the hydrodynamics of chemical cues among aquatic...

ANRV365-FL41-05 ARI 12 November 2008 18:19

The Hydrodynamics ofChemical Cues AmongAquatic OrganismsD.R. Webster1 and M.J. Weissburg2

1School of Civil and Environmental Engineering and 2School of Biology, Georgia Instituteof Technology, Atlanta, Georgia 30332; email: [email protected]

Annu. Rev. Fluid Mech. 2009. 41:73–90

First published online as a Review in Advance onJune 3, 2008

The Annual Review of Fluid Mechanics is online atfluid.annualreviews.org

This article’s doi:10.1146/annurev.fluid.010908.165240

Copyright c© 2009 by Annual Reviews.All rights reserved

0066-4189/09/0115-0073$20.00

Key Words

chemical transport, chemical cue structure, biological-physical interactions

AbstractChemical cues mediate many critical life processes, such as feeding, re-production, and benthic settling, for aquatic organisms. Depending on thefluid velocity and flow regime, released chemicals are transported via dif-fusion, laminar advection, or turbulent advection prior to organism recep-tion. Here, we review transport mechanisms and ecological consequences ineach regime. We discuss cue structures in terms of concentration gradients,concentration fluctuations, and spatial patterns and draw conclusions aboutstrategies that animals use to acquire information. In some cases, chemicaltransport occurs through a combination of mechanisms, which requires amultiscale analysis. Regime and scaling are major themes that emerge fromrecent research. In particular, nondimensional parameters that combine bi-ological and physical variables reveal general principles under which organ-isms respond to chemical cues and facilitate defining regimes of behavior.

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Chemical signals:chemical stimuluspatterns shaped by thetransmitting organismto enhance itsinformation-transmitting function(e.g., pheromoneplumes)

Chemical cues:patterns of chemicalconcentrationresulting fromincidental release andtransmission (e.g.,plumes of wastemetabolites used bypredators to find prey)

1. INTRODUCTION

Dissolved chemicals are ubiquitous in aquatic habitats and provide a major source of informationfor animals immersed in water. Studies of marine and freshwater organisms have shown that nearlyevery critical activity in the life of an animal can be regulated by the perception of chemicals(Hay 1996, Zimmer & Butman 2000). Water-borne chemicals initiate feeding behaviors andplay large roles in determining food choice (Hay 1996, Zimmer-Faust 1989), and organisms(including single cells, zooplankton, snails, urchins, crustaceans, and fish) find food using chemicaltrails or plumes (Koehl 2006, Weissburg 2000). Reproductive processes such as recognizing orlocating potential mates also are mediated frequently by water-borne chemicals (e.g., Doall et al.1998, Hardege et al. 1996). Organisms use chemicals to detect and recognize dominant versussubordinate individuals (Breithaupt & Atema 2000, Gherardi & Daniels 2003). Other processescontrolled by water-borne chemicals include predator avoidance (Covich et al. 1994, Zimmer et al.2006), chemical defense (Larsson & Dodson 1993), habitat choice (Gerlach et al. 2007, Pawlik1992), and sibling and individual recognition (Bronmark & Hansson 2000, Gherardi et al. 2005).All these chemically mediated processes directly affect individuals and indirectly affect organismpopulations, community organization, and overall ecosystems.

An attempt to understand chemically mediated processes must consider fluid properties andflow because the fluid environment determines the spatial and temporal patterns of dissolved chem-ical concentration (Weissburg 2000). Meaningful patterns can result from incidental transmission(e.g., the release of waste or metabolic by-products), which are referred to as cues (Dusenbery1992). Alternatively, the term signals refers to those patterns resulting from deliberate release,although it is sometimes used synonymously with cues. Regardless of the intent of the releasingentity, the specific spatial and temporal patterns critically mediate interactions. As a result, therehas been increasing dialogue between researchers in fluid mechanics and biology as we attempt todetermine where, when, and how animals use chemical cues to regulate behavior and physiologicalprocesses. Further progress will require a broadening and deepening of these collaborative efforts.

Describing the hydrodynamics of chemical cues is challenging because chemical signal trans-mission involves physical processes, biological processes, and their interaction. The large sizerange of organisms (micrometers to meters) that respond to chemical cues combined with thelarge range of flow and movement speeds means that diffusive, advective, and turbulent transportmechanisms are relevant. For the purposes of this review, we describe small organisms as thoseless than 0.1 mm, large organisms as those greater than 10 mm, and medium-sized organisms asthose between the two ranges. Unicellular organisms, gametes (i.e., sperm and eggs), and smallplanktonic organisms generally exist in a regime in which diffusion or laminar advection is the pre-dominant transport process that establishes the odorant field occurring around an egg, potentialmate, or sinking food particle. Large creatures follow turbulent plumes (on the scale of centimetersto meters) emanating from a point source in flows that are often unpredictable in time and space.At even larger scales, a homing salmon may follow the chemical signature from its birth streamfor many kilometers to reach its breeding site (Dittman & Quinn 1996). Furthermore, chemicalcues may be transported and shaped by multiple transport modes (e.g., turbulent advection atrelatively large scales between or surrounding organisms and laminar advection at smaller scalesin the vicinity of sensory organs).

Our goal in this review is to summarize recent progress in understanding hydrodynamicprocesses that influence chemically mediated biological interactions. We concentrate on char-acteristics of the overall flow environment that lend insight to the chemical cue structure, cuetransmission, and the resulting influence of fluid mechanics processes on organismal and ecologicalproperties.

