The flow field around a freely swimming copepod in steady motion. Part I: Theoretical analysis

The three-dimensional flow field around a free-swimming copepodin steady motion was studiedtheoretically. This study was basedon coupling the Navier–Stokes equations with the dynamicequations for an idealized body of a copepod. To allow analyticalsolutions to the flow field, three simplifications were made:(a) to simulate the effect of the beating movement of the cephalicappendages, a force-field was added to the Navier–Stokesequations, (b) to linearize the problem, Stokes flow was used,and (c) to simplify the morphologies of the copepods, a sphericalbody shape was assumed. Analytical solutions were derived forfive steady motions: (1) hovering, (2) sinking, (3) upwardsswimming, (4) backwards swimming and (5) forwards swimming.The results show that thegeometry of the flow field around afreely swimming copepod varies significantly with the differentswimming behaviours. When a copepod hovers in the water, orswims very slowly, it generates a wide, cone-shaped flow field.In contrast, when a copepod sinks, or swims fast, the flow geometryis not cone-shaped, but cylindrical, narrow and long. Theseresults are consistent with published observations on live copepods.It is shown that the differences in the flow geometry with thedifferent swimming behaviours are due to the relative importancebetween the two factors in generating the flow field: the copepod'sswimming motion and the requirement to counterbalance the copepod'sexcess weight. The results also highlight the importance ofconsidering freely swimming copepods as self-propelled ratherthan as towed bodies. ‘Self-propelled’ means a freelyswimming copepod must gain thrust from the surrounding waterin order to counterbalance the drag force by water and its excessweight. Regardless of swimming behaviours and velocities, thefar-field velocity field decays to that of the velocity fieldgenerated by a point force of magnitude equal to the copepod'sexcess weight in an infinite domain. On the other hand, usingthe towed body model yields a flow field with much differentfar- and near-field flow characteristics. Hence, the towed bodymodel is inherently unable to reproduce fundamental characteristicsof the flow field around a freely swimming copepod.     

Chemoreception and the deformationof the active space in freely swimming copepods: a numerical study

A three-dimensional alga-tracking, chemical advection–diffusionmodel was used to calculate the deformation of the active spacesurrounding an alga entrained within the flow field around afreely swimming copepod. From the model, the advance warningtime resulting from the copepod's chemo-reception of the entrainedalga was quantified, and copepod chemoreception capability comparedfor several different swimming behaviors: hovering in the water,swimming slowly (swimming upward, swimming backward and swimmingforward), swimming fast (swimming upward, swimming backwardand swimming forward) and sinking (with the anterior pointingupward or downward). The results show that when it hovers orswims slowly, a copepod can use chemoreception to remotely detectindividual algae entrained by the flow field around itself.In contrast, a fast-swimming copepod is not able to rely onchemoreception to remotely detect individual algae. The possibilityof a free-sinking copepod using chemoreception to detect algalparticles is also indicated. It is shown that advection by thefluid motion dominates over diffusion in transporting the chemicalsignals inside the active space to the location of a copepod'schemoreceptors. The feeding current structure for a hoveringcopepod is described. It is suggested that the feeding currentstructure and re-routing or re-orienting response by a copepodin response to its antennule or other cephalic appendage inputsallow the copepod to capture the food particles that would otherwisepass outside its capture area and increase the amount of foodcaptured.     

