Hydromechanics of Fish Schooling

Combining Computational Fluid Dynamics and Experimental Data to Understand Fish Schooling Behavior

Understanding the flow physics behind fish schooling poses significant challenges due to the difficulties in directly measuring hydrodynamic performance and the three-dimensional, chaotic, and complex flow structures generated by collective moving organisms. Numerous previous simulations and experiments have utilized computational, mechanical, or robotic models to represent live fish. And existing studies of live fish schools have contributed significantly to dissecting the complexities of fish schooling. But the scarcity of combined approaches that include both computational and experimental studies, ideally of the same fish schools, has limited our ability to understand the physical factors that are involved in fish collective behavior. This underscores the necessity of developing new approaches to working directly with live fish schools. An integrated method that combines experiments on live fish schools with computational fluid dynamics (CFD) simulations represents an innovative method of studying the hydrodynamics of fish schooling. CFD techniques can deliver accurate performance measurements and high-fidelity flow characteristics for comprehensive analysis. Concurrently, experimental approaches can capture the precise locomotor kinematics of fish and offer additional flow information through particle image velocimetry (PIV) measurements, potentially enhancing the accuracy and efficiency of CFD studies via advanced data assimilation techniques. The flow patterns observed in PIV experiments with fish schools and the complex hydrodynamic interactions revealed by integrated analyses highlight the complexity of fish schooling, prompting a reevaluation of the classic Weihs model of school dynamics. The synergy between CFD models and experimental data grants us comprehensive insights into the flow dynamics of fish schools, facilitating the evaluation of their functional significance and enabling comparative studies of schooling behavior. In addition, we consider the challenges in developing integrated analytical methods and suggest promising directions for future research.

Inferring the metabolic rate of zebrafish from ventilation frequency

Fish schooling has attracted the interest of the scientific community for centuries. Energy savings have been long posited to be a key determinant for the emergence of schooling patterns. Yet, current methodologies do not allow the precise quantification of the metabolic rate of specific individuals within the school, typically leaving researchers with only a single, global measurement of metabolic rate for the collective. In this paper, we demonstrate the feasibility of inferring metabolic rate of swimming fish using the mouth-opening frequency, a simple proxy that can be scored utilizing video recordings in the laboratory or in the field, even for small fish. The mouth-opening frequency is independent of hydrodynamic interactions within the school, thereby mitigating potential confounding factors that arise when using locomotory measures associated with tail-beat motion. We assessed the reliability of mouth-opening frequency as a proxy for metabolic rate by conducting experiments on zebrafish (Danio rerio) using swimming respirometry. We varied the flow speed from 0.8 to 3.2 body lengths per second and extracted tail-beat motion and mouth opening from video recordings. Our results revealed a strong correlation between oxygen uptake and mouth-opening frequency for nonzero flow speeds but not in quiescent water. Contrary to our expectations, we did not find evidence in favor of the use of tail-beat frequency as a proxy for metabolic rate. Overall, our results open the door to the study of individual metabolic rates in fish schools without confounding factors related to hydrodynamic interactions.

Representation of bulk water flow in the goldfish (Carassius auratus) midbrain

With the mechanosensory lateral line system, fish and semi-aquatic amphibians detect water movements and pressure gradients. Hydrodynamic information picked up by the lateral line receptors is relayed via peripheral nerves to the lateral line brainstem and from there to the midbrain torus semicircularis. Most prior electrophysiological studies of the lateral line were done under still-water conditions, even though natural environments encountered by fish include bulk-flow. Flow velocity and direction sensing are likely important to fish as they navigate variable, turbulent environments, but to date, only few studies have gathered information on the processing of bulk water flow by midbrain units. Here, we recorded from lateral line units in the torus semicircularis while presenting various bulk flow velocities in anterior-to-posterior and posterior-to-anterior flow directions. We studied (1) the temporal spike patterns of mechanosensory midbrain units, (2) the processing of bulk water flow velocity by these units, and (3) the processing of bulk water flow direction. We found that midbrain mechanosensory units alter their discharge rate during bulk water flow - some units responded to flow by increasing their discharge rate but did not vary this rate significantly with flow velocity, while others exhibited increasing discharge rates with increasing flow velocity. Units directly coding for flow direction were not found.

Drafting behaviors in fish induced by a local pressure drop around a hydrofoil model

Fish schooling has the improvement in hydrodynamic propulsive efficiency through the interaction of flow field induced by fish bodies and tail beat. Such energy-saving behaviors due to flow interactions also occur with changes in the flow field caused by structures. We examined the differences between a live fish swimming around a streamlined hydrofoil model prepared to represent fish body and swimming alone in a flow tank. We observed that the fish can remain in the same place without tail beating. It called "drafting" behavior. The analysis of fish drafting showed that fish obtained thrust using a local pressure drop caused by the high velocity flow even in the vicinity of the hydrofoil model at an angle of attack α of 10° to 20°without flow separation, and fish balanced forces by using an α of fish body. This tendency was confirmed in the model experiment using a two-axis load cell, and the forces acting on the fish body was the smallest value when the fish model was placed in the same conditions as a live fish experiment. We also confirmed by simulation and found that the α of fish body generated lift force and counteract the suction force. Above results indicate that a fish can balance the anterior-posterior and lateral direction forces by using a local pressure drop around a hydrofoil model as suction force, and using angle of attack on its body, thereby realizing drafting.

Swimming in a school shelters fish from turbulence

Much has been written about the energetic effects of animals moving in schools or flocks, but experimental results are few and often ambiguous. A new study in PLOS Biology shows that schooling greatly reduces the cost of transport for fish in turbulent flow.

Flow interactions lead to self-organized flight formations disrupted by self-amplifying waves

Collectively locomoting animals are often viewed as analogous to states of matter in that group-level phenomena emerge from individual-level interactions. Applying this framework to fish schools and bird flocks must account for visco-inertial flows as mediators of the physical interactions. Motivated by linear flight formations, here we show that pairwise flow interactions tend to promote crystalline or lattice-like arrangements, but such order is disrupted by unstably growing positional waves. Using robotic experiments on "mock flocks" of flapping wings in forward flight, we find that followers tend to lock into position behind a leader, but larger groups display flow-induced oscillatory modes - "flonons" - that grow in amplitude down the group and cause collisions. Force measurements and applied perturbations inform a wake interaction model that explains the self-ordering as mediated by spring-like forces and the self-amplification of disturbances as a resonance cascade. We further show that larger groups may be stabilized by introducing variability among individuals, which induces positional disorder while suppressing flonon amplification. These results derive from generic features including locomotor-flow phasing and nonreciprocal interactions with memory, and hence these phenomena may arise more generally in macroscale, flow-mediated collectives.

