A quasi three-dimensional visualization of unsteady wake flow in human undulatory swimming

Human undulatory underwater swimming (UUS) is an underwater propelling technique in competitive swimming and its propulsive mechanism is poorly understood. The purpose of this study was to visualize the three-dimensional (3D) flow field in the wake region during human UUS in a water flume. A national level male swimmer performed 41 UUS trials in a water flume. A motion capture system and stereo particle image velocimetry (PIV) equipment were used to investigate the 3D coordinates of the swimmer and 3D flow fields in the wake region. After one kick cycle was divided into eight phases, we conducted coordinate transformations and phase averaging method to construct quasi 3D flow fields. At the end of the downward kick, the lower limbs external rotations of the lower limbs were observed, and the feet approached towards each other. A strong downstream flow, i.e. a jet was observed in the wake region during the downward kick, and the paired vortex structure was accompanied by a jet. In the vortex structure, a cluster of vortices and a jet were generated in the wake during the downward kick, and the vortices were subsequently shed from the feet by the rotated leg motion. This suggested that the swimmer gained a thrust by creating vortices around the foot during the downward kick, which collided to form a jet. This paper describes, illustrates, and explains the propulsive mechanism of human UUS.     

Disentangling the functional roles of morphology and motion in the swimming of fish

In fishes the shape of the body and the swimming mode generally are correlated. Slender-bodied fishes such as eels, lampreys, and many sharks tend to swim in the anguilliform mode, in which much of the body undulates at high amplitude. Fishes with broad tails and a narrow caudal peduncle, in contrast, tend to swim in the carangiform mode, in which the tail undulates at high amplitude. Such fishes also tend to have different wake structures. Carangiform swimmers generally produce two staggered vortices per tail beat and a strong downstream jet, while anguilliform swimmers produce a more complex wake, containing at least two pairs of vortices per tail beat and relatively little downstream flow. Are these differences a result of the different swimming modes or of the different body shapes, or both? Disentangling the functional roles requires a multipronged approach, using experiments on live fishes as well as computational simulations and physical models. We present experimental results from swimming eels (anguilliform), bluegill sunfish (carangiform), and rainbow trout (subcarangiform) that demonstrate differences in the wakes and in swimming performance. The swimming of mackerel and lamprey was also simulated computationally with realistic body shapes and both swimming modes: the normal carangiform mackerel and anguilliform lamprey, then an anguilliform mackerel and carangiform lamprey. The gross structure of simulated wakes (single versus double vortex row) depended strongly on Strouhal number, while body shape influenced the complexity of the vortex row, and the swimming mode had the weakest effect. Performance was affected even by small differences in the wakes: both experimental and computational results indicate that anguilliform swimmers are more efficient at lower swimming speeds, while carangiform swimmers are more efficient at high speed. At high Reynolds number, the lamprey-shaped swimmer produced a more complex wake than the mackerel-shaped swimmer, similar to the experimental results. Finally, we show results from a simple physical model of a flapping fin, using fins of different flexural stiffness. When actuated in the same way, fins of different stiffnesses propel themselves at different speeds with different kinematics. Future experimental and computational work will need to consider the mechanisms underlying production of the anguilliform and carangiform swimming modes, because anguilliform swimmers tend to be less stiff, in general, than are carangiform swimmers.     

The scaling and structure of aquatic animal wakes

Animal generated water movements are visualized and quantifiedusing two-dimensional particle image velocimetry (PIV). Theresulting vector flow fields allow for the study of the distributionof velocity, vorticity and vortices. Structural and temporalaspects of animal-induced flows covering a range of Reynolds(Re) numbers between less than 1 to more than 10⁴ are presented. Maps of flow induced by continuous foraging and intermittentescape responses of tethered nauplius and copepodid stages ofthe marine copepod Temora longicornis offer insight in viscosity-dominatedflow regimes. Fast escape responses of the equally sized largestnauplius stage and the smallest copepodid stage are compared.The nauplius moves by generating a viscous flow pattern withhigh velocities and vorticity; the copepodid moves by usinginertial effects to produce a vortex ring with a rearward jetthrough the center. Larvae and small adult fish (zebra danio) use a burst-and-coast-swimmingmode at Re numbers up to 6,000, shedding a vortex ring withthe associated jet at the tail during the burst phase. Flowpatterns during the coasting phase differ between the smalllarvae and larger adults due to the changes in importance ofviscosity. A 12 cm long mullet swimming in a continuous mode generatesa chain of vortex rings with a backward undulating jet throughthe centers of the rings at Re numbers of 4 x 10⁴ in inertia-dominatedregimes. Our empirical results provide realistic insight in the scaleeffects determining the morphology of the interactions betweenanimals and water.     

