 5-s period (SE) 0.015 (0.0006) 0.015 (0.0006) 1.4 0.23

Escape acceleration [mm s�2] (SE) 199 (10.0) 247 (9.6) 4.8 0.005*

Notes: P-values are reported for the effect of treatment (i.e., treatment versus control). *P50.05.





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Discussion

Acartia tonsa

Acartia tonsa exhibited strong changes in swimming

kinematics and escape behavior in the presence of

the turbulence-level-3 vortex (Table 3). As summa-

rized in Table 6, A. tonsa increased relative speed of

swimming, angle of alignment with the axis of the

vortex, NGDR, and escape acceleration, as well as

decreased turn frequency, when in the presence of

a turbulence-level-3 vortex (relative to control).

These specific changes in swimming kinematics effec-

tively moved the copepod away from the core of the

vortex (i.e., faster, straighter trajectories aligned more

perpendicular to the axis of the vortex). Further, the

normalized histograms of escape density revealed an

increase in escape density near the region of the core

of the vortex when copepods were exposed to a tur-

bulence-level-3 vortex (Fig. 4d).

This contrasted with the observation in the pres-

ence of the turbulence-level-2 vortex. The data

showed that the replicate effect was responsible for

the variability in the turbulence-level-2 dataset, and

that the effect of the treatment itself (i.e., the presence

of the vortex) was inconclusive at best (Table 2). Also,

the normalized histograms of escape density for the

turbulence-level-2 vortex did not exhibit preferred lo-

cations of escape (Fig. 4b). Therefore, it was reason-

able to conclude that the presence of a turbulence-

level-2 Burgers’ vortex did not significantly affect the

swimming kinematics of A. tonsa.

The transition between turbulence level 2 and level

3 was consistent with our hypothesis that A. tonsa

sense hydrodynamic cues associated with turbulent

vortices and actively respond via changes in swim-

ming kinematics. As discussed further below, it also

suggested that there was a threshold hydrodynamic

cue that induced the behavioral response. It was also

consistent with the observations by Yen et al. (2008)

of a transition in swimming kinematics between tur-

bulence level 2 and level 3 (Acartia hudsonica in their

study).

Table 5 Variables of swimming kinematics for Temora longicornis for the turbulence-level-3 treatment

Parameter Control A Treatment A Control B Treatment B Treatment effect Replicate effect


n 25 35 41 24

Relative speed [mm s�1] (SE) 3.0 (0.32) 5.5 (0.28) 5.0 (0.34) 5.2 (0.33) 18.0 0.0002* 10.3 0.0003*

Turn frequency [turn ind�1 s�1] (SE) 0.76 (0.024) 0.92 (0.020) 0.90 (0.025) 0.77 (0.024) 0.26 0.61 19.7 0.0002*

Alignment of the trajectory to

the axis of the vortex [8] (SE)

68.8 (1.9) 60.9 (1.6) 56.4 (2.0) 72.0 (1.9) 4.4 0.066 20.4 0.0004*

NGDR (SE) 0.48 (0.035) 0.48 (0.030) 0.49 (0.036) 0.56 (0.036) 1.5 0.27 1.6 0.28

Number of escapes per

copepod per 5-s period (SE)

0.016 (0.0011) 0.009 (0.00089) 0.013 (0.00082) 0.018 (0.0011) 1.1 0.32 26.0 0.0006*

Escape acceleration [mm s�2] (SE) 165 (14.9) 244 (13.0) 224 (12.0) 182 (15.2) 1.8 0.25 9.5 0.0012*


Table 4 Variables of swimming kinematics for Temora longicornis for the turbulence-level-2 treatment

Parameter Control A Treatment A Control B Treatment B Treatment Effect Replicate Effect


n 30 20 46 49

Relative speed [mm s�1] (SE) 3.3 (0.25) 4.7 (0.31) 3.6 (0.29) 4.5 (0.25) 17.7 0.0012* 0.49 0.67

Turn frequency [turn ind�1 s�1] (SE) 0.84 (0.026) 0.93 (0.032) 0.84 (0.030) 0.79 (0.025) 0.38 0.65 6.3 0.016*

Alignment of the trajectory to the

axis of the vortex [8] (SE)

57.4 (2.2) 64.9 (2.7) 65.8 (2.5) 65.6 (2.1) 2.3 0.23 3.3 0.13

NGDR (SE) 0.48 (0.036) 0.57 (0.044) 0.61 (0.041) 0.63 (0.035) 2.0 0.24 3.1 0.12

Number of escapes per copepod

per 5-s period (SE)

0.012 (0.00097) 0.012 (0.0012) 0.013 (0.00079) 0.015 (0.00076) 0.58 0.60 4.1 0.07

Escape acceleration [mm s�2] (SE) 166 (11.2) 191 (13.7) 172 (9.0) 183 (8.8) 2.8 0.19 0.22 0.80






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Temora longicornis

Temora longicornis did not show a strong behavioral

response to either vortex treatment (relative to con-

trol). Among the cases in which significant differ-

ences were observed, the replicate effect was

significant for almost every case, which meant the

effect of the treatment was inconclusive at best

(Tables 4 and 5). The plots of escape density

showed a slight increase in the core of the vortex

(Fig. 5a, d), but again there was significant variability

between replicates and the response was not nearly as

clear as for A. tonsa. Thus, we concluded that T.

longicornis did not strongly respond to the presence

of either treatment, in contrast to the clear transition

described above for A. tonsa.