Alternation of social behaviors for zebrafish (Danio rerio) in response to acute cold stress

Low temperature is one of the most common abiotic stresses for aquatic ectotherms. Ambient low temperatures reduce the metabolic rate of teleosts, therefore, teleosts have developed strategies to modulate their physiological status for energy saving in response to cold stress, including behaviors, circulatory system, respiratory function, and metabolic adjustments. Many teleosts are social animals and they can live in large schools to serve a variety of functions, including predator avoidance, foraging efficiency, and reproduction. However, the impacts of acute cold stress on social behaviors of fish remain unclear. In the present study, we test the hypothesis that zebrafish alter their social behaviors for energy saving as a strategy in response to acute cold stress. We found that acute cold stress increased shoaling behavior that reflected a save-energy strategy for fish to forage and escape from the predators under cold stress. The aggressive levels measured by fighting behavior tests and mirror fighting tests were reduced by cold treatment. In addition, we also found that acute cold stress impaired the learning ability but did not affect memory. Our findings provided evidence that acute cold stress alters the social behaviors of aquatic ectotherms for energy saving; knowledge of their responses to cold is essential for their conservation and management.

Water velocity shapes fish movement behavior

Stream and river ecosystems present fluvial fishes with a dynamic energy landscape because moving water generates heterogeneous flow fields that are rarely static in space and time. Fish movement behavior should be consistent with conserving energy in these dynamic flowing environments, but little evidence supporting this hypothesis exists. Here, we tested experimentally whether three general movement behaviors-against the current, with the current, or holding position (i.e., staying in one position and location)-were performed in a way consistent with minimizing the cost of swimming in a heterogeneous flow field. We tested the effects of water velocity on movement behavior across three age classes (0, 1, and 5 years) of two different fluvial specialist fishes, the pallid sturgeon (Scaphirhynchus albus) and shovelnose sturgeon (Scaphirhynchus platorynchus). Individuals from the three age classes were exposed to a continuous and dynamic velocity field ranging from 0.02 to 0.53 m s-1, which represented natural benthic flow regimes occupied by these species in rivers. Both sturgeon species exhibited the same pattern with regard to their tendency to hold position, move upstream, or move downstream. Moving downstream was positively associated with velocity for all age groups. Moving upstream was inversely related to velocity for young fish, but as the fish aged, moving upstream was not related to water velocity. The oldest fish (age 5) moved upstream more frequently compared to the younger age classes. Holding position within a water current was the most frequent behavior and occurred with similar probability across the range of experimental velocity for youngest fish (age 0), but was inversely related to velocity in older fish. Our experiment across age classes suggests that the suite of swimming behaviors exhibited by fluvial specialists might have evolved to mitigate the energetic costs of complex energy landscapes generated by moving water to ultimately maximize net energy gain.

Tailbeat perturbations improve swimming efficiency by reducing the phase lag between body motion and the resulting fluid response

Understanding how animals swim efficiently and generate high thrust in complex fluid environments is of considerable interest to researchers in various fields, including biology, physics, and engineering. However, the influence of often-overlooked perturbations on swimming fish remains largely unexplored. Here, we investigate the propulsion generated by oscillating tailbeats with superimposed rhythmic perturbations of high frequency and low amplitude. We reveal, using a combination of experiments in a biomimetic fish-like robotic platform, computational fluid dynamics simulations, and theoretical analysis, that rhythmic perturbations can significantly increase both swimming efficiency and thrust production. The introduction of perturbations increases pressure-induced thrust, while reduced phase lag between body motion and the subsequent fluid dynamics response improves swimming efficiency. Moreover, our findings suggest that beneficial perturbations are sensitive to kinematic parameters, resolving previous conflicts regarding the effects of such perturbations. Our results highlight the potential benefits of introducing perturbations in propulsion generators, providing potential hypotheses for living systems and inspiring the design of artificial flapping-based propulsion systems.

Energy conservation by collective movement in schooling fish

Many animals moving through fluids exhibit highly coordinated group movement that is thought to reduce the cost of locomotion. However, direct energetic measurements demonstrating the energy-saving benefits of fluid-mediated collective movements remain elusive. By characterizing both aerobic and anaerobic metabolic energy contributions in schools of giant danio (Devario aequipinnatus), we discovered that fish schools have a concave upward shaped metabolism-speed curve, with a minimum metabolic cost at ~1 body length s-1. We demonstrate that fish schools reduce total energy expenditure (TEE) per tail beat by up to 56% compared to solitary fish. When reaching their maximum sustained swimming speed, fish swimming in schools had a 44% higher maximum aerobic performance and used 65% less non-aerobic energy compared to solitary individuals, which lowered the TEE and total cost of transport by up to 53%, near the lowest recorded for any aquatic organism. Fish in schools also recovered from exercise 43% faster than solitary fish. The non-aerobic energetic savings that occur when fish in schools actively swim at high speed can considerably improve both peak and repeated performance which is likely to be beneficial for evading predators. These energetic savings may underlie the prevalence of coordinated group locomotion in fishes.

Self-organization of active colloids mediated by chemical interactions

Self-propelled colloidal particles exhibit rich non-equilibrium phenomena and have promising applications in fields such as drug delivery and self-assembled active materials. Previous experimental and theoretical studies have shown that chemically active colloids that consume or produce a chemical can self-organize into clusters with diverse characteristics depending on the effective phoretic interactions. In this paper, we investigate self-organization in systems with multiple chemical species that undergo a network of reactions and multiple colloidal species that participate in different reactions. Active colloids propelled by complex chemical reactions with potentially nonlinear kinetics can be realized using enzymatic reactions that occur on the surface of enzyme-coated particles. To demonstrate how the self-organizing behavior depends on the chemical reactions active colloids catalyze and their chemical environment, we consider first a single type of colloid undergoing a simple catalytic reaction, and compare this often-studied case with self-organization in binary mixtures of colloids with sequential reactions, and binary mixtures with nonlinear autocatalytic reactions. Our results show that in general active colloids at low particle densities can form localized clusters in the presence of bulk chemical reactions and phoretic attractions. The characteristics of the clusters, however, depend on the reaction kinetics in the bulk and on the particles and phoretic coefficients. With one or two chemical species that only undergo surface reactions, the space for possible self-organizations are limited. By considering the additional system parameters that enter the chemical reaction network involving reactions on the colloids and in the fluid, the design space of colloidal self-organization can be enlarged, leading to a variety of non-equilibrium structures.

