Efficiency of fish propulsion

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.

Numerical Investigation of Dimensionless Parameters in Carangiform Fish Swimming Hydrodynamics

Research into how fish and other aquatic organisms propel themselves offers valuable natural references for enhancing technology related to underwater devices like vehicles, propellers, and biomimetic robotics. Additionally, such research provides insights into fish evolution and ecological dynamics. This work carried out a numerical investigation of the most relevant dimensionless parameters in a fish swimming environment (Reynolds Re, Strouhal St, and Slip numbers) to provide valuable knowledge in terms of biomechanics behavior. Thus, a three-dimensional numerical study of the fish-like lambari, a BCF swimmer with carangiform kinematics, was conducted using the URANS approach with the k-ω-SST transition turbulence closure model in the OpenFOAM software. In this study, we initially reported the equilibrium Strouhal number, which is represented by St∗, and its dependence on the Reynolds number, denoted as Re. This was performed following a power-law relationship of St∝Re(-α). We also conducted a comprehensive analysis of the hydrodynamic forces and the effect of body undulation in fish on the production of swimming drag and thrust. Additionally, we computed propulsive and quasi-propulsive efficiencies, as well as examined the influence of the Reynolds number and Slip number on fish performance. Finally, we performed a vortex dynamics analysis, in which different wake configurations were revealed under variations of the dimensionless parameters St, Re, and Slip. Furthermore, we explored the relationship between the generation of a leading-edge vortex via the caudal fin and the peak thrust production within the motion cycle.

Complex Modal Characteristic Analysis of a Tensegrity Robotic Fish's Body Waves

A bionic robotic fish based on compliant structure can excite the natural modes of vibration, thereby mimicking the body waves of real fish to generate thrust and realize undulate propulsion. The fish body wave is a result of the fish body's mechanical characteristics interacting with the surrounding fluid. Thoroughly analyzing the complex modal characteristics in such robotic fish contributes to a better understanding of the locomotion behavior, consequently enhancing the swimming performance. Therefore, the complex orthogonal decomposition (COD) method is used in this article. The traveling index is used to quantitatively describe the difference between the real and imaginary modes of the fish body wave. It is defined as the reciprocal of the condition number between the real and imaginary components. After introducing the BCF (body and/or caudal fin) the fish's body wave curves and the COD method, the structural design and parameter configuration of the tensegrity robotic fish are introduced. The complex modal characteristics of the tensegrity robotic fish and real fish are analyzed. The results show that their traveling indexes are close, with two similar complex mode shapes. Subsequently, the relationship between the traveling index and swimming performance is expressed using indicators reflecting linear correlation (correlation coefficient (Rc) and p value). Based on this correlation, a preliminary optimization strategy for the traveling index is proposed, with the potential to improve the swimming performance of the robotic fish.

The hydrodynamics of jet propulsion swimming in hatchling and juvenile European common cuttlefish, Sepia officinalis

Cuttlefish swim using jet propulsion, taking a small volume of fluid into the mantle cavity before it is expelled through the siphon to generate thrust. Jet propulsion swimming has been shown to be more metabolically expensive than undulatory swimming, which has been suggested to be due to the lower efficiency of jet propulsion. The whole-cycle propulsive efficiency of cephalopod molluscs ranges from 38 to 76%, indicating that in some instances jet propulsion can be relatively efficient. Here, we determined the hydrodynamics of hatchling and juvenile cuttlefish during jet propulsion swimming to understand the characteristics of their jets, and whether their whole-cycle propulsive efficiency changes during development. Cuttlefish were found to utilise two jet types: isolated jet vortices (termed jet mode I) and elongated jets (leading edge vortex ring followed by a trailing jet; termed jet mode II). The use of these jet modes differed between the age classes, with newly hatched animals nearly exclusively utilising mode I jets, while juveniles showed no strong preferences. Whole-cycle propulsive efficiency was found to be high, ranging from 72 to 80%, and did not differ between age classes. During development, Strouhal number decreased as Reynolds number increased, which is consistent with animals adjusting their jetting behaviour in order to maximise whole-cycle propulsive efficiency and locomotor performance. Although jet propulsion swimming can have a relatively high energetic cost, in cuttlefish and nautilus, both neutrally buoyant species, the whole-cycle propulsive efficiency is actually relatively high.