The locomotory function of the fins in the squid Loligo pealei

Kinematic data of high spatial and temporal resolution, acquired from image sequences of adult long-finned squid, Loligo pealei, during steady swimming in a flume, were used to examine the role of fins and the coordination between fin and jet propulsion in squid locomotion. Fin shape and body outlines were digitized and used to calculate fin wave speed, amplitude, frequency, angle of attack, body deformation, speed, and acceleration. L. pealei were observed to have two fin gait patterns with a transition at 1.4-1.8 mantle lengths per second (Lm s-1) marked by alternation between the two patterns. Fin motion in L. pealei exhibited characteristics of both traveling waves and flapping wings. At low speeds, fin motion was more wave-like; at high speeds, fin motion was more flap-like and was marked by regular periods during which the fins were wrapped tightly against the mantle. Fin cycle frequencies were dependent on swimming speed and gait, and obvious coordination between the fins and jet were observed. Fin wave speed, angle of attack, and body acceleration confirmed the role of fins in thrust production and revealed a role of fins at all swimming speeds by a transition from drag-based to lift-based thrust when fin wave speed dropped below swimming speed. Estimates of peak fin thrust were as high as 0.44-0.96 times peak jet thrust in steady swimming over the range of swimming speeds observed. Fin downstrokes generally contributed more to thrust than did upstrokes, especially at high speeds.     

Swimming kinematics and wake elements in a worm-like insect: the larva of the midge Chironomus plumosus (Diptera)

The kinematics and hydrodynamics of swimming chironomid larvae were investigated with the aid of videography and dye streamers used to visualize near-body flow. Chironomids employ a characteristic 'figure-of-eight' swimming technique based on high-amplitude side-to-side bending of the body. These scissor-like movements produce relatively slow (two body lengths (BL) s⁻¹) forward motion but also serve to support the weight of the insect against its own negative buoyancy. The main wake element identified by the present technique consisted of a discrete ring vortex with an external diameter of c. 0.3 BL which was shed to the rear of the body towards the end of each half-stroke. During level swimming, the jet of the vortex was directed 10° below the horizontal plane indicating that it was mainly providing thrust. An additional, but poorly defined, flow was associated with the rapid downwards motion of the head at the start of each half-stroke and it is proposed that this contributes to the vertical force needed to support the weight of the body during swimming.     

The locomotory function of the fins in the squid Loligo pealei

Kinematic data of high spatial and temporal resolution, acquired from image sequences of adult long-finned squid, Loligo pealei, during steady swimming in a flume, were used to examine the role of fins and the coordination between fin and jet propulsion in squid locomotion. Fin shape and body outlines were digitized and used to calculate fin wave speed, amplitude, frequency, angle of attack, body deformation, speed, and acceleration. L. pealei were observed to have two fin gait patterns with a transition at 1.4-1.8 mantle lengths per second (L_m s^-1) marked by alternation between the two patterns. Fin motion in L. pealei exhibited characteristics of both traveling waves and flapping wings. At low speeds, fin motion was more wave-like; at high speeds, fin motion was more flap-like and was marked by regular periods during which the fins were wrapped tightly against the mantle. Fin cycle frequencies were dependent on swimming speed and gait, and obvious coordination between the fins and jet were observed. Fin wave speed, angle of attack, and body acceleration confirmed the role of fins in thrust production and revealed a role of fins at all swimming speeds by a transition from drag-based to lift-based thrust when fin wave speed dropped below swimming speed. Estimates of peak fin thrust were as high as 0.44-0.96 times peak jet thrust in steady swimming over the range of swimming speeds observed. Fin downstrokes generally contributed more to thrust than did upstrokes, especially at high speeds.     