Yen et al. (2008) observed a significant change in

motility number between turbulence level 2 and level

3 for T. longicornis, whereas the current data did not

reveal a significant change in response to a typical

vortex for these levels. Possible explanations were

that T. longicornis was not responding to the struc-

ture of the vortex, but rather was affected by the

advection of turbulence or perhaps was responding

to another characteristic, such as unsteadiness of

flow, that the Burgers’ vortex apparatus was not rep-

licating. Further, since a turbulent flow consisted of a

broad range of vortices, it was possible that T. long-

icornis was responding to stronger vortices present in

the turbulent conditions compared with the typical

vortex that was mimicked in the Burgers’ vortex

apparatus. It would be very interesting to evaluate

behavior (particularly for T. longicornis) in a stronger

vortex in order to assess potential behavioral re-

sponses and the ability to swim relative to the stron-

ger velocities of flow.

Further, there were a number of differences be-

tween A. tonsa and T. longicornis that could help to

explain the present data. First, the setal array on the

antennae has quite different morphology. The setae

of A. tonsa extend in all directions from the antennae

Fig. 5 Normalized histograms of escape jump locations for Temora longicornis as a function of radius for the turbulence-level-2 (a)

control, and (b) treatment, and turbulence-level-3 (c) control, and (d) treatment. The dashed line indicates the characteristic radius of

the Burgers’ vortex rB .





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to form a complex three-dimensional array. The setal

array for T. longicornis is much more confined to

a single plane. Therefore, it is possible that the

three-dimensional setal array for A. tonsa was more

tuned to sense the disturbance to flow associated

with a turbulent-like vortex. Second, the style of

swimming was quite distinct between these species,

with A. tonsa swimming in a hop-sink manner and

T. longicornis swimming in a cruise fashion. Thus, it

is possible that the behavioral changes in T. longicor-

nis were more subtle and therefore more difficult to

quantify. In fact, Yen et al. (2008) observed that the

transport speed of A. hudsonica in isotropic turbu-

lence was significantly different between turbulence

level 2 and level 3, whereas there was no significant

difference in transport speed for T. longicornis.

Furthermore, although not for these specific species,

Incze et al. (2001) and Manning and Bucklin (2005)

showed considerable variability in the vertical distri-

butions among species of copepods; hence, it was not

too surprising to observe a difference between species

in the present data.

Hydrodynamic cue inducing escapes

It was desirable to quantify the hydrodynamic cue

that triggered the dramatic increase in escape density

in the core of the vortex for A. tonsa at turbulence

level 3 (Fig. 4b). The most likely hydrodynamic cues

that could trigger an escape response were: circum-

ferential velocity u�, shear strain rate er�, maximum

principal strain rate (MPSR), and vorticity !x , since

these were the primary parameters of flow that vary

with radial position for a Burgers’ vortex (Fig. 6). It

was interesting to note that relative swimming speed

is in the range of 3–6 mms�1 (Tables 2–5) and the

maximum velocity of flow (3.9 mms�1) was a very

similar value in Fig. 6a. The similarity in swimming

speed and flow velocity suggested that for these

conditions copepods were likely able to propel them-

selves relative to the motion of the fluid.

Circumferential velocity u� was unlikely to be the

trigger for an escape response for two reasons. First,

the magnitude of u� was already quite high as the

copepod approached the center of the vortex; u�gradually increased to its peak value as the copepod

moved from peripheral radial positions inward

(Fig. 6a). In fact as a copepod moved radially

inward, u� was already decreasing after passing the

location of maximum u�. Therefore, if one assumed

that the copepod had a threshold sensitivity to the

magnitude of u�, the threshold would be met for a

radial distance greater than rB (unless the threshold

magnitude of u� was exactly ðu�Þmax for the turbu-

lence-level-3 vortex—a very unlikely event). Second,

prior results by Haury et al. (1980), Fields and Yen

(1997), Kiørboe and Visser (1999), and Kiørboe et al.

(1999) all indicated that quantities related to veloc-

ity-gradient, such as strain rate, were the least vari-

able in eliciting an escape response from copepods.

Neither MPSR nor er� were good candidates for

triggering the escape behavior of A. tonsa seen in the

Burgers’ vortex treatment. MPSR was constant in the

near-the-vortex-core region (due to the constant rate

of axial strain), increased to a maximum value at a

radial position slightly greater than rB, and decreased

back to the same constant value (as the near-the-

vortex-core region) at peripheral radial positions

(Fig. 6b). The shear-strain rate, er�, was zero at the

axis of the vortex, increased to a maximum value at

a radial position greater than rB, and decreased back

to zero at peripheral radial positions (Fig. 6b).