Target-Following Control of a Biomimetic Autonomous System Based on Predictive Reinforcement Learning

Biological fish often swim in a schooling manner, the mechanism of which comes from the fact that these schooling movements can improve the fishes' hydrodynamic efficiency. Inspired by this phenomenon, a target-following control framework for a biomimetic autonomous system is proposed in this paper. Firstly, a following motion model is established based on the mechanism of fish schooling swimming, in which the follower robotic fish keeps a certain distance and orientation from the leader robotic fish. Second, by incorporating a predictive concept into reinforcement learning, a predictive deep deterministic policy gradient-following controller is provided with the normalized state space, action space, reward, and prediction design. It can avoid overshoot to a certain extent. A nonlinear model predictive controller is designed and can be selected for the follower robotic fish, together with the predictive reinforcement learning. Finally, extensive simulations are conducted, including the fix point and dynamic target following for single robotic fish, as well as cooperative following with the leader robotic fish. The obtained results indicate the effectiveness of the proposed methods, providing a valuable sight for the cooperative control of underwater robots to explore the ocean.

A comprehensive review of hydrodynamic studies on fish schooling

Collective motion of organisms is a widespread phenomenon exhibited by many species, most commonly associated with colonial birds and schools of fish. The benefits of schooling behavior vary from defense against predators, increased feeding efficiency, and improved endurance. Schooling motions can be energetically beneficial as schools allow for channeling and vortex-based interactions, creating a less demanding stroke rate to sustain high swimming velocities and increased movement efficiency. Biomimetics is a fast-growing field, and there have been several attempts to quantify the hydrodynamics behind group dynamics and the subsequent benefits of increased maneuverability, which can be applied to unmanned vehicles and devices traveling in a group or swarm-like scenarios. Earlier efforts to understand these phenomena have been composed of physical experimentation and numerical simulations. This literature review examines the existing studies performed to understand the hydrodynamics of group collective motion inspired by schooling habits. Both numerical simulation and physical experimentation are discussed, and the benefits and drawbacks of the two approaches are compared to help future researchers and engineers expand on these models and concepts. This paper also identifies some of the limitations associated with different approaches to studies on fish schooling and suggests potential directions for future work.

Energetic benefits in coordinated circular swimming motion of two swimmers

The coordinated movement of multiple swimmers is a crucial component of fish schools. Fish swimming in different formations, such as tandem, side-by-side, diamond, and phalanx, can achieve significant energetic advantages. However, the energetic benefits of nonstraight swimming behaviors, such as the collective motion of a milling pattern, are not well understood. To fill in this gap, we consider two swimmers in circular tracks, controlled by a PID approach to reach stable configurations. Our study finds that the optimal phase is affected by circumferential effects, and that substantial energy savings can result from both propulsion and turning. We also explore the radial effect in terms of energetic benefits. In a milling pattern, the inner swimmers can easily gain a certain energetic benefit (-8%), while their peers on the outside must be close enough to the inner swimmer with a proper phase to gain the energetic benefit (-14%). When the radial spacing becomes larger or is in an unmatched phase, the swimming of the outer swimmers becomes more laborious (+16%). Our results indicate that swimmers who maintain a matched phase and minimum radial effect obtain the highest energetic benefits (-26%). These findings highlight the energetic benefits of swimmers, even in a milling pattern, where the position difference dominates the extent of benefit.

Effects of Different Motion Parameters on the Interaction of Fish School Subsystems

For a long time, fish school swimming has attracted a great deal of attention in biological systems, as fish schools can have complex hydrodynamic effects on individuals. This work adopted a non-iterative, immersed boundary-lattice Boltzmann method (IB-LBM). A numerical simulation of two-dimensional three-degree-of-freedom self-propelled fish, in side-by-side, staggered, and triangle formations, was conducted by adjusting spacing and motion parameters. A comprehensive analysis of individual speed gains and energy efficiencies in these formations was carried out. Furthermore, an analysis of the hydrodynamic characteristics of fish schools was performed, using instantaneous vorticity profiles and pressure fields. Certain studies have shown that passive interactions between individuals cannot always bring hydrodynamic benefits. The swimming efficiency of side-by-side formations in the same phase gradually increases as the distance decreases, but it also brings certain burdens to individuals when the phases are different. This paper also shows that the roles of passive interactions, spacing, and deflections affect fish school subsystems differently. When the low-pressure areas created by a wake vortex act on one side of an individual's body, the tail-end fish are good at gaining hydrodynamic benefits from it. This effect is not universal, and the degree to which individuals benefit from changes in exercise parameters varies. This study provides a theoretical basis for bioinspired robots, as well as providing certain insights into the mechanism of collective biological movement.

Energetics of collective movement in vertebrates

The collective directional movement of animals occurs over both short distances and longer migrations, and is a critical aspect of feeding, reproduction and the ecology of many species. Despite the implications of collective motion for lifetime fitness, we know remarkably little about its energetics. It is commonly thought that collective animal motion saves energy: moving alone against fluid flow is expected to be more energetically expensive than moving in a group. Energetic conservation resulting from collective movement is most often inferred from kinematic metrics or from computational models. However, the direct measurement of total metabolic energy savings during collective motion compared with solitary movement over a range of speeds has yet to be documented. In particular, longer duration and higher speed collective motion must involve both aerobic and non-aerobic (high-energy phosphate stores and substrate-level phosphorylation) metabolic energy contributions, and yet no study to date has quantified both types of metabolic contribution in comparison to locomotion by solitary individuals. There are multiple challenging questions regarding the energetics of collective motion in aquatic, aerial and terrestrial environments that remain to be answered. We focus on aquatic locomotion as a model system to demonstrate that understanding the energetics and total cost of collective movement requires the integration of biomechanics, fluid dynamics and bioenergetics to unveil the hydrodynamic and physiological phenomena involved and their underlying mechanisms.