Unilateral ablation of trunk superficial neuromasts increases directional instability during steady swimming in the yellowtail kingfish Seriola lalandi

Detailed swimming kinematics of the yellowtail kingfish Seriola lalandi were investigated after unilateral ablation of superficial neuromasts (SNs). Most kinematic variables, such as tail‐beat frequency, stride length, caudal fin‐beat amplitude and propulsive wavelength, were unaffected but lateral amplitude at the tip of the snout (A₀) was significantly increased in SN‐disrupted fish compared with sham‐operated controls. In addition, the orientation of caudal fin‐tip relative to the overall swimming direction of SN‐disrupted fish was significantly deflected (two‐fold) in comparison with sham‐operated control fish. In some fish, SN disruption also led to a phase distortion of the propulsive body‐wave. These changes would be expected to increase both hydrodynamic drag and thrust production which is consistent with the finding that SN‐disrupted fish had to generate significantly greater thrust power when swimming at ≥1·3 fork lengths (L_F) s^?1. In particular, hydrodynamic drag would increase as a result of any increase in rotational (yaw) perturbation and sideways slip resulting from the sensory disturbance. In conclusion, unilateral SN ablation produced directional instability of steady swimming and altered propulsive movements, suggesting a role for sensory feedback in correcting yaw and slip disturbances to maintain efficient locomotion.     

Kinematics, dynamics, and energetics of rowing and flapping propulsion in fishes

The shape and motion of the pectoral fins vary considerablyamong fishes that swim in the labriform mode. Pectoral fin motionin fishes is highly variable, but one conspicuous axis of thisvariation is the rowing-flapping axis. At one extreme of thisaxis, paddle-shaped fins row back and forth in a plane thatis parallel to fish motion, while at the other extreme, wing-shapedfins flap up and down in a plane that is perpendicular to fishmotion. We have used two fish, the threespine stickleback (Gasterosteusaculeatus) and the bird wrasse (Gomphosus varius), that fallnear the extremes of the rowing-flapping axis to study the dynamic,energetic, and ecological and evolutionary consequences of thiskinematic variation. Our work confirms some traditionally heldassumptions about rowing and flapping dynamics and energeticsbut reject others. A computer simulation experiment of virtualrowing and flapping appendages makes several predictions aboutdifferences in maneuvering performance and swimming energeticsbetween rowing and flapping, which, in turn, make predictionsabout the behavior and ecological distribution of fishes thatvary along the rowing-flapping axis. Both laboratory and fieldstudies of labrid swimming ability and distribution supportthese predictions.     

Biological Inspiration: From Carangiform Fish to Multi-Joint Robotic Fish

This paper presents a novel approach to modelling carangiform fish-like swimming motion for multi-joint robotic fish so that they can obtain fish-like behaviours and mimic the body motion of carangiform fish. A given body motion function of fish swimming is firstly converted to a tail motion function which describes the tail motion relative to the head. Then, the tail motion function is discretized into a series of tail postures over time. Thirdly, a digital approximation method calculates the taming angles of joints in the tail to approximate each tail posture; and finally, these angles are grouped into a look-up table, or re-gressed to a time-dependent function, for practically controlling the tail motors in a multi-joint robotic fish. The paper made three contributions: tail motion relative to the head, an error function for digital approximation and regressing a look-up table for online optimization. To prove the feasibility of the proposed methodology, two basic swimming motion patterns, cruise straight and C-shape sharp turning, are modelled and implemented in our robotic fish. The experimental results show that the relative tail motion and the approximation error function are good choices and the proposed method is feasible.     