How Free Swimming Fosters the Locomotion of a Purely Oscillating Fish-like Body

The recoil motions in free swimming, given by lateral and angular rigid motions due to the interaction with the surrounding water, are of great importance for a correct evaluation of both the forward locomotion speed and efficiency of a fish-like body. Their contribution is essential for calculating the actual movements of the body rear end whose prominent influence on the generation of the proper body deformation was established a long time ago. In particular, the recoil motions are found here to promote a dramatic improvement of the performance when damaged fishes, namely for a partial functionality of the tail or even for its complete loss, are considered. In fact, the body deformation, which turns out to become oscillating and symmetric in the extreme case, is shown to recover in the water frame a kind of undulation leading to a certain locomotion speed though at the expense of a large energy consumption. There has been a deep interest in the subject since the infancy of swimming studies, and a revival has recently arisen for biomimetic applications to robotic fish-like bodies. We intend here to apply a theoretical impulse model to the oscillating fish in free swimming as a suitable test case to strengthen our belief in the beneficial effects of the recoil motions. At the same time, we intend to exploit the linearity of the model to detect from the numerical simulations the intrinsic physical reasons related to added mass and vorticity release behind the experimental observations.

Cost of Transport of Undulating Fin Propulsion

Autonomous robots are used to inspect, repair and maintain underwater assets. These tasks require energy-efficient robots, including efficient movement to extend available operational time. To examine the suitability of a propulsion system based on undulating fins, we built two robots with one and two fins, respectively, and conducted a parametric study for combinations of frequency, amplitude, wavenumber and fin shapes in free-swimming experiments, measuring steady-state swimming speed, power consumption and cost of transport. The following trends emerged for both robots. Swimming speed was more strongly affected by frequency than amplitude across the examined wavenumbers and fin heights. Power consumption was sensitive to frequency at low wavenumbers, and increasingly sensitive to amplitude at high wavenumbers. This increasing sensitivity of amplitude was more pronounced in tall rather than short fins. Cost of transport showed a complex relation with fin size and kinematics and changed drastically across the mapped parameter space. At equal fin kinematics as the single-finned robot, the double-finned robot swam slightly faster (>10%) with slightly lower power consumption (<20%) and cost of transport (<40%). Overall, the robots perform similarly to finned biological swimmers and other bio-inspired robots, but do not outperform robots with conventional propulsion systems.

A tale of two fish tails: does a forked tail really perform better than a truncate tail when cruising?

Many fishes use their tail as the main thrust producer during swimming. This fin's diversity in shape and size influences its physical interactions with water as well as its ecological functions. Two distinct tail morphologies are common in bony fishes: flat, truncate tails which are best suited for fast accelerations via drag forces, and forked tails that promote economical, fast cruising by generating lift-based thrust. This assumption is based primarily on studies of the lunate caudal fin of Scombrids (i.e. tuna, mackerel), which is comparatively stiff and exhibits an airfoil-type cross-section. However, this is not representative of the more commonly observed and taxonomically widespread flexible forked tail, yet similar assumptions about economical cruising are widely accepted. Here, we present the first comparative experimental study of forked versus truncate tail shape and compare the fluid mechanical properties and energetics of two common nearshore fish species. We examined the hypothesis that forked tails provide a hydrodynamic advantage over truncate tails at typical cruising speeds. Using experimentally derived pressure fields, we show that the forked tail produces thrust via acceleration reaction forces like the truncate tail during cruising but at increased energetic costs. This reduced efficiency corresponds to differences in the performance of the two tail geometries and body kinematics to maintain similar overall thrust outputs. Our results offer insights into the benefits and tradeoffs of two common fish tail morphologies and shed light on the functional morphology of fish swimming to guide the development of bio-inspired underwater technologies.

