Biological characterization of the skin of shortfin mako shark Isurus oxyrinchus and preliminary study of the hydrodynamic behaviour through computational fluid dynamics

This study characterized the morphology, density and orientation of the dermal denticles along the body of a shortfin mako shark Isurus oxyrinchus and identified the hydrodynamic parameters of its body through a computational fluid‐dynamics model. The study showed a great variability in the morphology, size, shape, orientation and density of dermal denticles along the body of I. oxyrinchus. There was a significant higher density in dorsal and ventral areas of the body and their highest angular deviations were found in the lower part of the mouth and in the areas between the pre‐caudal pit and the second dorsal and pelvic fins. A detailed three‐dimensional geometry from a scanned body of a shark was carried out to evaluate the hydrodynamic properties such as drag coefficient, lift coefficient and superficial (skin) friction coefficient of the skin together with flow velocity field, according to different roughness coefficients simulating the effect of the dermal denticles. This preliminary approach contributed to detailed information of the denticle interactions. As the height of the denticles was increased, flow velocity and the effect of lift decreased whereas drag increased. The highest peaks of skin friction coefficient were observed around the pectoral fins.     

Drag of suction cup tags on swimming animals: Modeling and measurement

Bio‐logging tags are widely used to study the behavior and movements of marine mammals with the tacit assumption of little impact to the animal. However, tags on fast‐swimming animals generate substantial hydrodynamic forces potentially affecting behavior and energetics adversely, or promoting early removal of the tag. In this work, hydrodynamic loading of three novel tag housing designs are compared over a range of swimming speeds using computational fluid dynamics (CFD). Results from CFD simulation were verified using tag models in a water flume with close agreement. Drag forces were reduced by minimizing geometric disruptions to the flow around the housing, while lift forces were reduced by minimizing the frontal cross‐sectional area of the housing and holding the tag close to the attachment surface. Hydrodynamic tag design resulted in an experimentally measured 60% drag force reduction in 5.6 m/s flow. For all housing designs, off‐axis flow increased the magnitude of the force on the tag. Experimental work with a common dolphin (Delphinus delphis) cadaver indicates that the suction cups used to attach the types of tags described here provide sufficient attachment force to resist failure to predicted forces at swimming speeds of up to 10 m/s.     

The determination of drag in front crawl swimming

The measurement of drag while swimming (i.e. active drag) is a controversial issue. Therefore, in a group of six elite swimmers two active drag measurement methods were compared to assess whether both measure the same retarding force during swimming. In method 1 push-off forces are measured directly using the system to measure active drag (MAD-system). In method 2 (the velocity perturbation method, VPM) drag is estimated from the difference in swimming speed when subjects swim twice at maximal effort (assuming equal power output and assuming a quadratic drag-speed relationship): once swimming free, and once swimming with a hydrodynamic body attached that created a known additional resistance. The average drag for the VPM tests (53.2 N) was statistically significant and different from the active drag for the MAD-test (66.9 N), paired Student's t-test: 2.484, 12 DF, p=0.029. A post hoc analysis was performed to assess whether the two methods measure a different phenomenon. Based on the drag speed curve obtained with the MAD-system, the VPM-data were re-examined. For diverging drag determinations the assumption of equal power output of the 'free' trial (swimming free) vs. the towing trial (swimming with hydrodynamic buoy) appeared to be violated. The regression of the relative difference in force (MAD vs. VPM) on the relative difference in power (swimming free vs. swimming with hydrodynamic body) was: %Deltadrag=1.898 x %Deltapower -4.498, r2=0.88. This suggests that the major part of the difference in active drag values is due to a non-equal power output in the 'free' relative towing trial during the VPM-test. The simulation of the violation of the equal power output assumption and the calculation of the effect of an other than quadratic drag-speed relationship corroborated the tentative conclusion that both methods measure essentially the same phenomenon and that active drag differences can be explained by a violation of test assumptions.     