74 Webster ·Weissburg

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2. TRANSPORT OF CHEMICAL STIMULI

Figure 1 describes the basic steps in chemically mediated interactions. Chemicals are releasedby the transmitting entity, transported through the fluid medium, and ultimately received byan organism that produces a physiological or behavioral response. The specific metabolites thatmediate such interactions often are unknown, and their presence and transport are generallyassumed based on responses of the receiver. Chemicals that induce responses include highly solublecompounds, such as amino acids, proteinaceous compounds, nucleic acid–related compounds,glycerolipids, and pheromones (Carr 1988, Dusenbery 1992). Diffusivity in water for moleculesof this size is typically of the order of 10−5 cm2 s−1 (e.g., Lide 2008, Yen et al. 1998).

Recent advances in the ability to couple the analysis of cue structure with observations of animalresponses have led to a new appreciation of the link between flow physics and organism ecology.The transmission and delivery of chemical cues are controlled by flow physics, and the mode oftransport is dictated by a combination of Reynolds number,

Re = ρULμ

= ULν

, (1)

and Peclet number,

Pe = UL�

, (2)

where U is the characteristic velocity; L is the characteristic length; ρ is the fluid density;μ and ν are the dynamic and kinematic viscosities, respectively; and � is the molecular dif-fusivity. Molecular diffusion is the dominant transport mode in the absence of fluid motion(Figure 1a). Fluid motion for small values of Re (i.e., order of 100 and smaller) indicatesthat the flow is laminar and transmission is characterized by advective transport (Figure 1b).Large values of Re (note that the transition Re is case dependent) denote a regime in whichthe flow is turbulent, leading to random fluctuations of chemical concentration, with the pat-tern becoming an important aspect of the cue (Figure 1c). Analogously, the value of the Pecletnumber distinguishes the diffusion-dominated transport regime (small Pe) from the advection-dominated transport regime (large Pe). Understanding transport is critically important for in-terpreting behavioral or physiological responses to the chemical cue because the transportprocess greatly influences the spatial and temporal patterns of the chemical concentrationfield.

2.1. Diffusion

Chemicals in a motionless fluid environment are transported via molecular diffusion. Assumingthat transport is described by Fickian diffusion, for which flux is proportional to the concentrationgradient (i.e., q = −� ∇c ), the equation that describes diffusive transport is

∂c∂t

= � ∇2c , (3)

where c is the concentration of the chemical solute.For Re < 10−3, chemical transport from the surface of individual cells is dominated by diffusion

because diffusive timescales are less than advective timescales. Hence, local stirring is ineffective.In the context of nutrient uptake, a minimum cell radius of 20 μm is needed before motionsubstantially increases the chemical flux. Organisms smaller than this limit cannot increase uptakeby moving (Karp-Boss et al. 1996), but they can increase chemical flux by increasing cell radius ordecreasing surface concentration.

www.annualreviews.org • Chemical Cues Among Aquatic Organisms 75

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Release of chemicals

Types:Waste productsLeaking chemicalsPheromones

BehavioralPhysiological

Responses

Transport modes

a Diffusionb Laminar advectionc Turbulence

Cue characteristics

Chemical compoundsConcentration levelConcentration spatial patternConcentration temporal pattern

a

c

b

Reception

Diffusive transport (no motion, Re and Pe << 1).Cue structure is characterized by slowly evolving,smooth concentration gradients.

Laminar advection (Re < order of 100).Cue structure is characterized by small-scale spatialand temporal concentration gradients and can beaffected by flow unsteadiness.

Turbulent advection (Re >> 1). Cue structure is characterized by chaotic spatial and temporal distributions ofconcentration filaments. The time-averaged field or filament properties are often inaccessible to the receiver.

Odorantfilaments

Flow path

Figure 1Mechanisms of chemically mediated interactions among aquatic organisms and their implications forrelevant signal structures. Examples of transport modes include (a) diffusion of a pheromone around a smallspherically shaped organism, (b) laminar advection through a lobster’s aesthetascs array, and (c) turbulentplume tracking of prey by a shark.


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Low High

Concentration field:

t5t4t3t2t1

t5

t6

t4t3

t2

t1

t3t2t1

S1S2

Kinesis: Undirected responses that dependon the intensity of the stimulus cue.

1

Orthokinesis: Indirect guiding in which thespeed of movement from time 1 (t1) to time2 (t2) depends on the intensity of the cue.

a

Klinokinesis: Indirect guiding viasequential sampling. In the example shown,the length of path before the next turndepends on the change in concentration.The turn direction is not correlated with thecue pattern.

b

Taxis: Orientation with respect to thegradient in stimulus cue.

2

Klinotaxis: Directed response to sequentialsamples of the cue pattern. Requires theability to remember the previous sample.

a

Tropotaxis: Directed response based onsimultaneous spatially separated samples(S1 and S2) of the cue pattern. Requiresmultiple sensors and comparison amongsensors.

b

Figure 2Classification of guidance mechanisms in an odorant field. Kinesis occurs typically in smoothly varyingchemical gradient fields, whereas taxis occurs in a variety of cue environments.

Chemoklinokinesis:an indirect guidingmechanism through achemicalconcentration field viasequential sampling

Dusenbery & Snell (1995) similarly analyzed pheromone transport from small spherical or-ganisms. An individual’s search rate for its mate depends on organism radius to the seventh powerlargely because of the diffusive rate of transport of pheromone molecules. Hence, the detectabilityand usefulness of pheromone release are strongly dependent on cell size. Pheromone release doesnot provide increased advantage for mate location below a critical size limit of 0.2–5 μm, whichis consistent with observations on organism behavior.