Numerical Study of the Fish-like Robot Swimming in Fluid with High Reynolds Number: Immersed Boundary Method

Fish-like robots have been widely used in intelligent surveillance and investigation because of their high swimming efficiency and low traveling noise. Numerical simulations are usually selected to simulate the movement modes and hydrodynamic characteristics of fish-like robots during design and manufacture. However, the body-fitted grid method traditionally utilized in numerical simulations often has difficulty dealing with moving solid boundaries. In this work, the immersed boundary method, superior in handling the moving boundary conditions, is employed to simulate the movement of a fish-like robot swimming in high Reynolds number flows in combination with the RANS turbulence model. The numerical method is first validated using a fluid flowing over a square block, and the corresponding results are in good agreement with the ones reported in reference. Then, the swing of the fish-like robot under three different Reynolds numbers is studied. The lift coefficient and the drag coefficient of the fish-like robot decrease with increasing the Reynolds number. This paper provides remarkable support for future designs and applications of fish-like robots.

A Novel Fish-Inspired Robot with a Double-Cam Mechanism

Fishes have evolved different excellent swimming strategies. To study the influence of tail fin swing on the swimming performance of bionic robot fish, with one joint under the same tail swing frequency and amplitude, we designed a novel robot fish, driven by a double-cam mechanism. By designing the profile of the cam in the mechanism, the robot fish can achieve different undulatory motion trajectory of the caudal fin under the same tail swing frequency and amplitude. The mechanism simulated the undulatory motion of crucian carp. We studied the influence of undulatory motion on the swimming speed of robot fish, which was analyzed by dynamic analysis of the undulatory motion and experiments. According to the experimental results, we can find that the swimming speed of the robotic fish is different under various wave motions. When other conditions are the same, the speed that the robot fish can achieve by imitating the swing motion of the real fish is 1.5 times that of the robot fish doing the cycloid motion. The experimental results correspond to the kinetic analysis results. Furthermore, it is proven that the robot fish with a low caudal peduncle stiffness swims faster under a low swinging frequency, and the speed of a robot fish with a high caudal peduncle stiffness is higher under a high tail swinging frequency.

Underwater Soft Robotics: A Review of Bioinspiration in Design, Actuation, Modeling, and Control

Nature and biological creatures are some of the main sources of inspiration for humans. Engineers have aspired to emulate these natural systems. As rigid systems become increasingly limited in their capabilities to perform complex tasks and adapt to their environment like living creatures, the need for soft systems has become more prominent due to the similar complex, compliant, and flexible characteristics they share with intelligent natural systems. This review provides an overview of the recent developments in the soft robotics field, with a focus on the underwater application frontier.

Innovative Energy-Saving Propulsion System for Low-Speed Biomimetic Underwater Vehicles

This article covers research on an innovative propulsion system design for a Biomimetic Unmanned Underwater Vehicle (BUUV) operating at low speeds. The experiment was conducted on a laboratory test water tunnel equipped with specialised sensor equipment to assess the Fluid-Structure Interaction (FSI) and energy consumption of two different types of propulsion systems. The experimental data contrast the undulating with the drag-based propulsion system. The additional joint in the drag-based propulsion system is intended to increase thrust and decrease energy input. The tests were conducted at a variety of fins oscillation frequencies and fluid velocities. The experiments demonstrate that, in the region of low-speed forward movement, the efficiency of the propulsion system with the additional joint is greater.

