Volumetric imaging of shark tail hydrodynamics reveals a three-dimensional dual-ring vortex wake structure

Form and function of anguilliform swimming

Anguilliform swimmers are long and narrow animals that propel themselves by undulating their bodies. Observations in nature and recent investigations suggest that anguilliform swimming is highly efficient. However, understanding the underlying reasons for the efficiency of this type of locomotion requires interdisciplinary studies spanning from biology to hydrodynamics. Regrettably, these different fields are rarely discussed together, which hinders our ability to understand the repeated evolution of this swimming mode in vertebrates. This review compiles the current knowledge of the anatomical features that drive anguilliform swimming, compares the resulting kinematics across a wide range of anguilliform swimmers, and describes the resulting hydrodynamic interactions using data from both in vivo experiments and computational studies.

Growing out of the fins: Implications of isometric and allometric scaling of morphology relative to increasing mass in blue sharks (Prionace glauca)

Disproportional changes (i.e. allometry) in shark morphology relative to increasing body size have been attributed to shifts in function associated with niche shifts in life history, such as in habitat and diet. Photographs of blue sharks (Prionace glauca, 26-145 kg) were used to analyze changes in parameters of body and fin morphology with increasing mass that are fundamental to swimming and feeding. We hypothesized that blue sharks would demonstrate proportional changes (i.e. isometry) in morphology with increasing mass because they do not undergo profound changes in prey and habitat type; accordingly, due to geometric scaling laws, we predicted that blue sharks would grow into bodies with greater turning inertias and smaller frontal and surface areas, in addition to smaller spans and areas of the fins relative to mass, which are parameters that are associated with the swimming performance in sharks. Many aspects of morphology increased with isometry. However, blue sharks demonstrated negative allometry in body density, whereas surface area, volume and roll inertia of the body, area, span and aspect ratio of both dorsal fins, span and aspect ratio of the ventral caudal fin, and span, length and area of the mouth increased with positive allometry. The dataset was divided in half based on mass to form two groups: smaller and larger sharks. Besides area of both dorsal fins, relative to mass, larger sharks had bodies with significantly greater turning inertia and smaller frontal and surface areas, in addition to fins with smaller spans and areas, compared to smaller sharks. In conclusion, isometric scaling does not necessarily imply functional similarity, and allometric scaling may sometimes be critical in maintaining, rather than shifting, function relative to mass in animals that swim through the water column.

The multidimensional spectrum of eco-evolutionary relationships between sharks and remoras

Remoras are a highly specialised group of fishes known to associate with a range of marine megafauna, including elasmobranchs, cetaceans and marine reptiles. Remoras appear to benefit from these interspecific interactions through consumption of host dermal parasites or reduced cost of transport. Shark-remora associations are widely documented, yet our understanding of the costs and benefits involved in these interactions is poor. Studies frequently make claims about mutualistic, commensalistic or parasitic relationships without providing the necessary quantitative information necessary to make these claims. Here I explain why this approach is problematic, and proceed to examine shark-remora interactions in a rigorous eco-evolutionary framework. These interactions cannot be properly classified without considering net evolutionary fitness and context dependence. In reality, shark-remora interactions are best defined by a multidimensional spectrum of fitness consequences, with net fitness outcomes shifting between mutualism and parasitism (and vice versa) through space and time.

The role of hydrodynamics in collective motions of fish schools and bioinspired underwater robots

Collective behaviour defines the lives of many animal species on the Earth. Underwater swarms span several orders of magnitude in size, from coral larvae and krill to tunas and dolphins. Agent-based algorithms have modelled collective movements of animal groups by use of social forces, which approximate the behaviour of individual animals. But details of how swarming individuals interact with the fluid environment are often under-examined. How do fluid forces shape aquatic swarms? How do fish use their flow-sensing capabilities to coordinate with their schooling mates? We propose viewing underwater collective behaviour from the framework of fluid stigmergy, which considers both physical interactions and information transfer in fluid environments. Understanding the role of hydrodynamics in aquatic collectives requires multi-disciplinary efforts across fluid mechanics, biology and biomimetic robotics. To facilitate future collaborations, we synthesize key studies in these fields.