Swimming dynamics and propulsive efficiency of squids throughout ontogeny

Squids encounter vastly different flow regimes throughout ontogeny as they undergo critical morphological changes to their two locomotive systems: the fins and jet. Squid hatchlings (paralarvae) operate at low and intermediate Reynolds numbers (Re) and typically have rounded bodies, small fins, and relatively large funnel apertures, whereas juveniles and adults operate at higher Re and generally have more streamlined bodies, larger fins, and relatively small funnel apertures. These morphological changes and varying flow conditions affect swimming performance in squids. To determine how swimming dynamics and propulsive efficiency change throughout ontogeny, digital particle image velocimetry (DPIV) and kinematic data were collected from an ontogenetic range of long-finned squid Doryteuthis pealeii and brief squid Lolliguncula brevis swimming in a holding chamber or water tunnel (Re = 20-20 000). Jet and fin wake bulk properties were quantified, and propulsive efficiency was computed based on measurements of impulse and excess kinetic energy in the wakes. Paralarvae relied predominantly on a vertically directed, high frequency, low velocity jet as they bobbed up and down in the water column. Although some spherical vortex rings were observed, most paralarval jets consisted of an elongated vortical region of variable length with no clear pinch-off of a vortex ring from the trailing tail component. Compared with paralarvae, juvenile and adult squid exhibited a more diverse range of swimming strategies, involving greater overall locomotive fin reliance and multiple fin and jet wake modes with better defined vortex rings. Despite greater locomotive flexibility, jet propulsive efficiency of juveniles/adults was significantly lower than that of paralarvae, even when juvenile/adults employed their highest efficiency jet mode involving the production of periodic isolated vortex rings with each jet pulse. When the fins were considered together with the jet for several juvenile/adult swimming sequences, overall propulsive efficiency increased, suggesting that fin contributions are important and should not be overlooked in analyses of the swimming performance of squids. The fins produced significant thrust and consistently had higher propulsive efficiency than did the jet. One particularly important area of future study is the determination of coordinated jet/fin wake modes that have the greatest impact on propulsive efficiency. Although such research would be technically challenging, requiring new, powerful, 3D approaches, it is necessary for a more comprehensive assessment of propulsive efficiency of the squid dual-mode locomotive system.     

Midwater and epibenthic behaviors of Mysis relicta Loven: observations from the Johnson-Sea-Link II submersible in Lake Superior and from a remotely operated vehicle in northern Lake Michigan

Submersible dives provided an opportunity to observe the opossumshrimp. Mysis relicta, in Lake Superior (64°54'N, 67°09'W,depth = 280 m). Observations included probable mating, midwaterand benthic responses, and several swimming modes. While matingthe male and female were joined in a ventral to ventral positionby interlaced thoracic appendages. During the evening ascentor predawn descent mysids actively swam vertically upwards anddownwards using their thoracic appendages which beat metachronally.When escaping from the bottom, mysids thrust their abdomensdownwards and rapidly accelerate directly forwards. The midwaterresponse, significantly slower than the benthic response, wasa jerky laterally undulatory movement which propelled the animalat a 45° angle from the forward motion. In a cruising modeMysis swims with its periopods, parallel to the bottom, at approximatespeeds of 2–5 cm^–1. A remotely operated vehiclewas employed to observe mysids at close range at the sediment–waterinterface at deep-water and nearshore stations in northern LakeMichigan (44°34'N, 87°7'W, depth = 100 m, Algoma, Wisconsinharbor, depth = 20 m) during May 23–25, 1987. At the 20m inshore station mysids occurred in significant numbers duringthe day in very bright light. Mysid swimming behavior on thebottom at deep-water stations significantly fashioned the sedimentlandscape, a potentially important form of superficial bioturbation.     

Volumetric imaging of fish locomotion

Fishes use multiple flexible fins in order to move and maintain stability in a complex fluid environment. We used a new approach, a volumetric velocimetry imaging system, to provide the first instantaneous three-dimensional views of wake structures as they are produced by freely swimming fishes. This new technology allowed us to demonstrate conclusively the linked ring vortex wake pattern that is produced by the symmetrical (homocercal) tail of fishes, and to visualize for the first time the three-dimensional vortex wake interaction between the dorsal and anal fins and the tail. We found that the dorsal and anal fin wakes were rapidly (within one tail beat) assimilated into the caudal fin vortex wake. These results show that volumetric imaging of biologically generated flow patterns can reveal new features of locomotor dynamics, and provides an avenue for future investigations of the diversity of fish swimming patterns and their hydrodynamic consequences.     