The locomotion of extinct secondarily aquatic tetrapods

The colonisation of freshwater and marine ecosystems by land vertebrates has repeatedly occurred in amphibians, reptiles, birds and mammals over the course of 300 million years. Functional interpretations of the fossil record are crucial to understanding the forces shaping these evolutionary transitions. Secondarily aquatic tetrapods have acquired a suite of anatomical, physiological and behavioural adaptations to locomotion in water. However, much of this information is lost for extinct clades, with fossil evidence often restricted to osteological data and a few extraordinary specimens with soft tissue preservation. Traditionally, functional morphology in fossil secondarily aquatic tetrapods was investigated through comparative anatomy and correlation with living functional analogues. However, in the last two decades, biomechanics in palaeobiology has experienced a remarkable methodological shift. Anatomy-based approaches are increasingly rigorous, informed by quantitative techniques for analysing shape. Moreover, the incorporation of physics-based methods has enabled objective tests of functional hypotheses, revealing the importance of hydrodynamic forces as drivers of evolutionary innovation and adaptation. Here, we present an overview of the latest research on the locomotion of extinct secondarily aquatic tetrapods, with a focus on amniotes, highlighting the state-of-the-art experimental approaches used in this field. We discuss the suitability of these techniques for exploring different aspects of locomotory adaptation, analysing their advantages and limitations and laying out recommendations for their application, with the aim to inform future experimental strategies. Furthermore, we outline some unexplored research avenues that have been successfully deployed in other areas of palaeobiomechanical research, such as the use of dynamic models in feeding mechanics and terrestrial locomotion, thus providing a new methodological synthesis for the field of locomotory biomechanics in extinct secondarily aquatic vertebrates. Advances in imaging technology and three-dimensional modelling software, new developments in robotics, and increased availability and awareness of numerical methods like computational fluid dynamics make this an exciting time for analysing form and function in ancient vertebrates.

Numerical Simulation of Self-Propelled Steady Jet Propulsion at Intermediate Reynolds Numbers: Effects of Orifice Size on Animal Jet Propulsion

Most marine jet-propelled animals have low swimming efficiencies and relatively small jet orifices. Motivated by this, the present computational fluid dynamics study simulates the flow for a jet-propelled axisymmetric body swimming steadily at intermediate Reynolds numbers of order 1–1000. Results show that swimming-imposed flow field, drag coefficients, swimming efficiencies, and performance index (a metric comparing swimming speeds sustained by differently sized orifices ejecting the same volume flow rate) all depend strongly on orifice size, and orifice size affects the configuration of oppositely signed body vorticity and jet vorticity, thereby affecting wake and efficiency. As orifice size decreases, efficiencies decrease considerably, while performance index increases substantially, suggesting that, for a given jet volume flow rate, a smaller orifice supports faster swimming than a larger one does, albeit at reduced efficiency. These results support the notion that most jet-propelled animals having relatively small jet orifices may be an adaptation to deal with the physical constraint of limited total volume of water available for jetting, while needing to compete for fast swimming. Finally, jet orifice size is discussed regarding the role of jet propulsion in jet-propelled animal ecology, particularly for salps that use two relatively large siphons to respectively draw in and expel water.

Using a robotic platform to study the influence of relative tailbeat phase on the energetic costs of side-by-side swimming in fish

A potential benefit of swimming together in coordinated schools is to allow fish to extract energy from vortices shed by their neighbours, thus reducing the costs of locomotion. This hypothesis has been very hard to test in real fish schools, and it has proven very difficult to replicate the complex hydrodynamics at relevant Reynolds numbers using computational simulations. A complementary approach, and the one we adopt here, is to develop and analyse the performance of biomimetic autonomous robotic models that capture the salient kinematics of fish-like swimming, and also interact via hydrodynamic forces. We developed bio-inspired robotic fish which perform sub-carangiform locomotion, and measured the speed and power consumption of robots when swimming in isolation and when swimming side-by-side in pairs. We found that swimming side-by-side confers a substantial increase in both the speed and efficiency of locomotion of both fish regardless of the relative phase relationship of their body undulations. However, we also find that each individual can slightly increase their own power efficiency if they change relative tailbeat phase by approximately 0.25π with respect to, and at the energetic expense of, their neighbour. This suggests the possibility of a competitive game-theoretic dynamic between individuals in swimming groups. Our results also demonstrate the potential applicability of our platform, and provide a natural connection between the biology and robotics of collective motion.

Tunabot Flex: a tuna-inspired robot with body flexibility improves high-performance swimming