The effect of tail stiffness on a sprawling quadruped locomotion

A distinctive feature of quadrupeds that is integral to their locomotion is the tail. Tails serve many purposes in biological systems, including propulsion, counterbalance, and stabilization while walking, running, climbing, or jumping. Similarly, tails in legged robots may augment the stability and maneuverability of legged robots by providing an additional point of contact with the ground. However, in the field of terrestrial bio-inspired legged robotics, the tail is often ignored because of the difficulties in design and control. In this study, we test the hypothesis that a variable stiffness robotic tail can improve the performance of a sprawling quadruped robot by enhancing its stability and maneuverability in various environments. In order to validate our hypothesis, we integrated a cable-driven, flexible tail with multiple segments into the underactuated sprawling quadruped robot, where a single servo motor working alongside a reel and cable mechanism regulates the tail's stiffness. Our results demonstrated that by controlling the stiffness of the tail, the stability of locomotion on rough terrain and the climbing ability of the robot are improved compared to the movement with a rigid tail and no tail. Our findings highlight that constant ground support provided by the flexible tail is key to maintaining stable locomotion. This ensured a predictable gait cycle, eliminating unexpected turning and slipping, resulting in an increase in locomotion speed and efficiency. Additionally, we observed the robot's enhanced climbing ability on surfaces inclined up to 20°. The flexibility of the tail enabled the robot to overcome obstacles without external sensing, exhibiting significant adaptability across various terrains.

Ontogenetic morphometry of the brown smoothhound shark Mustelus henlei with implications for ecology and evolution

The central tenet of ecomorphology links ecological and morphological variation through the process of selection. Traditionally used to rationalise morphological differences between taxa, an ecomorphological approach is increasingly being utilised to study morphological differences expressed through ontogeny. Elasmobranchii (sharks, rays and skates) is one clade in which such ontogenetic shifts in body form have been reported. Such studies are limited to a relatively small proportion of total elasmobranch ecological and morphological diversity, and questions remain regarding the extent to which ecological selection are driving observed morphometric trends. In this study, we report ontogenetic growth trajectories obtained via traditional linear morphometrics from a large data set of the brown smoothhound shark (Mustelus henlei). We consider various morphological structures including the caudal, dorsal and pectoral fins, as well as several girth measurements. We use an ecomorphological approach to infer the broad ecological characteristics of this population and refine understanding of the selective forces underlying the evolution of specific morphological structures. We suggest that observed scaling trends in M. henlei are inconsistent with migratory behaviour, but do not contradict a putative trophic niche shift. We also highlight the role of predation pressure and sex-based ecological differences in driving observed trends in morphometry, a factor which has previously been neglected when considering the evolution of body form in sharks.

Form and function of the caudal fin throughout the phylogeny of fishes

Fishes are the longest persisting living vertebrates and as such, display an incredible array of diversity. Variation in the tail, or caudal fin, is often a reflection of a fish's environment, and affects movement, predation, defense, and reproduction. Previous literature has discussed many aspects of caudal fin form and function in particular taxonomic groups; however, no previous work has synthesized these studies in order to detail how the caudal fin is structured, and what purpose this structure serves, throughout the phylogeny of fishes. This review examines the caudal fin throughout the main lineages of fish evolution, and highlights where changes in shape and usage have occurred. Such novelties in form and function tend to have far-reaching evolutionary consequences. Through integration of past and present work, this review creates a coherent picture of caudal fin evolution. Patterns and outliers that demonstrate how form and function of this appendage are intertwined can further inform hypotheses that fill critical gaps in knowledge concerning the caudal fin.

Hydrodynamic stress maps on the surface of a flexible fin-like foil

We determine the time dependence of pressure and shear stress distributions on the surface of a pitching and deforming hydrofoil from measurements of the three dimensional flow field. Period-averaged stress maps are obtained both in the presence and absence of steady flow around the foil. The velocity vector field is determined via volumetric three-component particle tracking velocimetry and subsequently inserted into the Navier-Stokes equation to calculate the total hydrodynamic stress tensor. In addition, we also present a careful error analysis of such measurements, showing that local evaluations of stress distributions are possible. The consistency of the force time-dependence is verified using a control volume analysis. The flapping foil used in the experiments is designed to allow comparison with a small trapezoidal fish fin, in terms of the scaling laws that govern the oscillatory flow regime. As a complementary approach, unsteady Euler-Bernoulli beam theory is employed to derive instantaneous transversal force distributions on the flexible hydrofoil from its deflection and the results are compared to the spatial distributions of hydrodynamic stresses obtained from the fluid velocity field.