Influence of a postural change of the swimmer's head in hydrodynamic performances using 3D CFD

This study deals with recent researches undertaken by the authors in the field of hydrodynamics of human swimming. The aim of this numerical study was to investigate the flow around the entire swimmer's body. The results presented in this article focus on the combination of a 3D computational fluid dynamics code and the use of the k–ω turbulence model, in the range of Reynolds numbers representative of a swimming level varying from national to international competition. Emphasis is placed on the influence of a postural change of the swimmer's head in hydrodynamic performances, which is directly related to the reduction of overall drag. These results confirm and complete those, less accurate, of a preliminary 2D study recently published by the authors and allow the authors to optimise the swimmer's head position in underwater swimming.     

Shifts in drag and swimming potential during grayling ontogenesis: relations with habitat use

The drag coefficient (C_d) of grayling Thymallus thymallus was dependent on body surface conditions and rigidity. At comparable flow conditions, C_d values of a fish preserved in formalin (high body rigidity) were 15–30% lower than those obtained on a freshly-killed fish (medium rigidity); the presence of skin mucus on fish could reduce C_d by 10%. The hydrodynamic potential of grayling increased during ontogenesis, because C_d values decreased (except for yolk sac larvae, which had a particular morphology) and the swimming capacities (in terms of relative muscular mass) increased. Grayling morphology evolves towards hydrodynamically efficient shape at high velocities, and there is a relationship between these shifts in hydrodynamic abilities and the different habitats (in terms of current velocity) used by five morphological groups. Therefore, the concept of hydrodynamic potential (i.e. hydrodynamics of shape and swimming capacities) could be a useful tool in fish ecomorphology and predictions of habitat use.     

The Orientation of Swimming Biflagellates in Shear Flows

Biflagellated algae swim in mean directions that are governed by their environments. For example, many algae can swim upward on average (gravitaxis) and toward downwelling fluid (gyrotaxis) via a variety of mechanisms. Accumulations of cells within the fluid can induce hydrodynamic instabilities leading to patterns and flow, termed bioconvection, which may be of particular relevance to algal bioreactors and plankton dynamics. Furthermore, knowledge of the behavior of an individual swimming cell subject to imposed flow is prerequisite to a full understanding of the scaled-up bulk behavior and population dynamics of cells in oceans and lakes; swimming behavior and patchiness will impact opportunities for interactions, which are at the heart of population models. Hence, better estimates of population level parameters necessitate a detailed understanding of cell swimming bias. Using the method of regularized Stokeslets, numerical computations are developed to investigate the swimming behavior of and fluid flow around gyrotactic prolate spheroidal biflagellates with five distinct flagellar beats. In particular, we explore cell reorientation mechanisms associated with bottom-heaviness and sedimentation and find that they are commensurate and complementary. Furthermore, using an experimentally measured flagellar beat for Chlamydomonas reinhardtii, we reveal that the effective cell eccentricity of the swimming cell is much smaller than for the inanimate body alone, suggesting that the cells may be modeled satisfactorily as self-propelled spheres. Finally, we propose a method to estimate the effective cell eccentricity of any biflagellate when flagellar beat images are obtained haphazardly.     

Using reverse engineering and computational fluid dynamics to investigate a lower arm amputee swimmer's performance

In front crawl swimming, the hand and the corresponding forearm generate major propulsive forces. Such forces have been studied largely through experimental tests and more recently through the use of steady computational fluid dynamics (CFD). However, the effect of the upper arm on the propulsive forces has generally not been taken into consideration. An understanding of such forces is fundamental for the performance of swimmers who have an arm amputation at the level of the elbow. This study introduces the great potential offered by the multidisciplinary approach combining reverse engineering and unsteady CFD in a novel dynamic and interactive way. A complex CFD mesh model, representing the swimmer body and its upper arm, is produced. The model, including the arm rotation and a body roll movement, interacts dynamically with the fluid flow. Forces generated by the upper arm can then be investigated in great detail. In this particular study, it is found that the upper arm effectively contributes to the propulsion of the body. The propulsive force was numerically computed throughout the pull and reaches maxima of 8N. Results obtained in this study could be extended in a similar way to any other limb movement within a fluid flow.     

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.     

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.     