Small organisms also exploit gradients in chemical concentration to locate food via guidingmechanisms (Figure 2). For instance, phytoplankton leak organic matter into solution, creatinga high-concentration region around the organism, thereby allowing bacteria to employ chemo-klinokinesis to locate the resource for feeding (Blackburn et al. 1998, Thar & Fenchel 2001).Chemoklinokinesis is a process of stimulus-induced movement in directions that are not cor-related with the direction of the concentration gradient (Figure 2) (Dusenbery 1992). In thiscase, bacteria maintain motion in a straight line for longer periods when sensing an increasein concentration, and alternatively, they more frequently shift to randomly directed move-ment when sensing a decrease in concentration. Other small organisms such as ciliates (Verity1988) and spermatozoa (Crenshaw 1996) also respond to chemical cues with attractive behavior.Spermatozoa of the purple-spined sea urchin, Arbacia punctulata, orient through a concentrationgradient using a helical klinotaxis strategy that is particularly effective because it requires only thatthe angle between the direction of translation and rotation be controlled by the stimulus intensity(Crenshaw 1996). Medium-sized organisms, such as nematodes, also use chemoklinokinesis toorient in chemical gradients (Pierce-Shimomura et al. 2005).


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Dusenbery (1997) found that organism size influences the ability to orient to chemical gradi-ents, with a size greater than 0.58 μm needed to effectively employ a spatial comparison. Similarly,when employing sequential temporal comparisons, one finds that a minimum size of 0.65 μm isrequired for effective orientation. These thresholds represent a size limit below which locationvia chemosensation is not beneficial owing to physical constraints. The difference in thresholdestimates results from the assumption that the time available to determine the stimulus directionis limited by Brownian motion, whereas the resolution of instantaneous spatial comparisons isconstrained by the scale of the organism relative to the concentration gradient. Dusenbery (2003)noted that in addition to the advantages of larger span, increased size confers benefits by facili-tating more numerous and larger sensors. In the context of two-dimensional orientation, spatialcomparisons are the distinctly superior strategy, whereas elongated shapes with temporal com-parison are most effective when organisms in the micrometer range orient in three dimensions,owing to improved signal-to-noise ratio (Dusenbery 2003).

2.2. Laminar Advection

Fluid motion, via movement of the organism or of the surrounding fluid, adds the advective fluxof solute (i.e., q = uc − � ∇c ). At low Re, the flow is laminar, and transport is described by theadvection-diffusion equation

∂c∂t

+ u · ∇c = � ∇2c . (4)

Phytoplankton larger than 20 μm can increase nutrient flux to their surface by swimming orsinking and hence inducing relative fluid motion (Karp-Boss et al. 1996). Typical Re for thesephytoplankton during such motion is less than 1. The concentration distribution at low Pe isgoverned by molecular diffusion near the organism surface and is more sensitive to morphologicalfeatures as the Pe increases. These features, such as spines and horns, influence the flow patternand magnitude of advective transport. Similarly, motion in the fluid surrounding the organismincreases nutrient transport and uptake and ultimately enhances the organism’s growth rate (Shortet al. 2006, Warnaars & Hondzo 2006). In either case, the Sherwood number (Sh = hL

ρ�, where

h is the overall mass transfer coefficient) describes the ratio of flux in the presence of motionto purely diffusional flux and provides a measure of transport enhancement due to relative fluidmotion.

Kiørboe et al. (2001) performed numerical simulations around spherical particles for Re < 20to gain a better appreciation of the chemical distribution and transport. A sinking particle (e.g.,live or dead organism, organic particle) leaves a long, slender plume in its wake. For example, fora 0.5-cm-diameter sinking particle, the wake region defined by concentration levels exceeding abiologically relevant threshold extends for 80 cm behind the particle and lasts for 13 min after theorganism passes in still water. Chemotactic bacteria may utilize the presence of chemicals in thewake plume to locate the odorant source via chemoklinokinesis ( Jackson 1989). The persistencetime period and spatial extent of the cue in comparison to scales of the searcher mediate the successof locating prey. Furthermore, Kiørboe & Thygesen (2001) found that the threshold required toexplain the detection of sinking aggregates via chemosensation of the wake plume was consistentwith the reported chemosensitivity of zooplankton, supporting the conclusion that the cue ischemical rather than hydromechanical.

Jumars et al. (2002) noted that flow unsteadiness influences chemical transport at low Reynoldsnumber and is potentially important to suspension feeding, prey detection and capture, and fer-tilization. Sources of unsteady flow motions at low Reynolds number include periodic beating ofappendages, interaction with neighboring organisms, and turbulent motion in the surrounding


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x (cm)

2.02.5

3.03.5

4.04.5

5.0

y (cm)

4.04.5

5.05.5

6.0

z (cm)

6.5

7.0

7.5

8.0

8.5

9.0

9.5

10.0

10.5

11.0

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

Male startposition

Female startposition

Matingstarts

Trackingstarts

Male swimming

speed (cm s-1)

Figure 3The mate-tracking trajectory of the male copepod Temora longicornis, which has a body length ofapproximately 2 mm, is shown via the thick line, with the color indicating swimming speed. The trajectory ofthe female, which is coincident with her pheromone trail, is illustrated by the thin black line. Maleswimming speed increases after contacting the female trail, and his path accurately follows the femaletrajectory. Data courtesy of Jeannette Yen.

