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.     

Unsteady flow field around a human hand and propulsive force in swimming

Much effort has been undertaken for the estimation of propulsive force of swimmers in the front crawl. Estimation is typically based on steady flow theory: the so-called quasi-steady analysis. Flow fields around a swimmer, however, are extremely unsteady because the change direction of hand produces unsteady vortex motions. To evaluate the force correctly, it is necessary to know the unsteady properties determined from the vortex dynamics because that unsteadiness is known to make the force greater. Unsteady flow measurements were made for this study using a sophisticated technique called particle image velocimetry (PIV) in several horizontal planes for subjects swimming in a flume. Using that method, a 100 time-sequential flow fields are obtainable simultaneously. Each flow field was calculated from two particle images using the cross-correlation method. The intensity of vortices and their locations were identified. A strong vortex was generated near the hand and then shed by directional change of the hand in the transition phase from in-sweep to out-sweep. When the vortex was shed, a new vortex rotating in the opposite direction around the hand was created. The pair of vortices induced the velocity component in the direction opposite to the swimming. Results of this study show that the momentum change attributable to the increase in this velocity component is the origin of thrust force by the hand.     

Turbulence model choice for the calculation of drag forces when using the CFD method

The aim of this work is to specify which model of turbulence is the most adapted in order to predict the drag forces that a swimmer encounters during his movement in the fluid environment. For this, a Computational Fluid Dynamics (CFD) analysis has been undertaken with a commercial CFD code (Fluent^®). The problem was modelled as 3D and in steady hydrodynamic state. The 3D geometry of the swimmer was created by means of a complete laser scanning of the swimmer’s body contour. Two turbulence models were tested, namely the standard k–ε model with a specific treatment of the fluid flow area near the swimmer’s body contour, and the standard k–ω model. The comparison of numerical results with experimental measurements of drag forces shows that the standard k–ω model accurately predicts the drag forces while the standard k–ε model underestimates their values. The standard k–ω model also enabled to capture the vortex structures developing at the swimmer’s back and buttocks in underwater swimming; the same vortices had been visualized by flow visualization experiments carried out at the INSEP (National Institute for Sport and Physical Education in Paris) with the French national swimming team.     

Vortex interactions with flapping wings and fins can be unpredictable

As they fly or swim, many animals generate a wake of vortices with their flapping fins and wings that reveals the dynamics of their locomotion. Previous studies have shown that the dynamic interaction of vortices in the wake with fins and wings can increase propulsive force. Here, we explore whether the dynamics of the vortex interactions could affect the predictability of propulsive forces. We studied the dynamics of the interactions between a symmetrically and periodically pitching and heaving foil and the vortices in its wake, in a soap-film tunnel. The phase-locked movie sequences reveal that abundant chaotic vortex-wake interactions occur at high Strouhal numbers. These high numbers are representative for the fins and wings of near-hovering animals. The chaotic wake limits the forecast horizon of the corresponding force and moment integrals. By contrast, we find periodic vortex wakes with an unlimited forecast horizon for the lower Strouhal numbers (0.2–0.4) at which many animals cruise. These findings suggest that swimming and flying animals could control the predictability of vortex-wake interactions, and the corresponding propulsive forces with their fins and wings.     

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.     

Riding the waves: the role of the body wave in undulatory fish swimming

A continuously swimming mullet modulates its thrust productionby changing slip-the ratio between its swimming speed U andthe speed V with which the body wave travels down its body.This variation in thrust is reflected in the wake of the fish.We obtained 2-dimensional impressions of the wake behind a mulletswimming at a slip of 0.7 equivalent to active swimming, ata slip of 0.9 close to free-wheeling, and at a slip of 1.1 whenthe fish is braking. Independent of the slip, vortices are shedat the tail when the tail tip reaches its maximum lateral excursion.The manner in which the wake changes as it decays depends onthe degree of slip: At a slip well below unity, the wake decayswithout any qualitative changes in shape, the medio-frontalcross section of the mature wake consists of a double row ofalternating vortices separated by an undulating jet, and theangle between the jet flow and the mean path of motion is closeto 45°; at a slip above unity, the vortices stretch outlaterally and the mature wake resembles a single row of ovalvortices with two vortex cores, and the jet between the vorticesis almost perpendicular to the mean path of motion; the wakeat slip of 0.9 exhibits a pattern intermediate between the wakesat slips 0.7 and 0.9 with slightly elongate vortices and a jetangle of 61°.     