Hydrodynamic interaction between two copepods: a numerical study

Numerical simulations were carried out to compute the flow fieldaround two tethered, stationary or swimming model-copepods withvaried separation distances between them and for different relativebody positions and orientations. Based on each simulated flowfield, the power expended by each copepod in generating theflow field and volumetric flux through the capture area of eachcopepod were calculated. The geometry of the flow field aroundeach copepod was visualized by tracking fluid particles to constructstream tubes. The hydrodynamic force on each copepod was calculated.Also, velocity magnitudes and deformation rates were calculatedalong a line just above the antennules of each copepod. Allthe results were compared to the counterpart results for a solitarycopepod (stationary or swimming) to evaluate the hydrodynamicinteraction between the two copepods. The calculations of thepower and volumetric flux show that no energetic benefits areavailable for two copepods in close proximity. The results ofthe stream tube and force calculations show that when two copepodsare in close proximity, the hydrodynamic interaction betweenthem distorts the geometry of the flow field around each copepodand changes the hydrodynamic force on each copepod. Two beneficialroles of the hydrodynamic interactions are suggested for copepodswarms: (1) to maintain the integrity of the swarms and (2)to separate the swarming members with large nearest neighbourdistances (usually more than five body lengths). To preventstrong hydrodynamic interactions, copepods in swarms have toavoid positions of strong interactions, such as those directlyabove or below their neighbours. The results of the velocitymagnitudes and deformation rates demonstrate that the hydrodynamicinteraction between two copepods generates the hydrodynamicsignals detectable by the setae on each copepod's antennules.Based on the threshold of Yen et al. (1992), the results showthat the detection distance between two copepods of comparablesize is about two to five body lengths. Copepods may employa simple form of pattern recognition to detect the distance,speed and direction of an approaching copepod of comparablesize.     

Numerical study of the feeding current around a copepod

Three-dimensional, numerical simulations of the feeding current around a tethered copepod were performed using a finite-volume code. The copepod's body shape was modeled to resemble Euchaeta norvegica, and was represented by a curvilinear body-fitted coordinate system. In the simulations, the appendages that generate the feeding current were replaced by a distribution of forces acting on the water adjacent and ventrally to the body. First, the accuracy of the code was verified by simulating two viscous, zero-Reynolds-number flows for which analytical solutions are available. Then, simulations with realistic body shape and Reynolds numbers were carried out. The main features of the computed feeding current were compared with observations from Yen and Strickler (Invert. Biol., 115, 191-205, 1996), and good agreement was obtained. The entrainment region, as visualized by tracking particles in the feeding current and by plotting the resulting stream-tube, is quite large. The result can be used to quantify how the copepod takes advantage of the feeding current to trap the algal particles in its capture area. The configuration of the feeding current near to the body surface of the copepod is controlled by how the copepod forces the feeding current and by the copepod's morphology. These parameters were varied and their effects studied in a systematic manner. Specifically, by comparing various spatial distributions of the same amount of total force, it was shown that a distributed force dissipates less energy (and increases the entrainment rate) than a concentrated force, it is thus energetically more desirable. Variations of the copepod's body shape and of the distribution of forces showed little effect on the far field of the feeding current, and therefore do not appear to affect the detectability by other mechano-receptional organisms. The length scale of the influence field of the feeding current was shown to be anisotropic in three directions, extending 5-7 mm above or ventrally to the copepod, <1 mm dorsally to the copepod and >1 cm down from the abdomen. The results also suggest that the net reaction force on the copepod from the feeding current is of the same order of magnitude as the excess weight of the copepod, but is not sufficient to balance the excess weight completely.      

Danger of zooplankton feeding: the fluid signal generated by ambush-feeding copepods

Zooplankton feed in any of three ways: they generate a feeding current while hovering, cruise through the water or are ambush feeders. Each mode generates different hydrodynamic disturbances and hence exposes the grazers differently to mechanosensory predators. Ambush feeders sink slowly and therefore perform occasional upward repositioning jumps. We quantified the fluid disturbance generated by repositioning jumps in a millimetre-sized copepod (Re ∼ 40). The kick of the swimming legs generates a viscous vortex ring in the wake; another ring of similar intensity but opposite rotation is formed around the decelerating copepod. A simple analytical model, that of an impulsive point force, properly describes the observed flow field as a function of the momentum of the copepod, including the translation of the vortex and its spatial extension and temporal decay. We show that the time-averaged fluid signal and the consequent predation risk is much less for an ambush-feeding than a cruising or hovering copepod for small individuals, while the reverse is true for individuals larger than about 1 mm. This makes inefficient ambush feeding feasible in small copepods, and is consistent with the observation that ambush-feeding copepods in the ocean are all small, while larger species invariably use hovering or cruising feeding strategies.     