Chemotaxis: directedorientation through achemicalconcentration field viaeither spatial ortemporal sampling

environment. For instance, unsteady fluid motion induced by oscillating propulsion enhanceschemical transport to organisms (Magar & Pedley 2005). Similarly, organisms with spheroidshapes rotate periodically in a simple shear flow, which induces an unsteady flow motion sur-rounding the organism (Karp-Boss & Jumars 1998, Koehl et al. 2003) and ultimately influencesthe rate of chemical transport to the organism (Pahlow et al. 1997).

Medium-sized organisms also communicate with chemicals transported via laminar advective-diffusive processes. Copepods are aquatic crustaceans that exist in many sizes but typically are inthe range of 0.1–10 mm. Male copepods detect and follow the chemical wake plume of females viachemotaxis (Figure 3) (Doall et al. 1998, Tsuda & Miller 1998, Weissburg et al. 1998). Chemotaxisis defined as finding a source as a result of movement oriented with respect to the concentrationgradient (Figure 2) (Dusenbery 1992). Male Temora longicornis can track successfully the wakeplume for up to 10 s after the female passes, and they initiate tracking for females up to 34 mmaway based on chemically sensing the wake plume (Doall et al. 1998). A key aspect is that thechemical wake plume retains a high concentration of female scent in an isolated region for longperiods owing to slow diffusive spread and dilution in the laminar regime (typically Re < 10 forcruising copepods) (Yen et al. 1998).


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Aesthetascs: a majorand well-studied classof hair-likechemosensors foundon the antennules ofcrustaceans

Leakiness: aparameter thatcharacterizes the effectof the physicalpresence of the hairson the volumetric flowrate through a hairarray

The female’s morphological and kinematic properties determine the chemical structure of thetrail. Bagøien & Kiørboe (2005) observed wake-plume-tracking behavior in male Centropages typicusand quantified plume length and width via a simple plume model. They observed that the plumewas narrower for a faster swimming female, whereas the plume length was independent of femaleswimming speed. This observation is consistent with those of T. longicornis males, which move moreslowly and display more chaotic paths when tracking slowly swimming females compared withmales tracking swiftly swimming females (Doall et al. 1998, Weissburg et al. 1998). Alternatively,female Oithona davisae copepods create a plume with odorant gaps owing to intermittent jumpsin swimming speed (Kiørboe 2007). Consequently, males of this species perform local searchbehaviors to bridge gaps between odorant segments. Similar relationships between swimmingkinematics and chemical cue patterns exist in other copepod species (e.g., Pseudocalanus elongatus)(Kiørboe et al. 2005).

Laminar advective-diffusive transport is also important for large aquatic organisms, particu-larly for the transport of chemicals through the boundary-layer flow surrounding chemosensoryappendages. Most large crustaceans, including lobsters (Gleeson et al. 1993), stomatopods (Meadet al. 2003), and crayfish (Humphrey & Mellon 2007), flick their antennules to sample the chemicalenvironment in a process that is analogous to sniffing. This chemosensory appendage is composedof dense tufts of aesthetascs, which are hair-like structures that contain chemosensory receptors(Gleeson et al. 1993). Fluid motion is inhibited by the dense morphology; hence antennule flick-ing is critical to reduce boundary-layer thickness and increase chemical transport to the sensitiveorgan. The typical Re range for hairs during the flick is 10−4 to 10, hence in the laminar advective-diffusive regime (Koehl 1996).

Koehl (1996) defines the leakiness of the array of hairs as the ratio of the volumetric flowrate through an array to the ideal volumetric flow rate if the hairs did not influence the velocitydistribution. Increased leakiness due to flicking may help increase the transport of chemicals to theaesthetascs, but it moves chemical filaments through the region rapidly, hence limiting the timeperiod in which diffusion can act to transport chemicals transversely across the boundary-layerflow. Koehl (2001) observed that for a given array of hairs, there is a transition from nonleakyto leaky flow behavior as Re increases. Animals appear to take advantage of this transition byperforming an asymmetric stroke sequence. A rapid down stroke with relatively large Re and highleakiness flushes out the old water sample and replaces it with a new sample. The return stroke isslower (lower Re and lower leakiness), which traps the new water sample in the hair array and allowssufficient time for diffusive transport to the surface (Stacey et al. 2002). The velocity gradient nearthe hairs, the morphology of the hair array, and the orientation during the flick also criticallymediate the transport process (Gleeson et al. 1993, Koehl 2001).

Laminar advection also characterizes internal transport in fish noses. Cox (2008) summarizes avariety of evidence that fish use both externally and internally generated flows to enable adequaterates of odorant delivery to olfactory sensors. Re varies from approximately 0.02 to 5, whereasPe ranges from 20 to 3000. Bulk fluid flow dominates the delivery of odorants to the region ofolfactory sensors, and diffusive transport to the substrate is enhanced by relatively steep boundary-layer profiles in the olfactory organ, particularly when flows are produced by ciliary movements.