The most efficient metazoan swimmer creates a ‘virtual wall’ to enhance performance

It has been well documented that animals (and machines) swimming or flying near a solid boundary get a boost in performance. This ground effect is often modelled as an interaction between a mirrored pair of vortices represented by a true vortex and an opposite sign ‘virtual vortex’ on the other side of the wall. However, most animals do not swim near solid surfaces and thus near body vortex–vortex interactions in open-water swimmers have been poorly investigated. In this study, we examine the most energetically efficient metazoan swimmer known to date, the jellyfish Aurelia aurita, to elucidate the role that vortex interactions can play in animals that swim away from solid boundaries. We used high-speed video tracking, laser-based digital particle image velocimetry (dPIV) and an algorithm for extracting pressure fields from flow velocity vectors to quantify swimming performance and the effect of near body vortex–vortex interactions. Here, we show that a vortex ring (stopping vortex), created underneath the animal during the previous swim cycle, is critical for increasing propulsive performance. This well-positioned stopping vortex acts in the same way as a virtual vortex during wall-effect performance enhancement, by helping converge fluid at the underside of the propulsive surface and generating significantly higher pressures which result in greater thrust. These findings advocate that jellyfish can generate a wall-effect boost in open water by creating what amounts to a ‘virtual wall’ between two real, opposite sign vortex rings. This explains the significant propulsive advantage jellyfish possess over other metazoans and represents important implications for bio-engineered propulsion systems.     

Unsteady hydrodynamic forces acting on a robotic arm and its flow field: Application to the crawl stroke

This study aims to clarify the mechanisms by which unsteady hydrodynamic forces act on the hand of a swimmer during a crawl stroke. Measurements were performed for a hand attached to a robotic arm with five degrees of freedom independently controlled by a computer. The computer was programmed so the hand and arm mimicked a human performing the stroke. We directly measured forces on the hand and pressure distributions around it at 200 Hz; flow fields underwater near the hand were obtained via 2D particle image velocimetry (PIV). The data revealed two mechanisms that generate unsteady forces during a crawl stroke. One is the unsteady lift force generated when hand movement changes direction during the stroke, leading to vortex shedding and bound vortex created around it. This bound vortex circulation results in a lift that contributes to the thrust. The other occurs when the hand moves linearly with a large angle of attack, creating a Kármán vortex street. This street alternatively sheds clockwise and counterclockwise vortices, resulting in a quasi-steady drag contributing to the thrust. We presume that professional swimmers benefit from both mechanisms. Further studies are necessary in which 3D flow fields are measured using a 3D PIV system and a human swimmer.     

Numerical streamline patterns at swimmer's surface using RANS equations

The objective of this article is to perform a numerical modeling on the flow dynamics around a competitive female swimmer during the underwater swimming phase for a velocity of 2.2 m/s corresponding to national swimming levels. Flow around the swimmer is assumed turbulent and simulated with a computational fluid dynamics method based on a volume control approach. The 3D numerical simulations have been carried out with the code ANSYS FLUENT and are presented using the standard k-ω turbulence model for a Reynolds number of 6.4 × 10(6). To validate the streamline patterns produced by the simulation, experiments were performed in the swimming pools of the National Institute of Sports and Physical Education in Paris (INSEP) by using the tufts method.     

Propulsion in Cubomedusae: Mechanisms and Utility

Evolutionary constraints which limit the forces produced during bell contractions of medusae affect the overall medusan morphospace such that jet propulsion is limited to only small medusae. Cubomedusae, which often possess large prolate bells and are thought to swim via jet propulsion, appear to violate the theoretical constraints which determine the medusan morphospace. To examine propulsion by cubomedusae, we quantified size related changes in wake dynamics, bell shape, swimming and turning kinematics of two species of cubomedusae, Chironex fleckeri and Chiropsella bronzie. During growth, these cubomedusae transitioned from using jet propulsion at smaller sizes to a rowing-jetting hybrid mode of propulsion at larger sizes. Simple modifications in the flexibility and kinematics of their velarium appeared to be sufficient to alter their propulsive mode. Turning occurs during both bell contraction and expansion and is achieved by generating asymmetric vortex structures during both stages of the swimming cycle. Swimming characteristics were considered in conjunction with the unique foraging strategy used by cubomedusae.     

What information do Kármán streets offer to flow sensing?

In this work, we focus on biomimetic lateral line sensing in Kármán vortex streets. After generating a Kármán street in a controlled environment, we examine the hydrodynamic images obtained with digital particle image velocimetry (DPIV). On the grounds that positioning in the flow and interaction with the vortices govern bio-inspired underwater locomotion, we inspect the fluid in the swimming robot frame of reference. We spatially subsample the flow field obtained using DPIV to emulate the local flow around the body. In particular, we look at various sensor configurations in order to reliably identify the vortex shedding frequency, wake wavelength and downstream flow speed. Moreover, we propose methods that differentiate between being in and out of the Kármán street with >70% accuracy, distinguish right from left with respect to Kármán vortex street centreline (>80%) and highlight when the sensor system enters the vortex formation zone (>75%). Finally, we present a method that estimates the relative position of a sensor array with respect to the vortex formation point within 15% error margin.     