Thrust generation during steady swimming and acceleration from rest in anguilliform swimmers

Escape swimming is a crucial behavior by which undulatory swimmers evade potential threats. The hydrodynamics of escape swimming have not been well studied, particularly for anguilliform swimmers, such as the sea lamprey Petromyzon marinus. For this study, we compared the kinematics and hydrodynamics of larval sea lampreys with those of lampreys accelerating from rest during escape swimming. We used experimentally derived velocity fields to calculate pressure fields and distributions of thrust and drag along the body. Lampreys initiated acceleration from rest with the formation of a high-amplitude body bend at approximately one-quarter body length posterior to the head. This deep body bend produced two high-pressure regions from which the majority of thrust for acceleration was derived. In contrast, steady swimming was characterized by shallower body bends and negative-pressure-derived thrust, which was strongest near the tail. The distinct mechanisms used for steady swimming and acceleration from rest may reflect the differing demands of the two behaviors. High-pressure-based mechanisms, such as the one used for acceleration from rest, could also be important for low-speed maneuvering during which drag-based turning mechanisms are less effective. The design of swimming robots may benefit from the incorporation of such insights from unsteady swimming.

Quantitative classification of vortical flows based on topological features using graph matching

Vortical flow patterns generated by swimming animals or flow separation (e.g. behind bluff objects such as cylinders) provide important insight to global flow behaviour such as fluid dynamic drag or propulsive performance. The present work introduces a new method for quantitatively comparing and classifying flow fields using a novel graph-theoretic concept, called a weighted Gabriel graph, that employs critical points of the velocity vector field, which identify key flow features such as vortices, as graph vertices. The edges (connections between vertices) and edge weights of the weighted Gabriel graph encode local geometric structure. The resulting graph exhibits robustness to minor changes in the flow fields. Dissimilarity between flow fields is quantified by finding the best match (minimum difference) in weights of matched graph edges under relevant constraints on the properties of the edge vertices, and flows are classified using hierarchical clustering based on computed dissimilarity. Application of this approach to a set of artificially generated, periodic vortical flows demonstrates high classification accuracy, even for large perturbations, and insensitivity to scale variations and number of periods in the periodic flow pattern. The generality of the approach allows for comparison of flows generated by very different means (e.g. different animal species).

Flexibility of Heterocercal Tails: What Can the Functional Morphology of Shark Tails Tell Us about Ichthyosaur Swimming?

The similarities between ichthyosaurs and sharks are a text-book example of convergence, and similarities in tail morphology have led many to theorize that they had similar swimming styles. The variation of ichthyosaur tail shapes is encompassed within the diversity of shark families. In particular early ichthyosaurs have asymmetrical tails like the heterocercal tails of carcharhinid sharks, while later occurring ichthyosaurs have lunate tails similar to those of lamnid sharks. Because it is not possible to measure ichthyosaur tail function, the goal of this study is to measure and compare the flexibility and stiffness of lunate and heterocercal shark tails, and to measure skeletal and connective tissue features that may affect tail flexibility. We measured flexibility in 10 species and focused on five species in particular, for dissection: one pelagic and one bottom-associated individual from each order, plus the common thresher shark (Alopias vulpinus), a tail-slapping specialist. As expected, lunate tails were overall less flexible than heterocercal tails and had greater flexural stiffness. Our results suggest that the cross-sectional profile of the skeletally supported dorsal lobe dictates flexural stiffness, but that changing tissue composition dictates flexural stiffness in the ventral lobe. We also found structural differences that may enable the tail slapping behavior of the common thresher shark. Finally, we discuss how our morphological measurements compare to ichthyosaur measurements from the literature; noting that similarities in functional morphology suggest sharks may be a good analog for understanding ichthyosaur swimming biomechanics.

New approaches for assessing squid fin motions: coupling proper orthogonal decomposition with volumetric particle tracking velocimetry

Squid, which swim using a coupled fin/jet system powered by muscular hydrostats, pose unique challenges for the study of locomotion. The high flexibility of the fins and complex flow fields generated by distinct propulsion systems require innovative techniques for locomotive assessment. For this study, we used proper orthogonal decomposition (POD) to decouple components of the fin motions and defocusing digital particle tracking velocimetry (DDPTV) to quantify the resultant 3D flow fields. Kinematic footage and DDPTV data were collected from brief squid, Lolliguncula brevis [3.1-6.5 cm dorsal mantle length (DML)], swimming freely in a water tunnel at speeds of 0.39-7.20 DML s^-1 Both flap and wave components were present in all fin motions, but the relative importance of the wave components was higher for arms-first swimming than for tail-first swimming and for slower versus higher speed swimming. When prominent wave components were present, more complex interconnected vortex ring wakes were observed, while fin movements dominated by flapping resulted in more spatially separated vortex ring patterns. Although the jet often produced the majority of the thrust for steady rectilinear swimming, our results demonstrated that the fins can contribute more thrust than the jet at times, consistently produce comparable levels of lift to the jet during arms-first swimming, and can boost overall propulsive efficiency. By producing significant drag signatures, the fins can also aid in stabilization and maneuvering. Clearly, fins play multiple roles in squid locomotion, and when coupled with the jet, allow squid to perform a range of swimming behaviors integral to their ecological success.