2.3. Turbulent Transport

For larger values of Reynolds number, the flow is turbulent, and the flux of solutes is additionallyinfluenced by advective transport owing to velocity fluctuations. In a time-averaged perspective,the additional turbulent flux of solutes is quantified by the covariance of velocity and concentration(q = u c − � ∇c + u′c ′, where the overbar notation indicates time averaging). The time-averaged


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concentration field is described by the Reynolds-averaged advection-diffusion equation:

∂c∂t

+ u · ∇c = � ∇2c − ∇ · (u ′c ′), (5)

where c ′ and u ′ are the instantaneous fluctuations relative to time-averaged values of concentrationand velocity, respectively (i.e., c = c + c ′ and u = u + u ′). Equation 5 retains the unsteady termto allow for temporal variation over periods much longer than turbulent timescales. AlthoughEquation 5 can provide insight into the time-averaged concentration field, we stress that many ofthe examples discussed in this section reveal the importance of unsteady turbulent stirring processesand instantaneous turbulent concentration fields for chemical cues and organism interactions. Theinstantaneous concentration field is described by the advection-diffusion equation (Equation 4)with a velocity field that varies unpredictably in both time and space.

Chemical cue transport among the small and medium-sized organisms discussed above canbe affected by ambient turbulence. For example, ambient turbulence enhances mass transport tocells, such as diatoms or Escherichia coli (Hondzo & Al-Homoud 2007, Karp-Boss et al. 1996).Furthermore, the chemical plume in the wake of a small sinking particle is mixed into the sur-rounding fluid by turbulence despite the low Reynolds number of the flow around the particle.Ambient turbulence breaks the plume into discrete segments. The plume length, volume, andcross-sectional area are controlled by the product of the average turbulent shear rate and thediffusive timescale (Visser & Jackson 2004). The resulting plume characteristics influence the en-counter rates of organisms and the ability of organisms to orient in the wake plume to locate thesource particle.

Koehl et al. (2007) provide an example of the effects of turbulent stirring processes on smallorganisms, specifically the importance of incorporating unsteady spatial distributions to analyzeorganism behavior. In this case, larvae encountering filaments of chemical inducer quickly stopswimming and sink, but rapidly resume swimming upon exiting these filaments. Modeling this sce-nario predicts lower larval settling rates in a turbulent reef flow compared with the overestimateproduced by considering the time-averaged concentration field. This occurs because the rapidresponses to small-scale filamentous structure do not result in consistent downward movementsproduced in time-averaged fields, and larvae may consequently be advected out of the settlementregion before they encounter the substrate. In another modeling effort, Crimaldi & Browning(2004) simulated stirring of two scalar quantities, representing sperm and eggs, by idealized vortexflows. The unsteady stirring process theoretically creates sufficient spatial coincidence of con-centrated filaments at intermediate timescales, which explains observed fertilization rates betterthan a time-averaged diffusion modeling approach. Riffell & Zimmer’s (2007) recent work furthersuggests that sperm behavior and the ability to swim relative to the surrounding (turbulent) flowalso are critical determinants of chemically mediated fertilization success.

Large organisms often inhabit regions in which turbulence is present in the ambient flow, andthe Re of the flow around the organism is often supercritical. A commonly studied chemicallymediated process in turbulent flows is a forager’s tracking of an odorant plume to locate prey. Thephysical configuration typically consists of a point source of odorant located in a benthic bound-ary layer. The flow transports chemical compounds downstream while turbulence stirs and mixesconcentration filaments to expand the plume and dilute the concentration. The result is a com-plex spatial and temporal pattern of concentration called a turbulent odorant plume (Figure 4)(Crimaldi et al. 2002, Webster et al. 2003). Within the plume, fine filaments of odorant con-centration are separated by unscented fluid. From a sequential sampling perspective at a singlelocation, the concentration record is highly fluctuating with intermittent bursts of large concen-tration (Finelli et al. 1999). Crimaldi et al. (2002) noted that the combination of the time average,


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Distance from source (cm)

Dis

tan

ce f

rom

ce

nte

rlin

e (

cm)

40 60 80 100 120

–20

–10

0

10

20

0.014 0.018 0.025 0.033 0.044 0.060 0.079 0.110 0.140 0.180 0.250 0.900Flow c /Co:

Figure 4Overhead perspective of the concentration field measured via laser-induced fluorescence in the region surrounding an actively trackingblue crab, Callinectes sapidus. The plane shown is at a height near the crab antennules, 5.5 cm above the bed. Crabs use cues in theturbulent odorant plume to rapidly track upstream to the source (less than 30 s to track 1.5 m) with a high degree of success (75%success rate for the plume shown).

variance, and intermittency factor provides a meaningful measure of the instantaneous plumestructure, whereas they fail individually.

Many organisms track successfully through a turbulent odorant plume (often in a benthicboundary layer) despite the intermittent and spatially unpredictable concentration field (Figure 4).These organisms include lobsters (Horner et al. 2004, Moore et al. 1991), blue crabs (Weissburg& Zimmer-Faust 1994), crayfish (Hazlett et al. 2006, Kozlowski et al. 2003), nautilus (Basil et al.2000), bony fish (Baker et al. 2002), sharks (Gardiner & Atema 2007), nudibranchs (Wyeth &Willows 2006), eels (Carton & Montgomery 2003), urchins (Weissburg et al. 2002), and gastropods(Ferner & Weissburg 2005). The orienting cues employed by these organisms vary by species, butwe see several themes emerge by examining the physical characteristics of the plume structure.

Observations indicate that organisms can use spatial variation in the turbulent plume to makerapid tracking decisions (Atema 1996, Keller et al. 2003, Zimmer-Faust et al. 1995). For instance,blue crabs use a spatial (bilateral) comparison of chemical cues acquired at chemosensors dis-tributed on their appendages (Keller et al. 2003). Crabs can steer relative to the plume centerlineby comparing the instantaneous concentration acquired by spatially separated sensors. Extractinginformation over a brief sampling period requires that the spatial separation of sensors is largerelative to the transverse integral length scale of the concentration field (Webster et al. 2001).Adjustable sensor spacing may be advantageous because the transverse integral length scale of theplume increases with distance from the chemical source as the plume becomes wider and morehomogeneous.