Analysis of the effect of swimmer's head position on swimming performance using computational fluid dynamics

The aim of this numerical work is to analyze the effect of the position of the swimmer's head on the hydrodynamic performances in swimming. In this initial study, the problem was modeled as 2D and in steady hydrodynamic state. The geometry is generated by the CAD software CATIA and the numerical simulation is carried out by the use of the CFD Fluent code. The standard k-epsilon turbulence model is used with a specific wall law. Three positions of the head were studied, for a range of Reynolds numbers about 10(6). The obtained numerical results revealed that the position of the head had a noticeable effect on the hydrodynamic performances, strongly modifying the wake around the swimmer. The analysis of these results made it possible to propose an optimal position of the head of a swimmer in underwater swimming.     

Relative distribution of blood flow in rats during surface and submerged swimming

The relative distribution of blood flow was investigated in conscious rats with a radiological imaging technique that utilizes technetium-99m ethyl cysteinate dimer (99mTc-ECD). The objective of the study was to determine the effects of locomotory activity on the distribution of blood flow during a dive response. We compared the relative distribution of systemic flow in rats at rest, surface swimming and during periods of voluntarily initiated underwater swimming. The pattern of blood flow differed considerably between the three groups of rats. In resting controls, blood flow was widely distributed throughout the whole body with the thoraco-abdominal region receiving the largest fraction of cardiac output. During surface swimming blood shifted towards the exercising limbs, while during underwater swimming systemic blood flow was largely restricted to the head and thorax. However, the active front and hind limbs were not rendered totally ischemic. This suggests that the demands of exercising skeletal muscle partially over-ride the peripheral vasoconstriction during asphyxic diving in conscious rats. Furthermore, relative blood flow to the head increased during underwater swimming, which supports the view that there is a preferential maintenance of blood flow to the brain.     

Effect of leg kick on active drag in front-crawl swimming: Comparison of whole stroke and arms-only stroke during front-crawl and the streamlined position

The purpose of this study was to examine the effect of leg kick on the resistance force in front-crawl swimming. The active drag in front-crawl swimming with and without leg motion was evaluated using measured values of residual thrust (MRT method) and compared with the passive drag of the streamlined position (SP) for the same swimmers. Seven male competitive swimmers participated in this study, and the testing was conducted in a swimming flume. Each swimmer performed front-crawl under two conditions: using arms and legs (whole stroke: WS) and using arms only (arms-only stroke: AS). Active drag and passive drag were measured at swimming velocities of 1.1 and 1.3 m s⁻¹ using load cells connected to the swimmer via wires. We calculated a drag coefficient to compare the resistances of the WS, AS and SP at each velocity. For both the WS and AS at both swimming velocities, active drag coefficient was found to be about 1.6–1.9 times larger than that in passive conditions. In contrast, although leg movement did not cause a difference in drag coefficient for front-crawl swimming, there was a large effect size (d = 1.43) at 1.3 m s⁻¹. Therefore, although upper and lower limb movements increase resistance compared to the passive condition, the effect of leg kick on drag may depend on swimming velocity.     

Functional morphology of the pectoral fins in bamboo sharks, Chiloscyllium plagiosum: benthic vs. pelagic station-holding

Bamboo sharks (Chiloscyllium plagiosum) are primarily benthic and use their relatively flexible pectoral and pelvic fins to rest on and move about the substrate. We examined the morphology of the pectoral fins and investigated their locomotory function to determine if pectoral fin function during both benthic station-holding and pelagic swimming differs from fin function described previously in leopard sharks, Triakis semifasciata. We used three-dimensional kinematics and digital particle image velocimetry (DPIV) to quantify pectoral fin function in five white-spotted bamboo sharks, C. plagiosum, during four behaviors: holding station on the substrate, steady horizontal swimming, and rising and sinking during swimming. During benthic station-holding in current flow, bamboo sharks decrease body angle and adjust pectoral fin angle to shed a clockwise fluid vortex. This vortex generates negative lift more than eight times that produced during open water vertical maneuvering and also results in an upstream flow that pushes against the posterior surface of the pectoral fin to oppose drag. In contrast, there is no evidence of significant lift force in the wake of the pectoral fin during steady horizontal swimming. The pectoral fin is held concave downward and at a negative dihedral angle during steady horizontal swimming, promoting maneuverability rather than stability, although this negative dihedral angle is much less than that observed previously in sturgeon and leopard sharks. During sinking, the pectoral fins are held concave upward and shed a clockwise vortex with a negative lift force, while in rising the pectoral fin is held concave downward and sheds a counterclockwise vortex with a positive lift force. Bamboo sharks appear to sacrifice maneuverability for stability when locomoting in the water column and use their relatively flexible fins to generate strong negative lift forces when holding position on the substrate and to enhance stability when swimming in the water column.     