A multi-body dynamics based numerical modelling tool for solving aquatic biomimetic problems

In this paper, a versatile multi-body dynamic algorithm is developed to integrate an incompressible fluid flow with a bio-inspired multibody dynamic system. Of particular interest to the biomimetic application, the algorithm is developed via four properly selected benchmark verifications. The present tool has shown its powerful capability for solving a variety of biomechanics fish swimming problems, including self-propelled multiple degrees of freedom with a rigid undulatory body, multiple deformable fins and an integrated system with both undulatory fish body and flexible fins. The established tool has paved the way for future investigation on more complex bio-inspired robots and live fish, for either propulsion or manoeuvring purposes.

Hydrodynamic function of dorsal fins in spiny dogfish and bamboo sharks during steady swimming

A key feature of fish functional design is the presence of multiple fins that allow thrust vectoring and redirection of fluid momentum to contribute to both steady swimming and maneuvering. A number of previous studies have analyzed the function of dorsal fins in teleost fishes in this context, but the hydrodynamic function of dorsal fins in freely swimming sharks has not been analyzed, despite the potential for differential functional roles between the anterior and posterior dorsal fins. Previous anatomical research has suggested a primarily stabilizing role for shark dorsal fins. We evaluated the generality of this hypothesis by using time-resolved particle image velocimetry to record water flow patterns in the wake of both the anterior and posterior dorsal fins in two species of freely swimming sharks: bamboo sharks (Chiloscyllium plagiosum) and spiny dogfish (Squalus acanthias). Cross-correlation analysis of consecutive images was used to calculate stroke-averaged mean longitudinal and lateral velocity components, and vorticity. In spiny dogfish, we observed a velocity deficit in the wake of the first dorsal fin and flow acceleration behind the second dorsal fin, indicating that the first dorsal fin experiences net drag while the second dorsal fin can aid in propulsion. In contrast, the wake of both dorsal fins in bamboo sharks displayed increased net flow velocity in the majority of trials, reflecting a thrust contribution to steady swimming. In bamboo sharks, fluid flow in the wake of the second dorsal fin had higher absolute average velocity than that for first dorsal fin, and this may result from a positive vortex interaction between the first and second dorsal fins. These data suggest that the first dorsal fin in spiny dogfish has primarily a stabilizing function, while the second dorsal fin has a propulsive function. In bamboo sharks, both dorsal fins can contribute thrust and should be considered as propulsive adjuncts to the body during steady swimming. The function of shark dorsal fins can thus differ considerably among fins and species, and is not limited to a stabilizing role.

Consequences of lost endings: caudal autotomy as a lens for focusing attention on tail function during locomotion

Autotomy has evolved in many animal lineages as a means of predator escape, and involves the voluntary shedding of body parts. In vertebrates, caudal autotomy (or tail shedding) is the most common form, and it is particularly widespread in lizards. Here, we develop a framework for thinking about how tail loss can have fitness consequences, particularly through its impacts on locomotion. Caudal autotomy is fundamentally an alteration of morphology that affects an animal's mass and mass distribution. These morphological changes affect balance and stability, along with the performance of a range of locomotor activities, from running and climbing to jumping and swimming. These locomotor effects can impact on activities critical for survival and reproduction, including escaping predators, capturing prey and acquiring mates. In this Commentary, we first review work illustrating the (mostly) negative effects of tail loss on locomotor performance, and highlight what these consequences reveal about tail function during locomotion. We also identify important areas of future study, including the exploration of new behaviors (e.g. prey capture), increased use of biomechanical measurements and the incorporation of more field-based studies to continue to build our understanding of the tail, an ancestral and nearly ubiquitous feature of the vertebrate body plan.