Numerical Study of Propulsion Mechanism for Oscillating Rigid and Flexible Tuna-Tails

Numerical study on the unsteady hydrodynamic characteristics of oscillating rigid and flexible tuna-tails in viscous flow-field is performed.Investigations are conducted using Reynolds-Averaged Navier-Stokes (RANS) equations with a moving adaptive mesh.The effect of swimming speed,flapping amplitude,frequency and flexure amplitude on the propulsion performance of the rigid and flexible tuna-tails are investigated.Computational results reveal that a pair of leading edge vortices develop along the tail surface as it undergoes an oscillating motion.The propulsive efficiency has a strong correlation with various locomotive parameters.Peak propulsive efficiency can be obtained by adjusting these parameters.Particularly,when input power coefficient is less than 2.8,the rigid tail generates larger thrust force and higher propulsive efficiency than flexible tail.However,when input power coefficient is larger than 2.8,flexible tail is superior to rigid tail.     

Experimental Hydrodynamics and Evolution: Function of Median Fins in Ray-finned Fishes

The median fins of fishes consist of the dorsal, anal, and caudal fins and have long been thought to play an important role in generating locomotor force during both steady swimming and maneuvering. But the orientations and magnitudes of these forces, the mechanisms by which they are generated, and how fish modulate median fin forces have remained largely unknown until the recent advent of Digital Particle Image Velocimetry (DPIV) which allows empirical analysis of force magnitude and direction. Experimental hydrodynamic studies of median fin function in fishes are of special utility when conducted in a comparative phylogenetic context, and we have examined fin function in four ray-finned fish clades (sturgeon, trout, sunfish, and mackerel) with the goal of testing classical hypotheses of fin function and evolution. In this paper we summarize two recent technical developments in DPIV methodology, and discuss key recent findings relevant to median fin function. High-resolution DPIV using a recursive local-correlation algorithm allows quantification of small vortices, while stereo-DPIV permits simultaneous measurement of x, y, and z flow velocity components within a single planar light sheet. Analyses of median fin wakes reveal that lateral forces are high relative to thrust force, and that mechanical performance of median fins (i.e., thrust as a proportion of total force) averages 0.35, a surprisingly low value. Large lateral forces which could arise as an unavoidable consequence of thrust generation using an undulatory propulsor may also enhance stability and maneuverability. Analysis of hydrodynamic function of the soft dorsal fin in bluegill sunfish shows that a thrust wake is generated that accounts for 12% of total thrust and that the thrust generation by the caudal fin may be enhanced by interception of the dorsal fin wake. Integration of experimental studies of fin wakes, computational approaches, and mechanical models of fin function promise understanding of instantaneous forces on fish fins during the propulsive cycle as well as exploration of a broader locomotor design space and its hydrodynamic consequences.     

The Roles of Pink and Red Muscle in Powering Steady Swimming in Scup, Stenotomus chrysops

Fishes power steady, undulatory swimming using both red andpink muscle. In this study we examined the roles of the twofiber types in generating power for swimming by using two-steptechnique. First, in vivo data is collected from swimming fish,and second, the electrical activity and muscle length changeconditions recorded in vivo are recreated in vitro with isolatedmuscle bundles. Force production and power generation by muscleduring swimming can then be estimated. In scup, both red andpink muscle are recruited to power swimming at the maximum sustainedswimming speed. For both fiber types, the duration of electricalactivity decreases from anterior to posterior. However, theamplitude of muscle length change increases anterior to posterior.Mass-specific power production increases posteriorly for bothmuscle types. The faster contraction kinetics of pink muscletranslate to higher power production pink muscle relative tored muscle for all longitudinal positions of the fish. Determinationof absolute power production, based on mass-specific power andmuscle mass, shows that the posterior regions of the fish generatethe most power for swimming. At 20°C, red muscle generatesmore absolute power than pink due to its higher muscle mass.However, at 10°C, pink muscle generates more absolute powerthan red, because red muscle produces little or no positivepower for all longitudinal positions.     