Copepod flow modes and modulation: a modelling study of the water currents produced by an unsteadily swimming copepod

Video observation has shown that feeding-current-producing calanoid copepods modulate their feeding currents by displaying a sequence of different swimming behaviours during a time period of up to tens of seconds. In order to understand the feeding-current modulation process, we numerically modelled the steady feeding currents for different modes of observed copepod motion behaviours (i.e. free sinking, partial sinking, hovering, vertical swimming upward and horizontal swimming backward or forward). Based on observational data, we also reproduced numerically a modulated feeding current associated with an unsteadily swimming copepod. We found that: (i) by changing its propulsive force, a copepod can switch between different swimming behaviours, leading to completely different flow-field patterns in self-generated surrounding flow; (ii) by exerting a time-varying propulsive force, a copepod can modulate temporally the basic flow modes to create an unsteady feeding current which manipulates precisely the trajectories of entrained food particles over a long time period; (iii) the modulation process may be energetically more efficient than exerting a constant propulsive force onto water to create a constant feeding current of a wider entrainment range. A probable reason is that the modulated unsteady flow entrains those water parcels containing food particles and leaves behind those without valuable food in them.     

Detection and capture of inert particles by calanoid copepods: the role of the feeding current

Although there is a scarcity of supporting empirical evidence,it has long been suspected that calanoid copepods use mechanoreceptionto detect the presence and location of potential prey itemsentrained in the feeding current. In this study, we documentthe first observations showing a freely swimming calanoid copepod,Skistodiaptomus oregonensis, attacking prey-sized, non-motile,inert particles entrained in the feeding current before theparticles contact the copepod's sensory appendages. Feedingcurrent geometry, fluid velocities and associated behavioursthat characterize these interactions are described. The resultsof this study show how copepod swimming behaviour, coupled witha low-velocity feeding current, not only increases copepod encounterrates with inert prey by increasing direct contact rates, butalso increases the probability of detecting and capturing remotelylocated prey that have well-developed escape responses. In turbulentregimes, a far-reaching, low-velocity feeding current shouldincrease encounter rates, but only if coupled with behavioursthat quickly minimize separation distances once prey is detected.     

Some notes on an ambivalent behaviour of the Greenland halibut Reinhardtius hippoglossoides (Walb.) Pisces: Pleuronectiformes

The ambivalent behaviour of the Greenland halibut with respect to its swimming position is discussed. The conclusion is that, when swimming close to the bottom, it swims the way all flatfishes do, viz. horizontally; when it swims freely, however, it adopts a vertical position.     

Size, Speed and Buoyancy Adaptations in Aquatic Animals

Animals are denser than either fresh water or sea water, andtherefore tend to sink, unless they have adaptations that givebuoyancy. Very small organisms sink slowly, reproduce rapidlyand can be kept suspended by natural turbulence: individualslost by sinking are replaced by reproduction. This is likelyto be effective only for organisms of less than 150µmdiameter. Larger animals will sink unless they swim or evolvebuoyancy organs. Hovering is one of the options available tothem, but the "hop and sink" technique used by some copepodsis more economical than steady hovering. Another option is touse fins as hydrofoils, as sharks, tunnies and many squids do.This implies an energy cost because work has to be done againstdrag on the hydrofoils. Many animals are made buoyant by gas-filledfloats, low-density organic compounds or body fluids of unusualionic composition. Such buoyancy aids increase the energy costof swimming at given speed because they increase the animal'sbulk. Buoyancy aids are more economical than hydrofoils foranimals that swim slowly but hydrofoils are more economicalfor those that swim fast.     

Plankton predation rates in turbulence: a study of the limitations imposed on a predator with a non-spherical field of sensory perception