Tunas are flexible, high-performance open ocean swimmers that operate at high frequencies to achieve high swimming speeds. Most fish-like robotic systems operate at low frequencies (≤3 Hz) resulting in low swim speeds (≤1.5 body lengths per second), and the cost of transport (COT) is often one to four orders of magnitude higher than that of tunas. Furthermore, the impact of body flexibility on high-performance fish swimming remains unknown. Here we design and test a research platform based on yellowfin tuna (Thunnus albacares) to investigate the role of body flexibility and to close the performance gap between robotic and biological systems. This single-motor platform, termed Tunabot Flex, measures 25.5 cm in length. Flexibility is varied through joints in the tail to produce three tested configurations. We find that increasing body flexibility improves self-propelled swimming speeds on average by 0.5 body lengths per second while reducing the minimum COT by 53%. The most flexible configuration swims 4.60 body lengths per second with a tail beat frequency of 8.0 Hz and a COT measuring 18.4 J kg^-1m^-1. We then compare these results in addition to the midline kinematics, stride length, and Strouhal number with yellowfin tuna data. The COT of Tunabot Flex's most flexible configuration is less than a half-order of magnitude greater than that of yellowfin tuna across all tested speeds. Tunabot Flex provides a new baseline for the development of future bio-inspired underwater vehicles that aim to explore a fish-like, high-performance space and close the gap between engineered robotic systems and fish swimming ability.

A resonant squid-inspired robot unlocks biological propulsive efficiency

Elasticity has been linked to the remarkable propulsive efficiency of pulse-jet animals such as the squid and jellyfish, but reports that quantify the underlying dynamics or demonstrate its application in robotic systems are rare. This work identifies the pulse-jet propulsion mode used by these animals as a coupled mass-spring-mass oscillator, enabling the design of a flexible self-propelled robot. We use this system to experimentally demonstrate that resonance greatly benefits pulse-jet swimming speed and efficiency, and the robot's optimal cost of transport is found to match that of the most efficient biological swimmers in nature, such as the jellyfish Aurelia aurita The robot also exhibits a preferred Strouhal number for efficient swimming, thereby bridging the gap between pulse-jet propulsion and established findings in efficient fish swimming. Extensions of the current robotic framework to larger amplitude oscillations could combine resonance effects with optimal vortex formation to further increase propulsive performance and potentially outperform biological swimmers altogether.

Soft Robots for Ocean Exploration and Offshore Operations: A Perspective

The ocean and human activities related to the sea are under increasing pressure due to climate change, widespread pollution, and growth of the offshore energy sector. Data, in under-sampled regions of the ocean and in the offshore patches where the industrial expansion is taking place, are fundamental to manage successfully a sustainable development and to mitigate climate change. Existing technology cannot cope with the vast and harsh environments that need monitoring and sampling the most. The limiting factors are, among others, the spatial scales of the physical domain, the high pressure, and the strong hydrodynamic perturbations, which require vehicles with a combination of persistent autonomy, augmented efficiency, extreme robustness, and advanced control. In light of the most recent developments in soft robotics technologies, we propose that the use of soft robots may aid in addressing the challenges posed by abyssal and wave-dominated environments. Nevertheless, soft robots also allow for fast and low-cost manufacturing, presenting a new potential problem: marine pollution from ubiquitous soft sampling devices. In this study, the technological and scientific gaps are widely discussed, as they represent the driving factors for the development of soft robotics. Offshore industry supports increasing energy demand and the employment of robots on marine assets is growing. Such expansion needs to be sustained by the knowledge of the oceanic environment, where large remote areas are yet to be explored and adequately sampled. We offer our perspective on the development of sustainable soft systems, indicating the characteristics of the existing soft robots that promote underwater maneuverability, locomotion, and sampling. This perspective encourages an interdisciplinary approach to the design of aquatic soft robots and invites a discussion about the industrial and oceanographic needs that call for their application.

Centre-of-mass and minimal speed limits of the great hammerhead

The great hammerhead is denser than water, and hence relies on hydrodynamic lift to compensate for its lack of buoyancy, and on hydrodynamic moment to compensate for a possible misalignment between centres of mass and buoyancy. Because hydrodynamic forces scale with the swimming speed squared, whereas buoyancy and gravity are independent of it, there is a critical speed below which the shark cannot generate enough lift to counteract gravity, and there are anterior and posterior centre-of-mass limits beyond which the shark cannot generate enough pitching moment to counteract the buoyancy-gravity couple. The speed and centre-of-mass limits were found from numerous wind-tunnel experiments on a scaled model of the shark. In particular, it was shown that the margin between the anterior and posterior centre-of-mass limits is a few tenths of the product between the length of the shark and the ratio between its weight in and out of water; a diminutive 1% body length. The paper presents the wind-tunnel experiments, and discusses the roles that the cephalofoil and the pectoral and caudal fins play in longitudinal balance of a shark.