Fluid Dynamics of Biomimetic Pectoral Fin Propulsion Using Immersed Boundary Method

Numerical simulations are carried out to study the fluid dynamics of a complex-shaped low-aspect-ratio pectoral fin that performs the labriform swimming. Simulations of flow around the fin are achieved by a developed immersed boundary (IB) method, in which we have proposed an efficient local flow reconstruction algorithm with enough robustness and a new numerical strategy with excellent adaptability to deal with complex moving boundaries involved in bionic flow simulations. The prescribed fin kinematics in each period consists of the power stroke and the recovery stroke, and the simulations indicate that the former is mainly used to provide the thrust while the latter is mainly used to provide the lift. The fin wake is dominated by a three-dimensional dual-ring vortex wake structure where the partial power-stroke vortex ring is linked to the recovery-stroke ring vertically. Moreover, the connection of force production with the fin kinematics and vortex dynamics is discussed in detail to explore the propulsion mechanism. We also conduct a parametric study to understand how the vortex topology and hydrodynamic characteristics change with key parameters. The results show that there is an optimal phase angle and Strouhal number for this complicated fin. Furthermore, the implications for the design of a bioinspired pectoral fin are discussed based on the quantitative hydrodynamic analysis.

Control of vortex rings for manoeuvrability

Manoeuvrability is critical to the success of many species. Selective forces acting over millions of years have resulted in a range of capabilities currently unmatched by machines. Thus, understanding animal control of fluids for manoeuvring has both biological and engineering applications. Within inertial fluid regimes, propulsion involves the formation and interaction of vortices to generate thrust. We use both volumetric and planar imaging techniques to quantify how jellyfish (Aurelia aurita) modulate vortex rings during turning behaviour. Our results show that these animals distort individual vortex rings during turns to alter the force balance across the animal, primarily through kinematic modulation of the bell margin. We find that only a portion of the vortex ring separates from the body during turns, which may increase torque. Using a fluorescent actin staining method, we demonstrate the presence of radial muscle fibres lining the bell along the margin. The presence of radial muscles provides a mechanistic explanation for the ability of scyphomedusae to alter their bell kinematics to generate non-symmetric thrust for manoeuvring. These results illustrate the advantage of combining imaging methods and provide new insights into the modulation and control of vorticity for low-speed animal manoeuvring.

Ontogeny of head and caudal fin shape of an apex marine predator: The tiger shark (Galeocerdo cuvier)

How morphology changes with size can have profound effects on the life history and ecology of an animal. For apex predators that can impact higher level ecosystem processes, such changes may have consequences for other species. Tiger sharks (Galeocerdo cuvier) are an apex predator in tropical seas, and, as adults, are highly migratory. However, little is known about ontogenetic changes in their body form, especially in relation to two aspects of shape that influence locomotion (caudal fin) and feeding (head shape). We captured digital images of the heads and caudal fins of live tiger sharks from Southern Florida and the Bahamas ranging in body size (hence age), and quantified shape of each using elliptical Fourier analysis. This revealed changes in the shape of the head and caudal fin of tiger sharks across ontogeny. Smaller juvenile tiger sharks show an asymmetrical tail with the dorsal (upper) lobe being substantially larger than the ventral (lower) lobe, and transition to more symmetrical tail in larger adults, although the upper lobe remains relatively larger in adults. The heads of juvenile tiger sharks are more conical, which transition to relatively broader heads over ontogeny. We interpret these changes as a result of two ecological transitions. First, adult tiger sharks can undertake extensive migrations and a more symmetrical tail could be more efficient for swimming longer distances, although we did not test this possibility. Second, adult tiger sharks expand their diet to consume larger and more diverse prey with age (turtles, mammals, and elasmobranchs), which requires substantially greater bite area and force to process. In contrast, juvenile tiger sharks consume smaller prey, such as fishes, crustaceans, and invertebrates. Our data reveal significant morphological shifts in an apex predator, which could have effects for other species that tiger sharks consume and interact with.