This paper presents an extension to previously published work which studied encounter rates of planktonic predators with restricted perception fields, to examine the related problems of prey capture and predation rates. Small-scale turbulence influences planktonic predation in two ways: the extra energy of the flow enhances the number of encounter events between individual predator and prey meso/micro-zooplankton, but it lowers the capture probability (because the time spent by the predator and prey in close proximity is reduced). Typically, an 'encounter' has usually been defined as an event when a potential prey swims (or is advected) to within a distance R of the predator in any direction. However, there is a considerable body of experimental evidence showing that predators perception fields are far from spherical; often they are wedge shaped (e.g. fish larvae), or strongly aligned with the directions of sensory antennae (e.g. copepods); and this is certain to influence optimal predation strategies. This paper presents a theoretical model which for the first time examines the combined problems of both encounter and capture for a predator with a restricted perception field swimming in a turbulent flow. If such a predator adopts a cruising strategy (continuous swimming, possibly with direction changes) the model predictions suggest that predation rates actually vary little with swimming speed, in contrast to predictions made for spherical perception fields. Consequently, cruising predators are predicted to swim at relatively low speeds whilst foraging. However, application of the model to examine the net energy gain of a typical pause-travel predator (the Atlantic cod larva), does predict the existence of an optimal ratio of the length of pauses to time spent swimming (specifically one pause phase to every two travel phases), in line with experimental observations. Kinematic simulations are presented which support these findings.     

Hydrodynamic interactions between two swimming bacteria

This article evaluates the hydrodynamic interactions between two swimming bacteria precisely. We assume that each bacterium is force free and torque free, with a Stokes flow field around it. The geometry of each bacterium is modeled as a spherical or spheroidal body with a single helical flagellum. The movements of two interacting bacteria in an infinite fluid otherwise at rest are computed using a boundary element method, and the trajectories of the two interacting bacteria and the stresslet are investigated. The results show that as the two bacteria approach each other, they change their orientations considerably in the near field. The bacteria always avoided each other; no stable pairwise swimming motion was observed in this study. The effects of the hydrodynamic interactions between two bacteria on the rheology and diffusivity of a semidilute bacterial suspension are discussed.     

Body temperatures during three long-distance polar swims in water of 0–3 °C

1.

We report body temperature responses in a single individual to 3 swims of 1000 m or longer in ice-cold water (0–3 °C) during which he swam the normal crawl stroke with his face in the water whilst wearing only a swimming costume, swimming cap and goggles.     

Whole-body lift and ground effect during pectoral fin locomotion in the northern spearnose poacher (Agonopsis vulsa)

The northern spearnose poacher, Agonopsis vulsa, is a benthic, heavily armored fish that swims primarily using pectoral fins. High-speed kinematics, whole-body lift measurements, and flow visualization were used to study how A. vulsa overcomes substantial negative buoyancy while generating forward thrust. Kinematics for five freely swimming poachers indicate that individuals tend to swim near the bottom (within 1 cm) with a consistently small (less than 1°) pitch angle of the body. When the poachers swam more than 1 cm above the bottom, however, body pitch angles were higher and varied inversely with speed, suggesting that lift may help overcome negative buoyancy. To determine the contribution of the body to total lift, fins were removed from euthanized fish (n=3) and the lift and drag from the body were measured in a flume. Lift and drag were found to increase with increasing flow velocity and angle of attack (ANCOVA, p<0.0001 for both effects). Lift force from the body was found to supply approximately half of the force necessary to overcome negative buoyancy when the fish were swimming more than 1 cm above the bottom. Lastly, flow visualization experiments were performed to examine the mechanism of lift generation for near-bottom swimming. A vortex in the wake of the pectoral fins was observed to interact strongly with the substratum when the animals approached the bottom. These flow patterns suggest that, when swimming within 1 cm of the bottom, poachers may use hydrodynamic ground effect to augment lift, thereby counteracting negative buoyancy.     