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.

Fish-inspired robotic algorithm: mimicking behaviour and communication of schooling fish

This study aims to present a novel flocking algorithm for robotic fish that will aid the study of fish in their natural environment. The algorithm, fish-inspired robotic algorithm (FIRA), amalgamates the standard flocking behaviors of attraction, alignment, and repulsion, together with predator avoidance, foraging, general obstacle avoidance, and wandering. The novelty of the FIRA algorithm is the combination of predictive elements to counteract processing delays from sensors and the addition of memory. Furthermore, FIRA is specifically designed to work with an indirect communication method that leads to superior performance in collision avoidance, exploration, foraging, and the emergence of realistic behaviors. By leveraging a high-latency, non-guaranteed communication methodology inspired by stigmergy methods inherent in nature, FIRA successfully addresses some of the obstacles associated with underwater communication. This breakthrough enables the realization of inexpensive, multi-agent swarms while concurrently harnessing the advantages of tetherless communication. FIRA provides a computational light control algorithm for further research with low-cost, low-computing agents. Eventually, FIRA will be used to assimilate robots into a school of biological fish, to study or influence the school. This study endeavors to demonstrate the effectiveness of FIRA by simulating it using a digital twin of a bio-inspired robotic fish. The simulation incorporates the robot's motion and sensors in a realistic, real-time environment with the algorithm used to direct the movements of individual agents. The performance of FIRA was tested against other collective flocking algorithms to determine its effectiveness. From the experiments, it was determined that FIRA outperformed the other algorithms in both collision avoidance and exploration. These experiments establish FIRA as a viable flocking algorithm to mimic fish behavior in robotics.

Ontogenetic Plasticity in Shoaling Behavior in a Forage Fish under Warming

Shoaling behavior is known to increase survival rates during attacks from predators, minimize foraging time, favor mating, and potentially increase locomotor efficiency. The onset of shoaling typically occurs during the larval phase, but it is unclear how it may improve across ontogenetic stages in forage fishes. Warming is known to increase metabolic rates during locomotion in solitary fish, and shoaling species may adjust their collective behavior to offset the elevated costs of swimming at higher temperatures. In this study, we quantified the effects of warming on shoaling performance across the ontogeny of a small forage fish, zebrafish (Danio rerio) at different speeds. Shoals of larval, juvenile, and adult zebrafish were acclimated at two temperatures (28°C and 32°C), and metabolic rates were quantified prior to and following nonexhaustive exercise at high speed. Shoals of five individuals were filmed in a flow tank to analyze the kinematics of collective movement. We found that zebrafish improve shoaling swimming performance from larvae to juveniles to adults. In particular, shoals become more cohesive, and both tail beat frequency (TBF) and head-to-tail amplitude decrease with ontogeny. Early life stages have higher thermal sensitivity in metabolic rates and TBF especially at high speeds, when compared to adults. Our study shows that shoaling behavior and thermal sensitivity improve as zebrafish shift from larval to juvenile to adult stages.

Learning to cooperate for low-Reynolds-number swimming: a model problem for gait coordination

Biological microswimmers can coordinate their motions to exploit their fluid environment-and each other-to achieve global advantages in their locomotory performance. These cooperative locomotion require delicate adjustments of both individual swimming gaits and spatial arrangements of the swimmers. Here we probe the emergence of such cooperative behaviors among artificial microswimmers endowed with artificial intelligence. We present the first use of a deep reinforcement learning approach to empower the cooperative locomotion of a pair of reconfigurable microswimmers. The AI-advised cooperative policy comprises two stages: an approach stage where the swimmers get in close proximity to fully exploit hydrodynamic interactions, followed a synchronization stage where the swimmers synchronize their locomotory gaits to maximize their overall net propulsion. The synchronized motions allow the swimmer pair to move together coherently with an enhanced locomotion performance unattainable by a single swimmer alone. Our work constitutes a first step toward uncovering intriguing cooperative behaviors of smart artificial microswimmers, demonstrating the vast potential of reinforcement learning towards intelligent autonomous manipulations of multiple microswimmers for their future biomedical and environmental applications.

Illuminance-tuned collective motion in fish

We experimentally investigate the role of illumination on the collective dynamics of a large school (ca. 50 individuals) of Hemigrammus rhodostomus. The structure of the group, defined using two order parameters, is quantified while progressively altering the visual range of the fish through controlled cycles of ambient light intensity. We show that, at low light levels, the individuals within the group are unable to form a cohesive group, while at higher illuminance the degree of alignment of the school correlates with the light intensity. When increasing the illuminance, the school structure is successively characterized by a polarized state followed by a highly regular and stable rotational configuration (milling). Our study shows that vision is necessary to achieve cohesive collective motion for free swimming fish schools, while the short-range lateral line sensing is insufficient in this situation. The present experiment therefore provides new insights into the interaction mechanisms that govern the emergence and intensity of collective motion in biological systems.

Differences in the Natural Swimming Behavior of Schizothorax prenanti Individual and Schooling in Spatially Heterogeneous Turbulent Flows

Spatially heterogeneous turbulent flow refers to nonuniform flow with coexisting multiple flow velocities, which is widely distributed in fish natural or husbandry environments, and its hydraulic parameters affect fish swimming behavior. In this study, a complex hydrodynamic environment with three flow velocity regions (low, medium, and high) coexisting in an open-channel flume was designed to explore volitional swimming ability, the spatial-temporal distribution of fish swimming trajectories, and the range of preferred hydrodynamic parameters of Schizothorax prenanti individual and schooling (three fish). The results showed that the swimming speed of individual fish during upstream migration was significantly higher than that of fish schools (p < 0.05). The swimming trajectories of fish schooling showed that they spent more time synchronously exploring the flow environment during upstream migration compared with individual fish. By superimposing the fish swimming trajectories on the environmental flow field, the range of hydrodynamic environments preferred by fish in complex flow fields was quantified. This research provides a novel approach for investigating the natural swimming behavior of fish species, and a theoretical reference for the restoration of fish natural habitats or flow enrichment of husbandry environments.