Computational modeling of swimming in marine invertebrates with implications for soft swimming robots

Marine flatworms (polyclads) employ a wide variety of body kinematics for swimming. In the current study, we employ computational fluid dynamics to study the hydrodynamics and swimming performance of a large variety of swimmers inspired directly from flatworms as well as two other marine invertebrates: Aplysia and Spanish dancers. The free-swimming performance is evaluated via two metrics: Froude efficiency and terminal swimming speed. The study examines the effect of the flapping of the lateral margins of the body as well as body undulation, which are used in various combinations by these animals to achieve swimming. The simulations suggest that a spanwise compact wake with distinct vortex ring structures is well correlated with a high swimming performance. We find that the addition of even a small magnitude of body undulation to lateral flapping results in significant changes in the wake patterns and noticeable improvements in the swimming performance compared to swimmers that employ only lateral flapping. Periodic body-bending synchronized with lateral flapping, as employed by the Spanish dancer, is found to be a very effective swimming gait. Some gaits that employ body undulations but no lateral flapping are found to generate high swimming speeds but with limited swimming efficiencies. Taken together, this study provides insights that could inform the design of swimming robots.

Dynamic Analysis of a Robotic Fish Propelled by Flexible Folding Pectoral Fins

Biological fish can create high forward swimming speed due to change of thrust/drag area of pectoral fins between power stroke and recovery stroke in rowing mode. In this paper, we proposed a novel type of folding pectoral fins for the fish robot, which provides a simple approach in generating effective thrust only through one degree of freedom of fin actuator. Its structure consists of two elemental fin panels for each pectoral fin that connects to a hinge base through the flexible joints. The Morison force model is adopted to discover the relationship of the dynamic interaction between fin panels and surrounding fluid. An experimental platform for the robot motion using the pectoral fin with different flexible joints was built to validate the proposed design. The results express that the performance of swimming velocity and turning radius of the robot are enhanced effectively. The forward swimming velocity can reach 0.231 m/s (0.58 BL/s) at the frequency near 0.75 Hz. By comparison, we found an accord between the proposed dynamic model and the experimental behavior of the robot. The attained results can be used to design controllers and optimize performances of the robot propelled by the folding pectoral fins.

A unified multi-soft-body dynamic model for underwater soft robots

A unified formulation that accounts for the dynamics of a general class of aquatic multi-body, soft-structured robots is presented. The formulation is based on a Cosserat formalism where the description of the ensemble of geometrical entities, such as shells and beams, gives rise to a multi-soft-body system capable of simulating both manipulation and locomotion. Conceived as an advanced tool for a priori hardware development, n-degree-of-freedom dynamics analysis and control design of underwater, soft, multi-body, vehicles, the model is validated against aquatic locomotion experiments of an octopus-inspired soft unmanned underwater robot. Upon validation, the general applicability of the model is demonstrated by predicting the self-propulsion dynamics of a diverse range of new viable combinations of multi-soft-body aquatic system.

Propulsive performance of an under-actuated robotic ribbon fin

Many aquatic animals propelled by elongated undulatory fins can perform complex maneuvers and swim with high efficiency at low speeds. In this propulsion, one or multiple waves travel along an elastic fin composed of flexible rays. In this study, we explore the potential benefits or disadvantages of passive fin motion based on the coupling of fluid-structure interactions and elasto-mechanical responses of the undulatory fin. The motivation is to understand how an under-actuated undulating fin can modify its active and passive fin motion to effectively control the hydrodynamic force and propulsive efficiency. We study the kinematics and propulsive performance of an under-actuated ribbon fin using a robotic device. During two experimental sets for fully-actuated fin and under-actuated fin respectively, we measured fin kinematics, surge forces and power consumption. Our results show that under-actuated fin can generate smaller thrust but consume less power comparing to a fully-actuated counterpart. The thrust generated by an under-actuated fin scales similarly to a fully-actuated fin-linear with the enclosed area and quadratic with the relative velocity. Power consumption scales with cube of lateral tangential velocity. Furthermore, we find that the under-actuated fin can keep the same propulsive efficiency as the fully-actuated fin at low relative velocities. This finding has profound implications to both natural swimmers and underwater vehicles using undulating fin-based propulsion, as it suggests that they can potentially exploit passive fin motion without decrementing propulsive efficiency. For underwater vehicles with undulatory fins, an under-actuated design can greatly simplify the mechanical design and control complexity of a versatile propulsion system.