The effect of Reynolds number on the propulsive efficiency of a biomorphic pulsed-jet underwater vehicle

The effect of Reynolds number on the propulsive efficiency of pulsed-jet propulsion was studied experimentally on a self-propelled, pulsed-jet underwater vehicle, dubbed Robosquid due to the similarity of its propulsion system with squid. Robosquid was tested for jet slug length-to-diameter ratios (L/D) in the range 2-6 and dimensionless frequency (St(L)) in the range 0.2-0.6 in a glycerin-water mixture. Digital particle image velocimetry was used for measuring the impulse and energy of jet pulses from the velocity and vorticity fields of the jet flow to calculate the pulsed-jet propulsive efficiency, and compare it with an equivalent steady jet system. Robosquid's Reynolds number (Re) based on average vehicle velocity and vehicle diameter ranged between 37 and 60. The current results for propulsive efficiency were compared to the previously published results in water where Re ranged between 1300 and 2700. The results showed that the average propulsive efficiency decreased by 26% as the average Re decreased from 2000 to 50 while the ratio of pulsed-jet to steady jet efficiency (η(P)/η(P, ss)) increased up to 0.15 (26%) as the Re decreased over the same range and for similar pulsing conditions. The improved η(P)/η(P, ss) at lower Re suggests that pulsed-jet propulsion can be used as an efficient propulsion system for millimeter-scale propulsion applications. The Re = 37-60 conditions in the present investigation, showed a reduced dependence of η(P) and η(P)/η(P, ss)on L/D compared to higher Re results. This may be due to the lack of clearly observed vortex ring pinch-off as L/D increased for this Re regime.     

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.     

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.     

Flow visualization of competitive swimming techniques: the tufts method

The purpose of this study was to evaluate the use of tufts to visualize the flow of water around the trunk and limbs of a swimmer. Numerous pilot studies were conducted to evaluate the effectiveness of different tuft materials, dimensions and methods of attachment for recording the characteristics of the flow around a swimmer performing various strokes and drills. Differences in the patterns of flow made visible by the tufts suggested that this method of flow visualization may well be useful in resolving both basic and applied questions concerning swimming techniques.     

Function of the dorsal fin in bluegill sunfish: Motor patterns during four distinct locomotor behaviors

The median fins of fishes are key features of locomotor morphology which function as complex control surfaces during a variety of behaviors. However, very few studies have experimentally assessed median fin function, as most workers focus on axial structures. In particular, the dorsal fin of many teleost fishes possesses both spiny anterior and soft posterior portions which may function separately during locomotion. We analyzed the function of the soft region of the dorsal fin and of the dorsal inclinator (Di) muscles which are the primary muscles responsible for lateral flexion. We used electromyography to measure in vivo Di activity, as well as activity of the red myomeric muscles located at a similar longitudinal position. We quantified motor patterns during four locomotor behaviors: braking and three propulsive behaviors (steady swimming, kick and glide swimming, and C-starts). During the three propulsive swimming behaviors, the timing of Di activity was more similar to that of ipsilateral red myomeric muscle rather than to contralateral myomeric activity, whereas during braking the timing of activity of the Di muscles was similar to that of the contralateral myomeric musculature. During the three propulsive behaviors, when the Di muscles had activity, it was consistent with the function of stiffening the soft dorsal fin to oppose its tendency to bend as a result of the body being swept laterally through the water. In contrast, activity of the Di muscles during braking was consistent with the function of actively flexing the soft dorsal fin towards the side of the fish that had Di activity. Activity of the Di muscles during steady speed swimming was generally sufficient to resist lateral bending of the soft dorsal fin, whereas during high speed kick and glide swimming and C-starts, Di activity was not sufficient to resist the bending caused by resistive forces imposed by the water. Cumulative data from all four behaviors suggest that the Di muscles can be activated independently relative to the myomeric musculature rather than having a single phase relationship with the myomeric muscle common to all of the observed behaviors. © 1996 Wiley-Liss, Inc.