In-line swimming dynamics revealed by fish interacting with a robotic mechanism

Schooling in fish is linked to a number of factors such as increased foraging success, predator avoidance, and social interactions. In addition, a prevailing hypothesis is that swimming in groups provides energetic benefits through hydrodynamic interactions. Thrust wakes are frequently occurring flow structures in fish schools as they are shed behind swimming fish. Despite increased flow speeds in these wakes, recent modeling work has suggested that swimming directly in-line behind an individual may lead to increased efficiency. However, only limited data are available on live fish interacting with thrust wakes. Here we designed a controlled experiment in which brook trout, Salvelinus fontinalis, interact with thrust wakes generated by a robotic mechanism that produces a fish-like wake. We show that trout swim in thrust wakes, reduce their tail-beat frequencies, and synchronize with the robotic flapping mechanism. Our flow and pressure field analysis revealed that the trout are interacting with oncoming vortices and that they exhibit reduced pressure drag at the head compared to swimming in isolation. Together, these experiments suggest that trout swim energetically more efficiently in thrust wakes and support the hypothesis that swimming in the wake of one another is an advantageous strategy to save energy in a school.

Learning to school in dense configurations with multi-agent deep reinforcement learning

Fish are observed to school in different configurations. However, how and why fish maintain a stable schooling formation still remains unclear. This work presents a numerical study of the dense schooling of two free swimmers by a hybrid method of the multi-agent deep reinforcement learning and the immersed boundary-lattice Boltzmann method. Active control policies are developed by synchronously training the leader to swim at a given speed and orientation and the follower to hold close proximity to the leader. After training, the swimmers could resist the strong hydrodynamic force to remain in stable formations and meantime swim in desired path, only by their tail-beat flapping. The tail movement of the swimmers in the stable formations are irregular and asymmetrical, indicating the swimmers are carefully adjusting their body-kinematics to balance the hydrodynamic force. In addition, a significant decrease in the mean amplitude and the cost of transport is found for the followers, indicating these swimmers could maintain the swimming speed with less efforts. The results also show that the side-by-side formation is hydrodynamically more stable but energetically less efficient than other configurations, while the full-body staggered formation is energetically more efficient as a whole.

Improved swimming performance in schooling fish via leading-edge vortex enhancement

The hydrodynamics of schooling fish has been the subject of continued investigation over the last 50 years; fish schools exhibit a variety of arrangements and several distinct mechanisms have been proposed to explain the hydrodynamic benefits of schooling. In the current study, we use direct numerical simulations to show that a caudal fin swimmer trailing another similar swimmer can significantly improve its swimming performance by positioning itself such that the wake-induced flow of the leading fish, enhances the leading-edge vortex (LEV) on the fin of the trailing fish. Improvements of up to 12% in both the thrust and efficiency of the trailing fish are possible with this mechanism. The mechanisms underlying these interactional effects are quantitatively analyzed by applying the force partitioning method, a powerful data-driven method that partitions the pressure forces on the fish into mechanistically distinct components. The analysis reveals that the LEV on the fin dominates the overall thrust production for these swimmers and its enhancement therefore provides an effective and robust means for harnessing fish-fish hydrodynamic interactions in a school. In addition to confirming the potential energetic benefits of schooling, the LEV enhancement mechanism could be exploited in coordinated swimming of bioinspired multi-vehicle or multi-foil flapping foil propulsion systems.

Flapping dynamics of an inverted flag behind a cylinder

The inverted flag configuration is inspired by biological structures (e.g. leaves on a tree branch), showing rich dynamics associated with instabilities at lower flow speeds than the regular flag configuration. In the biological counterpart, the arrangement of leaves and twigs on foliage creates a complex interacting environment that promotes certain dynamic fluttering modes. While enabling a large amplitude response for reduced flow speeds is advantageous in emerging fields such as energy harvesting, still, little is known about the consequence of such interactions. In this work, we numerically study the canonical bio-inspired problem of the flow-structural interaction of a 2D inverted flag behind a cylindrical bluff body, mimicking a leaf behind a tree branch, to investigate its distinct fluttering regimes. The separation distance between the cylinder and flag is gradually modified to determine the effective distance beyond which small-amplitude or large-amplitude flapping occurs for different flow velocities. It is shown that the flag exhibits a periodic large amplitude-low frequency response mode when the cylinder is placed at a sufficiently large distance in front of the flag. At smaller distances, when the flag is within the immediate wake of the cylinder, the flag undergoes a high frequency-small amplitude response. Finally, the flag's piezoelectric power harvesting capability is investigated numerically and experimentally for varying geometrical and electrical parameters associated with these two conditions. Two separate optimal response modes with the highest energy output have also been identified.

Variations in cost of transport and their ecological consequences: a review

Movement is essential in the ecology of most animals, and it typically consumes a large proportion of individual energy budgets. Environmental conditions modulate the energetic cost of movement (cost of transport, COT), and there are pronounced differences in COT between individuals within species and across species. Differences in morphology affect COT, but the physiological mechanisms underlying variation in COT remain unresolved. Candidates include mitochondrial efficiency and the efficiency of muscle contraction-relaxation dynamics. Animals can offset increased COT behaviourally by adjusting movement rate and habitat selection. Here, we review the theory underlying COT and the impact of environmental changes on COT. Increasing temperatures, in particular, increase COT and its variability between individuals. Thermal acclimation and exercise can affect COT, but this is not consistent across taxa. Anthropogenic pollutants can increase COT, although few chemical pollutants have been investigated. Ecologically, COT may modify the allocation of energy to different fitness-related functions, and thereby influence fitness of individuals, and the dynamics of animal groups and communities. Future research should consider the effects of multiple stressors on COT, including a broader range of pollutants, the underlying mechanisms of COT and experimental quantifications of potential COT-induced allocation trade-offs.

An inertial mechanism behind dynamic station holding by fish swinging in a vortex street

Many aquatic and aerial animal species are known to utilise their surrounding flow field and/or the induced flow field of a neighbour to reduce their physical exertion, however, the mechanism by which such benefits are obtained has remained elusive. In this work, we investigate the swimming dynamics of rainbow trout in the wake of a thrust-producing oscillating hydrofoil. Despite the higher flow velocities in the inner region of the vortex street, some fish maintain position in this region, while exhibiting an altered swimming gait. Estimates of energy expenditure indicate a reduction in the propulsive cost when compared to regular swimming. By examining the accelerations of the fish, an explanation of the mechanism by which energy is harvested from the vortices is proposed. Similar to dynamic soaring employed by albatross, the mechanism can be linked to the non-equilibrium hydrodynamic forces produced when fish encounter the cross-flow velocity generated by the vortex street.