Hydrodynamics of a robotic fish tail: effects of the caudal peduncle, fin ray motions and the flow speed

Recent advances in understanding fish locomotion with robotic devices have included the use of biomimetic flapping based and fin undulatory locomotion based robots, treating two locomotions separately from each other. However, in most fish species, patterns of active movements of fins occur in concert with the body undulatory deformation during swimming. In this paper, we describe a biomimetic robotic caudal fin programmed with individually actuated fin rays to mimic the fin motion of the Bluegill Sunfish (Lepomis macrochirus) and coupled with heave and pitch oscillatory motions adding to the robot to mimic the peduncle motion which is derived from the undulatory fish body. Multiple-axis force and digital particle image velocimetry (DPIV) experiments from both the vertical and horizontal planes behind the robotic model were conducted under different motion programs and flow speeds. We found that both mean thrust and lift could be altered by changing the phase difference (φ) from 0° to 360° between the robotic caudal peduncle and the fin ray motion (spanning from 3 mN to 124 mN). Notably, DPIV results demonstrated that the caudal fin generated multiple wake flow patterns in both the vertical and horizontal planes by varying φ. Vortex jet angle and thrust impulse also varied significantly both in these two planes. In addition, the vortex shedding position along the spanwise tail direction could be shifted around the mid-sagittal position between the upper and lower lobes by changing the phase difference. We hypothesize that the fish caudal fin may serve as a flexible vectoring propeller during swimming and may be critical for the high maneuverability of fish.

Investigation of Fish Caudal Fin Locomotion Using a Bio-Inspired Robotic Model

Due to its advantages of realizing repeatable experiments, collecting data and isolating key factors, the bio-robotic model is becoming increasingly important in the study of biomechanics. The caudal fin of fish has long been understood to be central to propulsion performance, yet its contribution to manoeuverability, especially for homocercal caudal fin, has not been studied in depth. In the research outlined in this paper, we designed and fabricated a robotic caudal fin to mimic the morphology and the three-dimensional (3D) locomotion of the tail of the Bluegill Sunfish ( Lepomis macrochirus). We applied heave and pitch motions to the robot to model the movement of the caudal peduncle of its biological counterpart. Force measurements and 2D and 3D digital particle image velocimetry were then conducted under different movement patterns and flow speeds. From the force data, we found the addition of the 3D caudal fin locomotion significantly enhanced the lift force magnitude. The phase difference between the caudal fin ray and peduncle motion was a key factor in simultaneously controlling the thrust and lift. The increased flow speed had a negative impact on the generation of lift force. From the average 2D velocity field, we observed that the vortex wake directed water both axially and vertically, and formed a jet-like structure with notable wake velocity. The 3D instantaneous velocity field at 0.6 T indicated the 3D motion of the caudal fin may result in asymmetry wake flow patterns relative to the mid-sagittal plane and change the heading direction of the shedding vortexes. Based on these results, we hypothesized that live fish may actively tune the movement between the caudal fin rays and the peduncle to change the wake structure behind the tail and hence obtain different thrust and lift forces, which contributes to its high manoeuvrability.

Volumetric flow imaging reveals the importance of vortex ring formation in squid swimming tail-first and arms-first

Squids use a pulsed jet and fin movements to swim both arms-first (forward) and tail-first (backward). Given the complexity of the squid multi-propulsor system, 3D velocimetry techniques are required for the comprehensive study of wake dynamics. Defocusing digital particle tracking velocimetry, a volumetric velocimetry technique, and high-speed videography were used to study arms-first and tail-first swimming of brief squid Lolliguncula brevis over a broad range of speeds (0-10 dorsal mantle lengths (DML) s−1) in a swim tunnel. Although there was considerable complexity in the wakes of these multi-propulsor swimmers, 3D vortex rings and their derivatives were prominent reoccurring features during both tail-first and arms-first swimming, with the greatest jet and fin flow complexity occuring at intermediate speeds (1.5 – 3.0 DML s−1). The jet generally produced the majority of thrust during rectilinear swimming, increasing in relative importance with speed, and the fins provided no thrust at speeds >4.5 DML s−1. For both swimming orientations, the fins sometimes acted as stabilizers, producing negative thrust (drag), and consistently provided lift at low/intermediate speeds (<2.0 DML s−1) to counteract negative buoyancy. Propulsive efficiency (η) increased with speed irrespective of swimming orientation, and η for swimming sequences with clear isolated jet vortex rings was significantly greater (η = 78.6 ± 7.6% (s.d.)) than swimming sequences with clear elongated regions of concentrated jet vorticity (η = 67.9 ± 19.2% (s.d.)). This study reveals the complexity of 3D vortex wake flows produced by nekton with hydrodynamically distinct propulsors.