The undulatory swimming gait of elongated swimmers revisited

An undulatory swimming gait is characterized by short lateral displacement waves that propagate backwards along the body of the swimmer faster than it swims. Hydrodynamic theory of elongated bodies predicts that if the amplitude of the displacement waves does not increase toward the caudal end, the part of the swimmer posteriad of the dorso-ventrally widest point takes no part in propulsion. It also predicts that if the amplitude does increase, then the hydrodynamic propulsion efficiency suffers. Cusk eels have their widest point located in the anterior half of the body with the bulk of their locomotive muscles located posteriad of it; indeed, they swim so that the amplitude of the propulsion wave increases toward the caudal end. Anguillid eels have their widest point posteriad of the mid-body, and their locomotive muscles are distributed along their entire length-but they swim as cusk eels, using the posterior half only. Apparently, both use hydrodynamically inefficient gaits. The paper questions the definition of propulsion efficiency and shows that biomechanical considerations are more important than hydrodynamic, and that most probably fish adjust their gait to maximize the ratio between the energy made good (the product of thrust and distance) and the chemical energy consumed by the muscles. The role of body shape is discussed.

Relations between morphology, buoyancy and energetics of requiem sharks

Sharks have a distinctive shape that remained practically unchanged through hundreds of millions of years of evolution. Nonetheless, there are variations of this shape that vary between and within species. We attempt to explain these variations by examining the partial derivatives of the cost of transport of a generic shark with respect to buoyancy, span and chord of its pectoral fins, length, girth and body temperature. Our analysis predicts an intricate relation between these parameters, suggesting that ectothermic species residing in cooler temperatures must either have longer pectoral fins and/or be more buoyant in order to maintain swimming performance. It also suggests that, in general, the buoyancy must increase with size, and therefore, there must be ontogenetic changes within a species, with individuals getting more buoyant as they grow. Pelagic species seem to have near optimally sized fins (which minimize the cost of transport), but the majority of reef sharks could have reduced the cost of transport by increasing the size of their fins. The fact that they do not implies negative selection, probably owing to decreased manoeuvrability in confined spaces (e.g. foraging on a reef).

Assessing hydrodynamic space use of brown trout, Salmo trutta, in a complex flow environment: a return to first principles

It is commonly assumed that stream-dwelling fish should select positions where they can reduce energetic costs relative to benefits gained and enhance fitness. However, the selection of appropriate hydrodynamic metrics that predict space use is the subject of recent debate and a cause of controversy. This is for three reasons: (1) flow characteristics are often oversimplified, (2) confounding variables are not always controlled and (3) there is limited understanding of the explanatory mechanisms that underpin the biophysical interactions between fish and their hydrodynamic environment. This study investigated the space use of brown trout, Salmo trutta, in a complex hydrodynamic flow field created using an array of different sized vertically oriented cylinders in a large open-channel flume in which confounding variables were controlled. A hydrodynamic drag function (D) based on single-point time-averaged velocity statistics that incorporates the influence of turbulent fluctuations was used to infer the energetic cost of steady swimming. Novel hydrodynamic preference curves were developed and used to assess the appropriateness of D as a descriptor of space use compared with other commonly used metrics. Zones in which performance-enhancing swimming behaviours (e.g. Kármán gaiting, entraining and bow riding) that enable fish to hold position while reducing energetic costs (termed 'specialised behaviours') were identified and occupancy was recorded. We demonstrate that energy conservation strategies play a key role in space use in an energetically taxing environment with the majority of trout groups choosing to frequently occupy areas in which specialised behaviours may be adopted or by selecting low-drag regions.