EcoPhysioMechanics: Integrating energetics and biomechanics to understand fish locomotion under climate change

Ecological physiologists and biomechanists have been broadly investigating swimming performance in a diversity of fishes, however the connection between form, function and energetics of locomotion has been rarely evaluated in the same system and under climate change scenarios. In this perspective I argue that working within the framework of 'EcoPhysioMechanics', i.e., integrating energetics and biomechanics tools, to measure locomotor performance and behavior under different abiotic factors, improves our understanding of the mechanisms, limits and costs of movement. To demonstrate how ecophysiomechanics can be applied to locomotor studies, I outline how linking biomechanics and physiology allows us to understand how fishes may modulate their movement to achieve high speeds or reduce the costs of locomotion. I also discuss how the framework is necessary to quantify swimming capacity under climate change scenarios. Finally, I discuss current dearth of integrative studies and gaps in empirical datasets that are necessary to understand fish swimming under changing environments.

Fish swimming efficiency

Every spring a 600 lb Atlantic bluefin tuna travels over 3000 miles from Newfoundland to its spawning grounds in the Gulf of Mexico. That it does so on a meal of a couple of bluefish is nothing short of remarkable. Humans will likely never engineer such an efficient swimming machine. Of course, that has not stopped us from trying. We have achieved remarkable progress by following a strategy of inspiration by nature. At the same time, our fish-like robots often fall short of matching fish performance by a considerable margin. Despite our advances, we are still left asking the question: How do fish swim so well?

Hydrodynamic Interaction of Two Self-Propelled Fish Swimming in a Tandem Arrangement

Collective locomotion in biological systems is ubiquitous and attracts much attention, and there are complex hydrodynamics involved. The hydrodynamic interaction for fish schooling is examined using two-dimensional numerical simulations of a pair of self-propelled swimming fish in this paper. The effects of different parameters on swimming speed gain and energy-saving efficiency are investigated by adjusting swimming parameters (initial separation distance d0, tail beat amplitude A, body wavelength λ, and period of oscillation T) at different phase difference δϕ between two fish. The hydrodynamic interaction performance of fish swimming in a tandem arrangement is analyzed with the help of the instantaneous vorticity contours, pressure contours, and mean work done. Using elementary hydrodynamic arguments, a unifying mechanistic principle, which characterizes the fish locomotion by deriving a scaling relation that links swimming speed u to body kinematics (A, T, and λ), arrangement of formation (d0), and fluid properties (kinematic viscosity ν), is revealed. It is shown that there are some certain scaling laws between similarity criterion number (Reynolds number (Re) and Strouhal number (St)) and energy-consuming coefficient (CE) under different parameters (Δ). In particular, a generality in the relationships of St–Re and CE–(Re ·Δ) can emerge despite significant disparities in locomotory performance.

Collective behavior and hydrodynamic advantage of side-by-side self-propelled flapping foils

Fish schools and their potential hydrodynamic advantages are intriguing problems and many underlying mechanisms are unclear due to the complexity of the system, especially for large schools. Here large schools containing four, six, and eight self-propelled foils in a side-by-side configuration are numerically studied. The effect of different combinations out of phase and in phase between two neighboring foils is studied. The results show that the multiple abreast self-propelled foils driven by synchronized harmonic flapping motions can spontaneously form stable side-by-side configurations. When compared with a single foil flapping alone, for cases in which any two neighboring foils are in an out-of-phase state, foils consume more energy with a specific cruising speed. For cases where any two neighboring foils are in an in-phase state, foils propel at a lower speed for a specific flapping frequency. Interestingly, the foils in hybrid states in which both out of phase and in phase coexist are preferred to enhance speed and save power. Further analysis indicates that the stability of the configuration and the lower cost of transport are attributed to the synchronized collaborative wake vortex structure and bow configuration formed by any three neighboring foils in a hybrid state. The collaborative vortices in the wake help the foils move forward alternatively during one flapping cycle. The bow configuration prevents the wake from spreading laterally and enhances the performance. Our paper sheds some light on understanding the self-organized collective behavior and hydrodynamic advantages of large schools.

Intermittent propulsion in largemouth bass, Micropterus salmoides, increases power production at low swimming speeds

Locomotion dominates animal energy budgets, and selection should favour behaviours that minimize transportation costs. Recent fieldwork has altered our understanding of the preferred modes of locomotion in fishes. For instance, bluegill employ a sustainable intermittent swimming form with 2-3 tail beats alternating with short glides. Volitional swimming studies in the laboratory with bluegill suggest that the propulsive phase reflects a fixed-gear constraint on body-caudal-fin activity. Largemouth bass (Micropterus salmoides) also reportedly display intermittent swimming in the field. We examined swimming by bass in a static tank to quantify the parameters of volitional locomotion, including tailbeat frequency and glide duration, across a range of swimming speeds. We found that tailbeat frequency was not related to speed at low swimming speeds. Instead, speed was a function of glide duration between propulsive events, with glide duration decreasing as speed increased. The propulsive Strouhal number remained within the range that maximizes propulsive efficiency. We used muscle mechanics experiments to simulate power production by muscle operating under intermittent versus steady conditions. Workloop data suggest that intermittent activity allows fish to swim efficiently and avoid the drag-induced greater energetic cost of continuous swimming. The results offer support for a new perspective on fish locomotion: intermittent swimming is crucial to aerobic swimming energetics.

Deep-reinforcement-learning-based self-organization of freely undulatory swimmers

It is fascinating that fish groups spontaneously form different formations. The collective locomotions of two and multiple undulatory self-propelled foils swimming in a fluid are numerically studied and the deep reinforcement learning (DRL) is applied to control the locomotion. We explored whether typical patterns emerge spontaneously under the driven two DRL strategies. One strategy is that only the following fish gets hydrodynamic advantages. The other is that all individuals in the group take advantage of the interaction. In the DRL strategy, we use swimming efficiency as the reward function, and the visual information is included. We also investigated the effect of involving hydrodynamic force information, which is an analogy to that detected by the lateral line of fish. Each fish can adjust its undulatory phase to achieve the goal. Under the two strategies, collective patterns with different characteristics, i.e., the staggered-following, tandem-following phalanx and compact modes emerge. They are consistent with the results in the literature. The hydrodynamic mechanism of the above high-efficiency collective traveling modes is analyzed by the vortex-body interaction and thrust. We also found that the time sequence feature and hydrodynamic information in the DRL are essential to improve the performance of collective swimming. Our research can reasonably explain the controversial issue observed in the relevant experiments. The paper may be helpful for the design of bionic fish.