Locomotion of Gymnarchus Niloticus： Experiment and Kinematics

In addition to forward undulatory swimming, Gymnarchus niloticus can swim via undulations of the dorsal fin while the body axis remains straight; furthermore, it swims forward and backward in a similar way, which indicates that the undulation of the dorsal fin can simultaneously provide bidirectional propulsive and maneuvering forces with the help of the tail fin. A high-resolution Charge-Coupled Device （CCD） imaging camera system is used to record kinematics of steady swimming as well as maneuvering in G. niloticus. Based on experimental data, this paper discusses the kinematics （cruising speed, wave speed, cycle frequency, amplitude, lateral displacement） of forward as well as backward swimming and maneuvering. During forward swimming, the propulsive force is generated mainly by undulations of the dorsal fin while the body axis remains straight. The kinematic parameters （wave speed, wavelength, cycle frequency, amplitude） have statistically significant correlations with cruising speed. In addition, the yaw at the head is minimal during steady swimming. From experimental data, the maximal lateral displacement of head is not more than 1% of the body length, while the maximal lateral displacement of the whole body is not more than 5% of the body length. Another important feature is that G. niloticus swims backwards using an undulatory mechanism that resembles the forward undulatory swimming mechanism. In backward swimming, the increase of lateral displacement of the head is comparatively significant; the amplitude profiles of the propulsive wave along the dorsal fin are significantly different from those in forward swimming. When G. niloticus does fast maneuvering, its body is first bent into either a C shape or an S shape, then it is rapidly unwound in a travelling wave fashion. It rarely maneuvers without the help of the tail fin and body bending.     

Resisting flow–laboratory study of rheotaxis of the estuarine copepod Pseudodiaptomus annandalei

Rheotaxis is a ubiquitous phenomenon among aquatic animals and thought to be an adaptation to maintain populations in flowing waters. While many estuarine copepods can retain their populations in estuaries with net seaward flow, rheotaxis of individual copepods has not been reported before. In this study, the behavior of a calanoid copepod Pseudodiaptomus annandalei in flow was examined in a recirculating laboratory flume. This estuarine copepod displayed different responses to ambient flow fields while swimming in the water column or attaching to the flume bed (walls). Copepods in the water column showed vigorous countercurrent swimming by occasional bounding when flow velocity was increased up to 2.1 cm s^?1, but none of the individuals in the water column were retained in the flume when flow speeds were higher than 4 cm s^?1. This indicates P. annandalei profits little from rheotaxis to withstand flow when they were swimming in the water column. Instead, more individuals attempted sinking downwards to the slow flow region near the flume bed (walls) and showed active substrate attachment to avoid being flushed out by the high-velocity channel flow. The results suggest that P. annandalei benefits from rheotaxis and association with the substrate which allows them to hold position well at ambient flow velocities up to 3 cm s^?1. These adaptive responses might be important for population maintenance.     

The time course and frequency content of hydrodynamic events caused by moving fish,frogs, and crustaceans

Summary In the present study the time course and spectral-amplitude distribution of hydrodynamic flow fields caused by moving fish, frogs, and crustaceans were investigated with the aid of laser-Doppler-anemometry. In the vicinity of a hovering fish sinusoidal water movements can be recorded whose velocity spectra peak below 10 Hz (Fig. 2). Single strokes during startle responses or during steady swimming of fish, frogs, and crustaceans cause short-lasting, low-frequency (<10 Hz), transient water movements (Fig. 3). Low-frequency transients also occur if a frog approaches and passes a velocity-sensitive hydrodynamic sensor. In contrast, transient water movements caused by a rapidly struggling or startled fish or water motions measured in the wake of a slowly swimming (47 cm/s) trout can be broadbanded, i.e., these water movements can contain frequency components up to at least 100 Hz (Figs. 4, 5A, 6). High-frequency hydrodynamic events can also be measured behind obstacles submerged in running water (Fig. 5C). The possible biological advantage of the ability to detect high-frequency hydroynamic events is discussed with respect to the natural occurrence of high frequencies and its potential role in orientation and predator-prey interactions of aquatic animals.Abbreviations LDA laser Doppler anemometer     

Comparison of response distance to prey via the lateral line in the ruffe and yellow perch

The ruffe Gymnocephalus cernuus and the yellow perch Perca flavescens (both Percidae), have very different cephalic lateral line systems. The ruffe, which is nocturnal and frequents turbid water, has a cephalic lateral line with very wide canals, large neuromasts, and membranes covering the canal openings. This anatomy is convergent with that of many deep-sea fishes. The yellow perch has a lateral line composed of neuromasts enclosed in narrow canals freely open to the water. This anatomy is typical of active, diurnal, shallow-water fishes. Laboratory experiments in the dark using infra-red video equipment revealed that the ruffe detects Daphnia magna (Crustacea: Daphnidae) and the mayfly Hexagenia limbata (Insecta: Ephemeridae) at a greater distance than the yellow perch and that it also swims faster whilst searching for prey. The swimming of the ruffe consists of a thrust by the pectoral and caudal fins, followed by a glide, the prey being detected during the glide. It is suggested that the membranes over the openings in the ruffe's lateral line function to eliminate self-generated laminar flow 'noise' from reaching the neuromasts.     