Fish locomotion: recent advances and new directions

Research on fish locomotion has expanded greatly in recent years as new approaches have been brought to bear on a classical field of study. Detailed analyses of patterns of body and fin motion and the effects of these movements on water flow patterns have helped scientists understand the causes and effects of hydrodynamic patterns produced by swimming fish. Recent developments include the study of the center-of-mass motion of swimming fish and the use of volumetric imaging systems that allow three-dimensional instantaneous snapshots of wake flow patterns. The large numbers of swimming fish in the oceans and the vorticity present in fin and body wakes support the hypothesis that fish contribute significantly to the mixing of ocean waters. New developments in fish robotics have enhanced understanding of the physical principles underlying aquatic propulsion and allowed intriguing biological features, such as the structure of shark skin, to be studied in detail.

The evolution of the sexually selected sword in Xiphophorus does not compromise aerobic locomotor performance

Sexual selection can increase morphological diversity within and among species. Little is known regarding how interspecific variation produced through sexual selection affects other functional systems. Here, we examine how morphological diversity resulting from sexual selection impacts aerobic locomotor performance. Using Xiphophorus (swordtail fish) and their close relatives (N = 19 species), we examined whether the evolution of a longer sexually selected sword affects critical swimming speed. We also examined the effect of other suborganismal, physiological, and morphological traits on critical swimming speed, as well as their relationship with sword length. In correlation analyses, we found no significant relationship between sword length and critical swimming speed. Unexpectedly, we found that critical swimming speed was higher in species with longer swords, after controlling for body size in multiple regression analyses. We also found several suborganismal and morphological predictors of critical swimming speed, as well as a significant negative relationship between sword length and heart and gill mass. Our results suggest that interspecific variation in sword length is not costly for this aspect of swimming performance, but further studies should examine potential costs for other types of locomotion and other components of Darwinian fitness (e.g., survivorship, life span).

Three-dimensional vortex wake structure of flapping wings in hovering flight

Flapping wings continuously create and send vortices into their wake, while imparting downward momentum into the surrounding fluid. However, experimental studies concerning the details of the three-dimensional vorticity distribution and evolution in the far wake are limited. In this study, the three-dimensional vortex wake structure in both the near and far field of a dynamically scaled flapping wing was investigated experimentally, using volumetric three-component velocimetry. A single wing, with shape and kinematics similar to those of a fruitfly, was examined. The overall result of the wing action is to create an integrated vortex structure consisting of a tip vortex (TV), trailing-edge shear layer (TESL) and leading-edge vortex. The TESL rolls up into a root vortex (RV) as it is shed from the wing, and together with the TV, contracts radially and stretches tangentially in the downstream wake. The downwash is distributed in an arc-shaped region enclosed by the stretched tangential vorticity of the TVs and the RVs. A closed vortex ring structure is not observed in the current study owing to the lack of well-established starting and stopping vortex structures that smoothly connect the TV and RV. An evaluation of the vorticity transport equation shows that both the TV and the RV undergo vortex stretching while convecting downwards: a three-dimensional phenomenon in rotating flows. It also confirms that convection and secondary tilting and stretching effects dominate the evolution of vorticity.

Volumetric quantification of fluid flow reveals fish's use of hydrodynamic stealth to capture evasive prey

In aquatic ecosystems, predation on zooplankton by fish provides a major pathway for the transfer of energy to higher trophic levels. Copepods are an abundant zooplankton group that sense hydromechanical disturbances produced by approaching predators and respond with rapid escapes. Despite this capability, fish capture copepods with high success. Previous studies have focused on the predatory strike to elucidate details of this interaction. However, these raptorial strikes and resulting suction are only effective at short range. Thus, small fish must closely approach highly sensitive prey without triggering an escape in order for a strike to be successful. We use a new method, high-speed, infrared, tomographic particle image velocimetry, to investigate three-dimensional fluid patterns around predator and prey during approaches. Our results show that at least one planktivorous fish (Danio rerio) can control the bow wave in front of the head during the approach and consumption of prey (copepod). This alters hydrodynamic profiles at the location of the copepod such that it is below the threshold required to elicit an escape response. We find this behaviour to be mediated by the generation of suction within the buccopharyngeal cavity, where the velocity into the mouth roughly matches the forward speed of the fish. These results provide insight into how animals modulate aspects of fluid motion around their bodies to overcome escape responses and enhance prey capture.