Webster & Weissburg (2001) tested hypotheses about the availability and usefulness of variouscues in the plume structure. The overarching conclusion is that the time-averaged concentrationconverges too slowly in an intermittent plume to be useful to a rapidly moving predator. Hence,


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Odor-gatedrheotaxis: directedorientation to fluidflow mediated byperception of adissolved chemicalstimulus

the sampling period required to perceive the subtle spatial variation in time-averaged quantitiesis much longer than the total tracking period for many organisms. All other cues that rely onsequential sampling, such as the average rising slope or the average shape of the concentrationburst, have the same inherent problem. Many of these quantities vary systematically with thedistance from the source location, but the extremely long sampling period required to assess themild variation is far too long for a rapidly moving organism, rendering these trends inaccessibleto the forager. Alternatively, organisms that move slowly, such as gastropods, may be able toacquire time-averaged measures of the plume structure. Hence, the relative timescale of sensoryacquisition plays a critical role in determining the usefulness of the cue structure.

Many aquatic organisms appear to combine sensory modalities to evaluate tracking cues. Forinstance, combining flow direction and chemical stimulation reliably orients an organism to anupstream odorant source. Fish and blue crabs use this strategy to move upstream when stimulatedby a desirable odor, which is called odor-gated rheotaxis (Baker et al. 2002, Keller et al. 2003,Zimmer-Faust et al. 1995). This forms the basis of a useful tracking strategy: the combinationof odor-gated rheotaxis and the spatial comparison of chemical cue intensity (Keller et al. 2003).However, organisms are clearly extracting more information from the concentration field to in-crease the success and efficiency of their search. Simple simulations of these combined strategiesin realistic odorant plumes predict some, but not all, features of animal navigation (Weissburg &Dusenbery 2002).

The physical conditions of the flow environment impact the turbulent plume structure andthe cues available to foraging organisms. Ambient flow speed and release characteristics (i.e.,height, orientation, and size) alter turbulence characteristics and the effectiveness of foraging(Finelli et al. 2000, Koehl 2006). The presence of bed roughness (Rahman & Webster 2005),emergent vegetation (Finelli 2000, Lightbody & Nepf 2006), and surface waves (Mead et al. 2003)greatly affects flow turbulence and mixing characteristics. In the case of blue crabs, increased bedroughness causes a decrease in walking speed and a decrease in source-finding success ( Jacksonet al. 2007). Concentrated odor filaments arriving at the antennules induce upstream walking, anddecreased walking speed results from a reduced number of these filaments. The steering abilityof blue crabs is less affected by bed roughness because moving to the edges of the plume enablesthem to utilize contrast across their chemosensory appendages to steer. However, the change inmixing characteristics over rough beds does not affect all organisms equally. For instance, whelks(Ferner & Weissburg 2005) and crayfish (Moore & Grills 1999) do not show diminished trackingperformance in the presence of increased turbulence intensity.

An organism’s ability to access the fine-scale turbulent structure of the chemical filamentsdepends on local flow conditions surrounding the chemical sensors. As discussed above, manyorganisms employ a flicking mechanism to draw fluid into the region of the chemosensory organs.Koehl et al. (2001) noted that fine-scale filaments are drawn into the receptor area during the rapiddown stroke, becoming only slightly blurred by the end of the stroke. The filament structure islargely maintained among the aesthetascs during the slow return stroke. Hence, the fine-scaleconcentration field structure created by turbulence in the ambient flow is transported near theantennules by laminar advection and diffusion. Preservation of these small-scale patterns poten-tially allows sensing of the turbulent chemical distribution, as long as the neural system retainsthat information at higher processing stages.

3. SCALE SIMILARITY IN BIOLOGICAL-PHYSICAL INTERACTIONS

The nondimensionalization of physical variables (e.g., Re, Pe) has revealed self-similarity thatenables the identification of general principles in fluid mechanics. In contrast, the analysis of


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Temporalintegration factor: anondimensionalparameterization ofthe samplingfrequency of anorganism relative tothe physicalenvironment

Spatial integrationfactor: anondimensionalparameterization ofthe spatial extent of anorganism’s samplingorgans relative to thephysical environment

chemically mediated biological principles often has proceeded in a case-based manner or has beenorganized along taxonomic groups (e.g., insects versus crustaceans). We suggest that the nondi-mensionalization of behavioral responses to odorant cue structure would allow easier identificationof general aspects of organism responses to chemical fields. However, identifying nondimensionalparameters is complicated because chemically mediated processes result from the relationshipbetween organism spatial and temporal sampling abilities and the spatial and temporal charac-teristics of the cue structure. Thus, relevant characterizations of the sensory environment arefunctions of both biological and physical parameters. There are relatively few successful examplesof nondimensional parameterization that characterize organism cues and behavior in relation tothe physical environment. Our purpose here is to review these few cases and inspire the reader toseek analogous parameters in future research.