Energetics of swimming by the ferret: consequences of forelimb paddling.

The domestic ferret (Mustela putorius furo) swims by alternate strokes of the forelimbs. This pectoral paddling is rare among semi-aquatic mammals. The energetic implications of swimming by pectoral paddling were examined by kinematic analysis and measurement of oxygen consumption. Ferrets maintained a constant stroke frequency, but increased swimming speed by increasing stroke amplitude. The ratio of swimming velocity to foot stroke velocity was low, indicating a low propulsive efficiency. Metabolic rate increased linearly with increasing speed. The cost of transport decreased with increasing swimming speed to a minimum of 3.59+/-0.28 J N(-1) m(-1) at U=0.44 m s(-1). The minimum cost of transport for the ferret was greater than values for semi-aquatic mammals using hind limb paddling, but lower than the minimum cost of transport for the closely related quadrupedally paddling mink. Differences in energetic performance may be due to the amount of muscle recruited for propulsion and the interrelationship hydrodynamic drag and interference between flow over the body surface and flow induced by propulsive appendages.     

Energetics of swimming by the ferret: consequences of forelimb paddling

The domestic ferret (Mustela putorius furo) swims by alternate strokes of the forelimbs. This pectoral paddling is rare among semi-aquatic mammals. The energetic implications of swimming by pectoral paddling were examined by kinematic analysis and measurement of oxygen consumption. Ferrets maintained a constant stroke frequency, but increased swimming speed by increasing stroke amplitude. The ratio of swimming velocity to foot stroke velocity was low, indicating a low propulsive efficiency. Metabolic rate increased linearly with increasing speed. The cost of transport decreased with increasing swimming speed to a minimum of 3.59+/-0.28 J N(-1) m(-1) at U=0.44 m s(-1). The minimum cost of transport for the ferret was greater than values for semi-aquatic mammals using hind limb paddling, but lower than the minimum cost of transport for the closely related quadrupedally paddling mink. Differences in energetic performance may be due to the amount of muscle recruited for propulsion and the interrelationship hydrodynamic drag and interference between flow over the body surface and flow induced by propulsive appendages.     

Persistent spatial and temporal abundance patterns for the late-stage copepodites of Centropages typicus (Copepoda: Calanoida) in the US Northeast continental shelf ecosystem

The annual cycle of abundance and the monthly distributions of the copepod Centropages typicus are described for US Northeast Continental Shelf waters from samples collected on broadscale plankton surveys during 1977-87. High numbers of the copepod were captured throughout the region during the autumn months in weak south-north and onshore-offshore abundance gradients. The highest individual station densities were found near the mouth of the major estuaries and the heaviest broad-scale concentrations were usually located where bottom depth ranged from 20 to 39 m. Numbers declined throughout the ecosystem after winter arrived, less so in the southern half of the region where C.typicus abundance remained high year round in nearshore and midshelf waters between New York City and Chesapeake Bay. The copepod's abundance fell to much lower levels further north in the Georges Bank and Gulf of Maine subareas, and disappeared entirely from shelf waters in the northernmost offshore region until summer. Interannual abundance variability was substantial, but no long-term trend was detected. Analyses of samples collected from 1988 to 1996 on Georges Bank during early autumn indicate that abundance levels of C.typicus have been high here in the 1990s, completely recovered from low density values measured there in 1986 and 1987. Temperature and food availability were found to be the key factors that determine the copepod's distribution and annual abundance cycle. Mean abundance was high throughout the ecosystem where surface temperature was >9C and in regions where annual mean chlorophyll levels exceeded 1 mg m^-3. The copepod's abundance appeared to be independent from variation in water column salinity.