Gyrotactic cluster formation of bottom-heavy squirmers

Squirmers that are bottom-heavy experience a torque that aligns them along the vertical so that they swim upwards. In a suspension of many squirmers, they also interact hydrodynamically via flow fields that are initiated by their swimming motion and by gravity. Swimming under the combined action of flow field vorticity and gravitational torque is called gyrotaxis. Using the method of multi-particle collision dynamics, we perform hydrodynamic simulations of a many-squirmer system floating above the bottom surface. Due to gyrotaxis they exhibit pronounced cluster formation with increasing gravitational torque. The clusters are more volatile at low values but compactify to smaller clusters at larger torques. The mean distance between clusters is mainly controlled by the gravitational torque and not the global density. Furthermore, we observe that neutral squirmers form clusters more easily, whereas pullers require larger gravitational torques due to their additional force-dipole flow fields. We do not observe clustering for pusher squirmers. Adding a rotlet dipole to the squirmer flow field induces swirling clusters. At high gravitational strengths, the hydrodynamic interactions with the no-slip boundary create an additional vertical alignment for neutral squirmers, which also supports cluster formation.

Real-time parametric estimation of periodic wake-foil interactions using bioinspired pressure sensing and machine learning

Periodic wake-foil interactions occur in the collective swimming of bio-inspired robots. Wake interaction pattern estimation (and control) is crucial to thrust enhancement and propulsive efficiency optimization. In this paper, we study the wake interaction pattern estimation of two flapping foils in tandem configurations. The experiments are conducted at a Reynolds number of 1.41 × 10⁴in a water channel. A modified wake-foil phase parameter Φ, which unifies the influences of inter-foil distanceL_x, motion phase difference Δφand wake convection velocityU_v, is introduced to describe the wake interaction patterns parametrically. We use a differential pressure sensor on the downstream foil to capture wake interaction characteristics. Data sets at different tandem configurations are collected. The wake-foil phase Φ is used to label the pressure signals. A one-dimensional convolutional neural networks (1D-CNN) model is used to learn an end-to-end mapping between the raw pressure measurements and the wake-foil phase Φ. The trained 1D-CNN model shows accurate estimations (average error 3.5%) on random wake interaction patterns and is fast enough (within 40 ms). Then the trained 1D-CNN model is applied to online thrust enhancement control of a downstream foil swimming in a periodic wake. Synchronous force monitoring and flow visualization demonstrate the effectiveness of the 1D-CNN model. The limitations of the model are discussed. The proposed approach can be applied to the online estimation and control of wake interactions in the collective swimming and flying of biomimetic robots.

Hydrodynamical Fingerprint of a Neighbour in a Fish Lateral Line

For fish, swimming in group may be favorable to individuals. Several works reported that in a fish school, individuals sense and adjust their relative position to prevent collisions and maintain the group formation. Also, from a hydrodynamic perspective, relative-position and kinematic synchronisation between adjacent fish may considerably influence their swimming performance. Fish may sense the relative-position and tail-beat phase difference with their neighbors using both vision and the lateral-line system, however, when swimming in dark or turbid environments, visual information may become unavailable. To understand how lateral-line sensing can enable fish to judge the relative-position and phase-difference with their neighbors, in this study, based on a verified three-dimensional computational fluid dynamics approach, we simulated two fish swimming adjacently with various configurations. The lateral-line signal was obtained by sampling the surface hydrodynamic stress. The sensed signal was processed by Fast Fourier Transform (FFT), which is robust to turbulence and environmental flow. By examining the lateral-line pressure and shear-stress signals in the frequency domain, various states of the neighboring fish were parametrically identified. Our results reveal that the FFT-processed lateral-line signals in one fish may potentially reflect the relative-position, phase-differences, and the tail-beat frequency of its neighbor. Our results shed light on the fluid dynamical aspects of the lateral-line sensing mechanism used by fish. Furthermore, the presented approach based on FFT is especially suitable for applications in bioinspired swimming robotics. We provide suggestions for the design of artificial systems consisting of multiple stress sensors for robotic fish to improve their performance in collective operation.

Stable Schooling Formations Emerge from the Combined Effect of the Active Control and Passive Self-Organization

This work presents a numerical study of the collective motion of two freely-swimming swimmers by a hybrid method of the deep reinforcement learning method (DRL) and the immersed boundary-lattice Boltzmann method (IB-LBM). An active control policy is developed by training a fish-like swimmer to swim at an average speed of 0.4 L/T and an average orientation angle of 0∘. After training, the swimmer is able to restore the desired swimming speed and orientation from moderate external perturbation. Then the control policy is adopted by two identical swimmers in the collective swimming. Stable side-by-side, in-line and staggered formations are achieved according to the initial positions. The stable side-by-side swimming area of the follower is concentrated to a small area left or right to the leader with an average distance of 1.35 L. The stable in-line area is concentrated to a small area about 0.25 L behind the leader. A detailed analysis shows that both the active control and passive self-organization play an important role in the emergence of the stable schooling formations, while the active control works for maintaining the speed and orientation in case the swimmers collide or depart from each other and the passive self-organization works for emerging a stable schooling configuration. The result supports the Lighthill conjecture and also highlights the importance of the active control.

Small increases in group size improve small shoals' response to water flow in zebrafish

Social context may influence the perception of sensory cues and the ability to display refined behavioral responses. Previous work suggests that effective responses to environmental cues can be contingent on having a sufficient number of individuals in a group. Thus, the changes in group size may have profound impacts, particularly on the behavior of small social groups. Using zebrafish (Danio rerio), here we examined how changes in group size influence the ability to respond to changes in water flow. We found that fish in relatively larger groups displayed stronger rheotaxis even when comparing pairs of fish with groups of four fish, indicating that a small increase in group size can enhance the responsiveness to environmental change. Individual fish in relatively larger groups also spent less time in the energetically costly leading position compared to individuals in pairs, indicating that even a small increase in group size may provide energetic benefits. We also found that the shoal cohesion was dependent on the size of the group but within a given group size, shoal cohesion did not vary with flow rate. Our study highlights that even a small change in group size could significantly affect the way social fish respond to the changes in water flow, which could be an important attribute that shapes the resilience of social animals in changing environments.