Hydrodynamic flow control in marine mammals

The ability to control the flow of water around the body dictates the performance of marine mammals in the aquatic environment. Morphological specializations of marine mammals afford mechanisms for passive flow control. Aside from the design of the body, which minimizes drag, the morphology of the appendages provides hydrodynamic advantages with respect to drag, lift, thrust, and stall. The flukes of cetaceans and sirenians and flippers of pinnipeds possess geometries with flexibility, which enhance thrust production for high efficiency swimming. The pectoral flippers provide hydrodynamic lift for maneuvering. The design of the flippers is constrained by performance associated with stall. Delay of stall can be accomplished passively by modification of the flipper leading edge. Such a design is exhibited by the leading edge tubercles on the flippers of humpback whales (Megaptera novaeangliae). These novel morphological structures induce a spanwise flow field of separated vortices alternating with regions of accelerated flow. The coupled flow regions maintain areas of attached flow and delay stall to high angles of attack. The delay of stall permits enhanced turning performance with respect to both agility and maneuverability. The morphological features of marine mammals for flow control can be utilized in the biomimetic design of engineered structures for increased power production and increased efficiency.     

Three-dimensional CFD analysis of the hand and forearm in swimming

The purpose of this study was to analyze the hydrodynamic characteristics of a realistic model of an elite swimmer hand/forearm using three-dimensional computational fluid dynamics techniques. A three-dimensional domain was designed to simulate the fluid flow around a swimmer hand and forearm model in different orientations (0°, 45°, and 90° for the three axes Ox, Oy and Oz). The hand/forearm model was obtained through computerized tomography scans. Steady-state analyses were performed using the commercial code Fluent. The drag coefficient presented higher values than the lift coefficient for all model orientations. The drag coefficient of the hand/forearm model increased with the angle of attack, with the maximum value of the force coefficient corresponding to an angle of attack of 90°. The drag coefficient obtained the highest value at an orientation of the hand plane in which the model was directly perpendicular to the direction of the flow. An important contribution of the lift coefficient was observed at an angle of attack of 45°, which could have an important role in the overall propulsive force production of the hand and forearm in swimming phases, when the angle of attack is near 45°.     

Ontogeny of form and function: locomotor morphology and drag in zebrafish (Danio rerio)

Many fish species transform in body shape during growth, but it remains unclear how this influences the mechanics of locomotion. Therefore, the present study focused on understanding how drag generation during coasting is affected by ontogenetic changes in the morphology of zebrafish (Danio rerio). The shapes of the body and fins were measured from photographs of fish ranging in size from small larvae to mature adults and these morphometrics were compared to drag coefficients calculated from high-speed video recordings of routine swimming. We found that the viscous drag coefficient of larval and juvenile fish increased by more than an order of magnitude during growth and the inertial drag coefficient decreased at a comparable rate in adults. These hydrodynamic changes occurred as zebrafish disproportionately increased the span of their fins and their body changed shape from elongated to streamlined, as reflected by the logistic growth of a newly defined streamlining index, SL. These results suggest that morphological changes incur a performance cost by generating greater drag when larvae and juveniles operate in the viscous regime, but later provide a performance benefit by reducing pressure drag in the inertial regime of the adult stage.     

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.     

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.     

Renewable fluid dynamic energy derived from aquatic animal locomotion

Aquatic animals swimming in isolation and in groups are known to extract energy from the vortices in environmental flows, significantly reducing muscle activity required for locomotion. A model for the vortex dynamics associated with this phenomenon is developed, showing that the energy extraction mechanism can be described by simple criteria governing the kinematics of the vortices relative to the body in the flow. In this way, we need not make direct appeal to the fluid dynamics, which can be more difficult to evaluate than the kinematics. Examples of these principles as exhibited in swimming fish and existing energy conversion devices are described. A benefit of the developed framework is that the potentially infinite-dimensional parameter space of the fluid-structure interaction is reduced to a maximum of eight combinations of three parameters. The model may potentially aid in the design and evaluation of unsteady aero- and hydrodynamic energy conversion systems that surpass the Betz efficiency limit of steady fluid dynamic energy conversion systems.     

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.     