Functional Morphology of Aquatic Flight in Fishes: Kinematics, Electromyography, and Mechanical Modeling of Labriform Locomotion

Labriform locomotion is the primary swimming mode for many fishesthat use the pectoral fins to generate thrust across a broadrange of speeds. A review of the literature on hydrodynamics,kinematics, and morphology of pectoral fin mechanisms in fishesreveals that we lack several kinds of morphological and kinematicdata that are critical for understanding thrust generation inthis mode, particularly at higher velocities. Several needsinclude detailed three-dimensional kinematic data on speciesthat are pectoral fin swimmers across a broad range of speeds,data on the motor patterns of pectoral fin muscles, and thedevelopment of a mechanical model of pectoral fin functionalmorphology. New data are presented here on pectoral fin locomotionin Gomphosus varius, a labrid fish that uses the pectoral finsat speeds of 1 –6 total body lengths per second. Three-dimensionalkinematic data for the pectoral fins of G. varius show thata typical "drag-based" mechanism is not used in this species.Instead, the thrust mechanics of this fish are dominated bylift forces and acceleration reaction forces. The fin is twistedlike a propeller during the fin stroke, so that angles of attackare variable along the fin length. Electromyographic data onsix fin muscles indicate the sequence of muscle activity thatproduces antagonistic fin abduction and adduction and controlsthe leading edge of the fin. EMG activity in abductors and adductorsis synchronous with the start of abduction and adduction, respectively,so that muscle mechanics actuate the fin with positive work.A mechanical model of the pectoral fin is proposed in whichfin morphometrics and computer simulations allow predictionsof fin kinematics in three dimensions. The transmission of forceand motion to the leading edge of the fin depends on the mechanicaladvantage of fin ray levers. An integrative program of researchis suggested that will synthesize data on morphology, physiology,kinematics, and hydrodynamics to understand the mechanics ofpectoral fin swimming.     

Experimental hydrodynamics of fish locomotion: functional insights from wake visualization

Despite enormous progress during the last twenty years in understandingthe mechanistic basis of aquatic animal propulsion—a taskinvolving the construction of a substantial data base on patternsof fin and body kinematics and locomotor muscle function—thereremains a key area in which biologists have little information:the relationship between propulsor activity and water movementin the wake. How is internal muscular force translated intoexternal force exerted on the water? What is the pattern offluid force production by different fish fins (e.g., pectoral,caudal, dorsal) and how does swimming force vary with speedand among species? These types of questions have received considerableattention in analyses of terrestrial locomotion where forceoutput by limbs can be measured directly with force plates.But how can forces exerted by animals moving through fluid bemeasured? The advent of digital particle image velocimetry (DPIV)has provided an experimental hydrodynamic approach for quantifyingthe locomotor forces of freely moving animals in fluids, andhas resulted in significant new insights into the mechanismsof fish propulsion. In this paper we present ten "lessons learned"from the application of DPIV to problems of fish locomotionover the last five years. (1) Three-dimensional DPIV analysisis critical for reconstructing wake geometry. (2) DPIV analysisreveals the orientation of locomotor reaction forces. (3) DPIVanalysis allows calculation of the magnitude of locomotor forces.(4) Swimming speed can have a major impact on wake structure.(5) DPIV can reveal interspecific differences in vortex wakemorphology. (6) DPIV analysis can provide new insights intothe limits to locomotor performance. (7) DPIV demonstrates thefunctional versatility of fish fins. (8) DPIV reveals hydrodynamicforce partitioning among fins. (9) DPIV shows that wake interactionamong fins may enhance thrust production. (10) Experimentalhydrodynamic analysis can provide insight into the functionalsignificance of evolutionary variation in fin design.     

Function of dorsal fins in bamboo shark during steady swimming

To gain insight into the function of the dorsal fins in white-spotted bamboo sharks (Orectolobiformes: Hemiscyillidae) during steady swimming, data on three-dimensional kinematics and electromyographic recordings were collected. Bamboo sharks were induced to swim at 0.5 and 0.75 body lengths per second in a laminar flow tank. Displacement, lag and angles were analyzed from high-speed video images. Onset, offset, duration, duty cycle and asynchrony index were calculated from three muscle implants on each side of each dorsal fin. The dorsal fins were displaced more laterally than the undulating body. In addition, the dorsal tips had larger lateral displacement than the trailing edges. Increased speed was accompanied by an increase in tail beat frequency with constant tail beat amplitude. However, lateral displacement of the fins and duration of muscle bursts remained relatively constant with increased speed. The range of lateral motion was greater for the second dorsal fin (mean 33.3°) than for the first dorsal fin (mean 28.4°). Bending within the fin was greater for the second dorsal fin (mean 43.8°) than for the first dorsal fin (mean 30.8°). Muscle onset and offset among implants on the same side of each dorsal fin was similar. Three-dimensional conformation of the dorsal fins was caused by interactions between muscle activity, material properties, and incident flow. Alternating bilateral activity occurred in both dorsal fins, further supporting the active role of these hydrofoils in thrust production during steady swimming. The dorsal fins in bamboo sharks are capable of thrust production during steady swimming and do not appear to function as stabilizing structures.     