Volumetric visualization of the near- and far-field wake in flapping wings

The flapping wings of flying animals create complex vortex wake structure; understanding its spatial and temporal distribution is fundamental to animal flight theory. In this study, we applied the volumetric 3-component velocimetry to capture both the near- and far-field flow generated by a pair of mechanical flapping wings. For the first time, the complete three-dimensional wake structure and its evolution throughout a wing stroke were quantified and presented experimentally. The general vortex wake structure maintains a quite consistent form: vortex rings in the near field and two shear layers in the far field. Vortex rings shed periodically from the wings and are linked to each other in successive strokes. In the far field, the shed vortex rings evolve into two parallel shear layers with dominant vorticity convected from tip and root vortices. The shear layers are nearly stationary in space compared to the periodic vortex rings shed in the near field. In addition, downwash passes through the centers of the vortex rings and extends downward between the two shear layers.

The fish tail motion forms an attached leading edge vortex

The tail (caudal fin) is one of the most prominent characteristics of fishes, and the analysis of the flow pattern it creates is fundamental to understanding how its motion generates locomotor forces. A mechanism that is known to greatly enhance locomotor forces in insect and bird flight is the leading edge vortex (LEV) reattachment, i.e. a vortex (separation bubble) that stays attached at the leading edge of a wing. However, this mechanism has not been reported in fish-like swimming probably owing to the overemphasis on the trailing wake, and the fact that the flow does not separate along the body of undulating swimmers. We provide, to our knowledge, the first evidence of the vortex reattachment at the leading edge of the fish tail using three-dimensional high-resolution numerical simulations of self-propelled virtual swimmers with different tail shapes. We show that at Strouhal numbers (a measure of lateral velocity to the axial velocity) at which most fish swim in nature (approx. 0.25) an attached LEV is formed, whereas at a higher Strouhal number of approximately 0.6 the LEV does not reattach. We show that the evolution of the LEV drastically alters the pressure distribution on the tail and the force it generates. We also show that the tail's delta shape is not necessary for the LEV reattachment and fish-like kinematics is capable of stabilising the LEV. Our results suggest the need for a paradigm shift in fish-like swimming research to turn the focus from the trailing edge to the leading edge of the tail.

Tomographic particle image velocimetry of desert locust wakes: instantaneous volumes combine to reveal hidden vortex elements and rapid wake deformation

Aerodynamic structures generated by animals in flight are unstable and complex. Recent progress in quantitative flow visualization has advanced our understanding of animal aerodynamics, but measurements have hitherto been limited to flow velocities at a plane through the wake. We applied an emergent, high-speed, volumetric fluid imaging technique (tomographic particle image velocimetry) to examine segments of the wake of desert locusts, capturing fully three-dimensional instantaneous flow fields. We used those flow fields to characterize the aerodynamic footprint in unprecedented detail and revealed previously unseen wake elements that would have gone undetected by two-dimensional or stereo-imaging technology. Vortex iso-surface topographies show the spatio-temporal signature of aerodynamic force generation manifest in the wake of locusts, and expose the extent to which animal wakes can deform, potentially leading to unreliable calculations of lift and thrust when using conventional diagnostic methods. We discuss implications for experimental design and analysis as volumetric flow imaging becomes more widespread.

The hydrodynamic function of shark skin and two biomimetic applications

It has long been suspected that the denticles on shark skin reduce hydrodynamic drag during locomotion, and a number of man-made materials have been produced that purport to use shark-skin-like surface roughness to reduce drag during swimming. But no studies to date have tested these claims of drag reduction under dynamic and controlled conditions in which the swimming speed and hydrodynamics of shark skin and skin-like materials can be quantitatively compared with those of controls lacking surface ornamentation or with surfaces in different orientations. We use a flapping foil robotic device that allows accurate determination of the self-propelled swimming (SPS) speed of both rigid and flexible membrane-like foils made of shark skin and two biomimetic models of shark skin to measure locomotor performance. We studied the SPS speed of real shark skin, a silicone riblet material with evenly spaced ridges and a Speedo® ‘shark skin-like’ swimsuit fabric attached to rigid flat-plate foils and when made into flexible membrane-like foils. We found no consistent increase in swimming speed with Speedo® fabric, a 7.2% increase with riblet material, whereas shark skin membranes (but not rigid shark skin plates) showed a mean 12.3% increase in swimming speed compared with the same skin foils after removing the denticles. Deformation of the shark skin membrane is thus crucial to the drag-reducing effect of surface denticles. Digital particle image velocimetry (DPIV) of the flow field surrounding moving shark skin foils shows that skin denticles promote enhanced leading-edge suction, which might have contributed to the observed increase in swimming speed. Shark skin denticles might thus enhance thrust, as well as reduce drag.