A non‐invasive dolphin telemetry tag: Computer design and numerical flow simulation

The impact of devices attached to animals remains a challenge in telemetry studies of dolphins. It was hypothesized that the hydrodynamic design of a tag could provide stable attachment to the dorsal fin by means of resultant hydrodynamic force appearing when a dolphin is swimming. To verify this hypothesis the computer fluid dynamics (CFD) study of tag performance was carried out. A virtual model presenting authentic geometry of a dolphin with tag attached to the dorsal fin was constructed. The same model without tag was used as a reference object to calculate tag impact as regards drag, lift, and moments coefficients. Flow around the models was simulated for the range of velocities as well as the ranges of pitch and yaw angles. It was shown that in 33 of 35 CFD scenarios the streamlined shape of a tag generates the lift force that facilitates keeping a tag attached to the fin. Throughout the set of calculations the tag‐associated drag coefficient does not exceed 4%, which indicates low impact. Data obtained present a baseline for the further development of non‐invasive dolphin telemetry tags.     

Skin-friction drag analysis from the forced convection modeling in simplified underwater swimming

This study deals with skin-friction drag analysis in underwater swimming. Although lower than profile drag, skin-friction drag remains significant and is the second and only other contribution to total drag in the case of underwater swimming. The question arises whether varying the thermal gradient between the underwater swimmer and the pool water may modify the surface shear stress distribution and the resulting skin-friction drag acting on a swimmer's body. As far as the authors are aware, such a question has not previously been addressed. Therefore, the purpose of this study was to quantify the effect of this thermal gradient by using the integral formalism applied to the forced convection theory. From a simplified model in a range of pool temperatures (20-30 degrees C) it was demonstrated that, whatever the swimming speeds, a 5.3% reduction in the skin-friction drag would occur with increasing average boundary-layer temperature provided that the flow remained laminar. However, as the majority of the flow is actually turbulent, a turbulent flow analysis leads to the major conclusion that friction drag is a function of underwater speed, leading to a possible 1.5% reduction for fast swimming speeds above 1m/s. Furthermore, simple correlations between the surface shear stress and resulting skin-friction drag are derived in terms of the boundary-layer temperature, which may be readily used in underwater swimming situations.     

Growth in response to sustained swimming in young montezumae swordtails,Xiphophorus montezumae

This study tested the effect of sustained swimming on growth, ingestion rate, and morphology of juvenile montezumae swordtails (Xiphophorus montezumae). Because montezumae swordtails inhabit running freshwater systems, it was expected that moderate exercise would increase feeding and growth rates, promoting also the hydrodynamic form of the fish. Experimental groups were subjected to different levels of sustained exercise by being forced to swim against water currents at four different velocities (0, 4.1, 7.8, and 12.9 cm/s). The results showed that growth-rate decrease in fish forced to swim, while the increase in exercise did not modify the ingestion rate. Thus, it is likely that the extra energy expenditure associated with the swimming cost was not compensated by an increase in food ingestion. Sustained exercise increased the fineness ratio towards a more hydrodynamic form. Morphological traits linked with minimum drag, such as caudal peduncle depth and amplitude of the caudal fin were not modified. Our results suggest that water velocity has an important role determining the physiology and, to a lesser extent, the morphology of young montezumae swordtails.     

Growth in response to sustained swimming in young montezumae swordtails, Xiphophorus montezumae

This study tested the effect of sustained swimming on growth, ingestion rate, and morphology of juvenile montezumae swordtails (Xiphophorus montezumae). Because montezumae swordtails inhabit running freshwater systems, it was expected that moderate exercise would increase feeding and growth rates, promoting also the hydrodynamic form of the fish. Experimental groups were subjected to different levels of sustained exercise by being forced to swim against water currents at four different velocities (0, 4.1, 7.8, and 12.9 cm/s). The results showed that growth-rate decrease in fish forced to swim, while the increase in exercise did not modify the ingestion rate. Thus, it is likely that the extra energy expenditure associated with the swimming cost was not compensated by an increase in food ingestion. Sustained exercise increased the fineness ratio towards a more hydrodynamic form. Morphological traits linked with minimum drag, such as caudal peduncle depth and amplitude of the caudal fin were not modified. Our results suggest that water velocity has an important role determining the physiology and, to a lesser extent, the morphology of young montezumae swordtails.