Weissburg (2000) introduced the temporal integration factor as

TIF = LfUorganism

, (6)

where L is the length scale of the chemical cue, Uorganism is the animal’s relative speed, and f isthe animal’s sampling frequency. The relevant length scale is case dependent and is related to thedominant transport mechanism. For example, plume width is a relevant length scale for a largeorganism operating in a high Re environment (e.g., a crab). Alternatively, L may be the Batchelorscale for a small organism immersed in a turbulent concentration field (e.g., a larvae) or the distancecorresponding to a fixed change in stimulus concentration for a single cell organism in a smoothgradient environment. Similarly, a spatial integration factor was defined as

SIF = AL

, (7)

where A is the length span of the organism’s sensor. By identifying efficient sensing strategies inhigh and low combinations of these parameters, we can create a matrix of behavior patterns thatexplains (or predicts) behavior in the context of interactions between scale-dependent physical andbiological properties. Ferner & Weissburg (2005) employed these concepts to predict that slowlymoving gastropods may employ different sensing strategies than those of rapidly moving crus-taceans in the same chemical cue environment. By operating in a different temporal-integration-factor regime, gastropods can use time averaging, and behavioral experiments show that they oftenlocate an odorant source in environments that confuse crustaceans. Similarly, Jackson et al. (2007)employed the spatial-integration-factor concept to nondimensionalize the transverse position offoraging blue crabs relative to the width of the chemical plume in different turbulence environ-ments. The normalized position is relatively constant regardless of flow-regime characteristics;blue crabs adjust to the local plume width by moving to the plume’s edge and hence maximizecontrast among transversely separated sensors. Occupying a constant nondimensional transverseposition suggests that blue crabs employ plume-tracking strategies that fix the contrast betweensensor pairs solely as function of downstream distance from the source (i.e., effectively scaling theinfluence of the turbulence environment).

The unsteadiness of chemical transport has also received nondimensional treatment. Loudon& Tordesillas (1998) discuss the Womersley number in many biological applications, includingchemical cues:

Wo = L2

√nν

, (8)

where n is the frequency of flow unsteadiness. Transport near chemoreceptive organs duringantennule flicking is an example of an unsteady flow influencing chemical cues. Estimates suggestthat Wo is less than 1 in many chemically mediated aquatic interactions, which implies that analysis


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can proceed in a quasi-steady approach. Crimaldi & Browning (2004) also discuss timescales ofunsteadiness. In the context of the mixing of gamete patches, they define a timescale of dilution(t∗ = 8Dt

�2 , where D is the effective diffusivity and � is the distance between the sperm and eggsources). This effectively introduces a mixing timescale that can be compared with the timescaleof fertilization. Although the authors did not include biological aspects in the modeling effort,they argue that fertilization may occur at intermediate timescales when dilution is minimal andthe patches spatially overlap.

In the context of foraging to an isolated patch, Grunbaum (2002) defined the Frost number as

Fr = U 2organismτT

L2, (9)

where τ is the interval between turns; and L and T are the length scale and timescale of theresource (chemical) patch, respectively. The combination of biological and environmental variablesin the Frost number indicates whether foragers can locate patches of certain characteristics. In thecase of Fr � 1, foraging movement is rapid across the resource distribution, and the patch isavailable to the forager. Alternatively for Fr � 1, the patch is relatively distant or ephemeral;hence the patch is unavailable to the forager. Gallager et al. (2004) examined a similar issue: theability of an animal to respond to chemical (and other resource) patches. They defined the motilitynumber, which parameterizes the ability of plankton to swim independent of ambient fluid motion:

Mn = Uswim

q, (10)

where Uswim is the plankton swimming speed, and q is the root mean square of turbulent velocityfluctuations. They conclude that Mn = 3 represents a transition value below which plankton areunable to swim against transport via turbulent fluid motion and hence cannot orient to resourcepatches (i.e., locate food via chemical cues). Riffell & Zimmer (2007) also examined the influenceof swimming against ambient turbulent flow, specifically the role of swimming behavior in chem-ically mediated sperm fertilization of eggs. They defined a nondimensional ratio of the propulsiveforce generated by swimming (Fswim) divided by the shear force produced by fluid motion sur-rounding the egg (Fshear). If Fswim/Fshear > 1, then sperm swim toward the egg, and encounter andfertilization rates are high. Alternatively if Fswim/Fshear < 1, then fluid motion dominates behavior,and encounter and fertilization rates are correspondingly low.

In another example, Gross et al. (1992) employed the Rouse number to examine settling larvae:

Ro = w f

κu∗ , (11)

where wf is the vertical velocity of the organism due to sinking or swimming, which is oftenmediated by chemical cues; κ is the Karman constant; and u∗ is the bed shear velocity. Theauthors identified a critical value of 0.75 that separates the well-mixed (small Ro) and near-bedconcentrated (large Ro) regimes. Tamburri et al. (1996) later experimentally verified this transitionvalue by observing that larval settling is not inhibited by turbulence in a high Ro regime, whereaslarvae remain suspended in a low Ro regime.

The few examples here suggest that nondimensional parameters are valuable for definingregimes of biological-physical interactions. Additional parameter combinations that have not yetbeen defined could describe interactions that influence chemical capture mechanisms, the de-tectability of cue structure, biologically induced flow and turbulence, and other phenomena.