Similar to the reasoning for u�, if one assumed

that copepods had a threshold sensitivity to MPSR

or to magnitude of er�, the threshold would be met

for radial locations greater than rB.

The most likely hydrodynamic cue for triggering

the escape behavior seen in these Burgers’ vortex

treatments was vorticity. Vorticity was zero far

from the core of the vortex, and began to rise at a

distance of approximately 2rB away from the axis of

the vortex (Fig. 6b). As a copepod approached a

distance rB away from the core, the vorticity in-

creased rapidly, until the vorticity peaked at the

axis of the vortex (Fig. 6b). Therefore, the locations

of the peak in vorticity and strain rate (both er� and

MPSR) were spatially segregated in the Burgers’

vortex flow, and the peak in vorticity was co-located

with the location of increased escape density by

A. tonsa (Fig. 4d). Further, the magnitude of vortic-

ity was substantially larger than the magnitude of

either strain-rate parameter (Fig. 6b). To our knowl-

edge this was the first direct observation of vorticity

Table 6 Behavior of Acartia tonsa in presence of a turbulence-

level-3 vortex during treatment in comparison to behavior under

control conditions

Relative speed "*

Turn frequency #*

Alignment of trajectory

to the axis of the vortex

"*

NGDR "*

Number of escapes

per copepod per 5-s period

No change

Escape acceleration "*

Notes: Indicators marked with an asterisk (*) are considered signifi-

cant (P50.05).





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inducing an escape response, although in many pre-

vious treatments the location of peaks (or variation)

in vorticity and strain rate was co-located. It is im-

portant to appreciate that vorticity (through the ro-

tation tensor) and strain rate both are components

of the velocity-gradient tensor; hence, they both

relate to spatial gradients of velocity. Therefore, if

copepods could sense the differential velocity associ-

ated with strain rate using their setal array, then they

similarly should be able to sense the differential ve-

locity associated with vorticity.

There was a substantial difference in the magnitude

of the vorticity for turbulence level 2 and level 3. For

the turbulence level 2, the peak vorticity equaled

1.0 s�1 in comparison to the peak value of 2.7 s�1

for turbulence level 3 (Fig. 6d). This suggested that

the threshold for inducing an escape response by A.

tonsa was in this range due to the change in escape

density between treatments (Fig. 4). As discussed

above, the lack of significant response for T. longicor-

nis in these treatments may indicate that a larger

threshold was required to induce a response, possibly

because the more planar morphology of their setal

array had poorer sensitivity to vorticity. In their

thin-layer mimic, Woodson et al. (2005) reported a

threshold for shear strain rate that was nearly identical

for these species: 0.035–0.06 s�1 for A. tonsa and 0.03–

0.06 s�1 for T. longicornis. Hence, the setal array of

both species may be effective at sensing a simple

two-dimensional shear flow, but the magnitude of

vorticity was much larger in Fig. 6 for the turbu-

lence-level-3 vortex, which suggested reduced sensitiv-

ity of A. tonsa to fluid rotation (i.e., vorticity)

compared with a simple two-dimensional shear flow

(i.e., shear strain rate). Further, sensing vorticity

required quantifying two orthogonal gradients in ve-

locity (i.e., vorticity in Cartesian coordinates is given

by !z ¼@v@x �

@u@y). Shear strain rate is given by the ex-

pression exy ¼12

@v@x þ

@u@y

� �(again in Cartesian coordi-

nates). While this expression includes the same spatial

derivatives of velocity (as the vorticity expression), in

the case of the thin-layer mimic of Woodson et al.

(2005), the term @v@x was extremely small. Hence, sens-

ing shear strain rate in the thin-layer mimic required

only sensing @u@y. Returning to the Burgers’ vortex, in

order to respond to vorticity the copepod must sense

both @v@x and @u

@y (or another pair of orthogonal velocity

gradients) accurately enough to perform the difference

and hence sense the local rate of fluid rotation. The

results here suggested that the three-dimensional setal

array of A. tonsa may be much more suited to the

task of sensing vorticity compared with the more

planar array of T. longicornis. This conclusion was

logically consistent with the morphology of the

arrays, since the three-dimensional setal array would

presumably be geometrically arranged in ways that

sensed orthogonal gradients in velocity (i.e., setae sep-

arated in two orthogonal directions), whereas the

planar array would not (i.e., setae separated in only

one direction).

Acknowledgments

The authors gratefully acknowledge the financial sup-

port of the National Science Foundation [OCE-

0928491 and DUE-1022778]. Thanks to Nerida H.

De Jesus Villanueva, Jennifer Young, John Jung,

Yichao Qian, Briana Corcoran, Julia Wang, and

Dorsa Elmi for help with the copepod-tracking analysis.

Fig. 6 Radial profiles of (a) velocity u�, (b) shear strain rate jer�j, MPSR, and vorticity !x. Values of parameters are equal to those for

the turbulence-level-3 treatment (shown in Table 1). The dashed-double-dotted line indicates the characteristic radius of the vortex rB.





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Thanks to Rachel Lasley-Rasher for collecting copepods

in the field.

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