Body Form and Locomotion in Sharks

A revised interpretation of the mode of action of the heterocercaltail in sharks shows that the upturned tail axis tends to producea thrust directed downwards behind the centre of balance ofthe fish and thus gives a moment turning the head upwards. Thisis countered in two ways—by the rotation of the tail alongits longitudinal axis during each lateral beat, and throughthe action of the ventral hypochordal lobe. The shape of thetail and the mode of action of the tail in all sharks so farconsidered reflects a balance between these three factors, inall of them the net effect being the production of a forwardthrust from the tail that passes directly through the centreof balance of the fiish. There is normally therefore no tendencyfor the fish to turn around the centre of balance in a sagittalplane but there is a net sinking effect that is countered bythe planning effect of the pectoral fins and the ventral surfaceof the head. A study of 56 species of sharks shows that the tail is constructedaccording to a remarkably consistent common plan, the extremesbeing the high angled rather symmetrical tail of pelagic sharkssuch as hums, Lamna and Rhincodon and the straight tails ofbenthic sharks such as Ginglymostoma in which a ventral hypochordallobe is absent. When the general body shape of sharks, includingthe position of insertion of the median and paired fins andthe pattern of growth of fin surface areas is considered, theuniformity of the shark body plan and locomolor function isfurther emphasised. Four patterns of body form in sharks are recognised: 1) Thefast swimming pelagic sharks and the whale sharks have a tailwith a high aspect ratio, a conical head, a lateral fluke onthe caudal peduncle. 2) The generalised sharks typified by theCarcharhinidae, have lower heterocercal angles, a flattenedventral surface on the head and lack the caudal fluke. 3) Thedemersal sharks typified by the catsharks (Scyliorhinidae) havea very low, almost straight tail. The ventral hypochordal lobeis absent and the first dorsal fin is posterior in position.4) The squalomorph sharks are distinct in the absence of theanal fin, presence of a marked epicaudal lobe in the tail andoften an elevated insertion of the pectorals. The anal and second dorsal fins are always the smallest finsand the pectorals grow at the fastest rate. In general thereis an inverse relationship between size and rale of growth ofall fins and the ventral surface of the head. In hammerheadsthe growth data confirms that the head has a significant planingaction in swimming. The pectoral, second dorsal and anal finsshow an extreme constancy of position of insertion in all sharksstudied. The locomotor mechanism of sharks is adapted for anefficient cruising swimming but at the same time, the potentialinstability in the sagittal plan allows for the production ofturning moments that are used in attack and feeding.     

Computational hydrodynamics of animal swimming: boundary element method and three-dimensional vortex wake structure.

The slender body theory, lifting surface theories, and more recently panel methods and Navier-Stokes solvers have been used to study the hydrodynamics of fish swimming. This paper presents progress on swimming hydrodynamics using a boundary integral equation method (or boundary element method) based on potential flow model. The unsteady three-dimensional BEM code 3DynaFS that we developed and used is able to model realistic body geometries, arbitrary movements, and resulting wake evolution. Pressure distribution over the body surface, vorticity in the wake, and the velocity field around the body can be computed. The structure and dynamic behavior of the vortex wakes generated by the swimming body are responsible for the underlying fluid dynamic mechanisms to realize the high-efficiency propulsion and high-agility maneuvering. Three-dimensional vortex wake structures are not well known, although two-dimensional structures termed 'reverse Karman Vortex Street' have been observed and studied. In this paper, simulations about a swimming saithe (Pollachius virens) using our BEM code have demonstrated that undulatory swimming reduces three-dimensional effects due to substantially weakened tail tip vortex, resulting in a reverse Karman Vortex Street as the major flow pattern in the three-dimensional wake of an undulating swimming fish.