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4. CONCLUDING REMARKS

The fluid mechanics community can make a potentially enormous contribution to ecology by con-fronting the challenge of quantifying and understanding flow and transport mechanisms in aquaticenvironments. Understanding the transport of chemicals in an aquatic environment is criticallyimportant to interpret behavioral and physiological responses of organisms or to predict the suc-cess by which organisms find resources. In particular, the spatial and temporal patterns of chemicalconcentration formed by transport processes usually are important aspects of the cue structure andstrongly influence organismal properties and abilities. For instance, the concentration field is oftensmoothly varying and slowly evolving in a stagnant environment in which diffusion is the dominanttransport mechanism. The concentration field, therefore, is well suited for organisms employingchemoklinokinesis to move efficiently toward high-concentration regions. Chemical plumes inthe laminar advective regime of an organism’s wake provide a reliable roadmap to predators andmates owing to the smoothly varying distribution of concentration. Turbulence also potentiallyinfluences the chemical cues received by organisms of all sizes. The fluctuating and intermittentnature of the chemical concentration field in turbulent flows creates a challenging environmentin which to interact via chemicals. Nevertheless, a wide range of organisms have adapted to thecharacteristics of turbulent chemical plumes and demonstrate successful tracking and other be-haviors in these conditions. Based on these observations, a fundamental contribution of the fluidmechanics community is to measure and model the transport of chemicals in environments ofecological relevance. In collaboration with biologists and ecologists, quantification of the physicalenvironment provides the ability to interpret observed organism responses, and, potentially, toextrapolate these responses to higher-order interactions (e.g., predation, mate finding) that governthe structure of populations and communities. Researchers have limited ability to understand thebiological and ecological consequences of chemical signal transmission without this information.

Another contribution of the fluid mechanics community is to provide inspiration via the long-standing success of employing nondimensional parameters to define flow regimes. As discussedabove, recent research has produced a few examples of nondimensional parameters that defineregimes of biological-physical interaction and behavior. A challenge for researchers in the com-ing years is to identify parameters that combine biological and physical variables in a mannerthat provides general understanding of phenomena. A potentially greater challenge is to de-sign experiments to verify that proposed nondimensional parameters correctly characterize thebiological-physical interaction in nature. Although there is a great need for new and additionaldata to describe these biological-physical interactions, it is already apparent that the nondimen-sionalization of combined physical and biological parameters is useful for describing behavior andfor defining scales of interaction.

DISCLOSURE STATEMENT

The authors are not aware of any biases that might be perceived as affecting the objectivity of thisreview.

ACKNOWLEDGEMENTS

Our research was supported in part by National Science Foundation grants DGE-0114400, IBN-0321444, and OCE-0424673, for which we are grateful. We thank Jennifer Jackson for creatingthe sketches featured in Figure 1, Jeannette Yen for providing the data in Figure 3, and BrianDickman and Jennifer Jackson for performing the experiment shown in Figure 4. We also thankBrock Woodson, Matt Ferner, and Jennifer Jackson for reviewing drafts of this article.


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AR365-FM ARI 12 November 2008 17:57

Annual Review ofFluid Mechanics

Volume 41, 2009Contents

Von Karman’s Work: The Later Years (1952 to 1963) and LegacyS.S. Penner, F.A. Williams, P.A. Libby, and S. Nemat-Nasser � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 1

Optimal Vortex Formation as a Unifying Principlein Biological PropulsionJohn O. Dabiri � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �17

Uncertainty Quantification and Polynomial Chaos Techniquesin Computational Fluid DynamicsHabib N. Najm � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �35

Fluid Dynamic Mechanism Responsible for Breaking the Left-RightSymmetry of the Human Body: The Nodal FlowNobutaka Hirokawa, Yasushi Okada, and Yosuke Tanaka � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �53

The Hydrodynamics of Chemical Cues Among Aquatic OrganismsD.R. Webster and M.J. Weissburg � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �73

Hemodynamics of Cerebral AneurysmsDaniel M. Sforza, Christopher M. Putman, and Juan Raul Cebral � � � � � � � � � � � � � � � � � � � � � � �91

The 3D Navier-Stokes ProblemCharles R. Doering � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 109

Boger FluidsDavid F. James � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 129

Laboratory Modeling of Geophysical VorticesG.J.F. van Heijst and H.J.H. Clercx � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 143

Study of High–Reynolds Number Isotropic Turbulence by DirectNumerical SimulationTakashi Ishihara, Toshiyuki Gotoh, and Yukio Kaneda � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 165

Detached-Eddy SimulationPhilippe R. Spalart � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 181

Morphodynamics of Tidal Inlet SystemsH.E. de Swart and J.T.F. Zimmerman � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 203

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Microelectromechanical Systems–Based Feedback Controlof Turbulence for Skin Friction ReductionNobuhide Kasagi, Yuji Suzuki, and Koji Fukagata � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 231

Ocean Circulation Kinetic Energy: Reservoirs, Sources, and SinksRaffaele Ferrari and Carl Wunsch � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 253

Fluid Mechanics in Disks Around Young StarsKarim Shariff � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 283

Turbulence, Magnetism, and Shear in Stellar InteriorsMark S. Miesch and Juri Toomre � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 317

Fluid and Solute Transport in Bone: Flow-InducedMechanotransductionSusannah P. Fritton and Sheldon Weinbaum � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 347

Lagrangian Properties of Particles in TurbulenceFederico Toschi and Eberhard Bodenschatz � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 375

Two-Particle Dispersion in Isotropic Turbulent FlowsJuan P.L.C. Salazar and Lance R. Collins � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 405

Rheology of the CytoskeletonMohammad R.K. Mofrad � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 433

Indexes

Cumulative Index of Contributing Authors, Volumes 1–41 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 455

Cumulative Index of Chapter Titles, Volumes 1–41 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 463

Errata

An online log of corrections to Annual Review of Fluid Mechanics articles may be foundat http://fluid.annualreviews.org/errata.shtml

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the hydrodynamics of chemical cues among aquatic...

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