Vectorial crystallization problems and collective behavior

We propose and analyze a class of vectorial crystallization problems, with applications to crystallization of anisotropic molecules and collective behavior such as birds flocking and fish schooling. We focus on two-dimensional systems of "oriented" particles: Admissible configurations are represented by vectorial empirical measures with density in [Formula: see text]. We endow such configurations with a graph structure, where the bonds represent the "convenient" interactions between particles, and the proposed variational principle consists in maximizing their number. The class of bonds is determined by hard sphere type pairwise potentials, depending both on the distance between the particles and on the angles between the segment joining two particles and their orientations, through threshold criteria. Different ground states emerge by tuning the angular dependence in the potential, mimicking ducklings swimming in a row formation and predicting as well, for some specific values of the angular parameter, the so-called diamond formation in fish schooling.

A scalable fish-school inspired self-assembled particle system for solar-powered water-solute separation

Complete separation of water and solute is the ultimate goal of water treatment, for maximized resource recycling. However, commercialized approaches such as evaporative crystallizers consume a large amount of electricity with a significant carbon footprint, leading to calls for alternative energy-efficient and eco-friendly strategies. Here, inspired by schooling fish, we demonstrate a collective system self-assembled by expanded polystyrene (EPS)-core/graphene oxide (GO)-shell particles, which enables autonomous, efficient and complete water-solute separation powered by sunlight. By taking advantage of surface tension, these tailored particles school together naturally and are bonded as a system to function collectively and coordinatively, to nucleate, grow and output salt crystals continuously and automatically out of even saturated brine, to complete water-solute separation. Solar-vapor conversion efficiency over 90% and salt production rate as high as 0.39 kg m^–2 h^–1 are achieved under 1-sun illumination for this system. It reduces the carbon footprint of ∼50 kg for treating 1-ton saturated brine compared with the commercialized approaches.

Mechanoethology: The Physical Mechanisms of Behavior

Research that integrates animal behavior theory with mechanics-including biomechanics, physiology, and functional morphology-can reveal how organisms accomplish tasks crucial to their fitness. Despite the insights that can be gained from this interdisciplinary approach, biomechanics commonly neglects a behavioral context and behavioral research generally does not consider mechanics. Here, we aim to encourage the study of "mechanoethology," an area of investigation intended to encompass integrative studies of mechanics and behavior. Using examples from the literature, including papers in this issue, we show how these fields can influence each other in three ways: (1) the energy required to execute behaviors is driven by the kinematics of movement, and mechanistic studies of movement can benefit from consideration of its behavioral context; (2) mechanics sets physical limits on what behaviors organisms execute, while behavior influences ecological and evolutionary limits on mechanical systems; and (3) sensory behavior is underlain by the mechanics of sensory structures, and sensory systems guide whole-organism movement. These core concepts offer a foundation for mechanoethology research. However, future studies focused on merging behavior and mechanics may reveal other ways by which these fields are linked, leading to further insights in integrative organismal biology.

Fish can save energy via proprioceptive sensing

Fish have evolved diverse and robust locomotive strategies to swim efficiently in complex fluid environments. However, we know little, if anything, about how these strategies can be achieved. Although most studies suggest that fish rely on the lateral line system to sense local flow and optimise body undulation, recent work has shown that fish are still able to gain benefits from the local flow even with the lateral line impaired. In this paper, we hypothesise that fish can save energy by extracting vortices shed from their neighbours using only simple proprioceptive sensing with the caudal fin. We tested this hypothesis on both computational and robotic fish by synthesising a central pattern generator (CPG) with feedback, proprioceptive sensing, and reinforcement learning. The CPG controller adjusts the body undulation after receiving feedback from the proprioceptive sensing signal, decoded via reinforcement learning. In our study, we consider potential proprioceptive sensing inputs to consist of low-dimensional signals (e.g. perceived forces) detected from the flow. With simulations on a computational robot and experiments on a robotic fish swimming in unknown dynamic flows, we show that the simple proprioceptive sensing is sufficient to optimise the body undulation to save energy, without any input from the lateral line. Our results reveal a new sensory-motor mechanism in schooling fish and shed new light on the strategy of control for robotic fish swimming in complex flows with high efficiency.

Spontaneous response of a self-organized fish school to a predator

While the collective movements of fish schools evading predators in nature are complex, they can be fundamentally represented by simplified mathematical models. Here we develop a numerical model, which considers self-propelled particles subject to phenomenological behavioural rules and the hydrodynamic interactions between individuals. We introduce a predator in this model, to study the spontaneous response of a group of simulated fish to the threat. A self-organized fish school with a milling pattern is considered, which was expected to be efficient to evade the threat of predators. Four different attack tactics are adopted by the predator. We find that the simulated fish form transiently smaller structures as some prey individuals split from the main group, but eventually they will re-organize, sometimes into sub groups when the simulated predator approaches the fish school unidirectionally or take a reciprocating action. As the predator is programmed to target the centroid, the school ends in a gradually enlarging circle. For the fourth tactic, as the predator chases its nearest prey, the fish school's response varies with the predator's delay factor. Moreover, the average speed of the group and the distance between individuals have also been studied, both demonstrating that the fish school is able to respond spontaneously to the predator's invasion. We demonstrate that the currently adopted model can predict prey-predator interactions.

Tail Beat Synchronization during Schooling Requires a Functional Posterior Lateral Line System in Giant Danios, Devario aequipinnatus

Swimming in schools has long been hypothesized to allow fish to save energy. Fish must exploit the energy from the wakes of their neighbors for maximum energy savings, a feat that requires them to both synchronize their tail movements and stay in certain positions relative to their neighbors. To maintain position in a school, we know that fish use multiple sensory systems, mainly their visual and flow sensing lateral line system. However, how fish synchronize their swimming movements in a school is still not well understood. Here, we test the hypothesis that this synchronization may depend on functional differences in the two branches of the lateral line sensory system that detects water movements close to the fish's body. The anterior branch, located on the head, encounters largely undisturbed free-stream flow, while the posterior branch, located on the trunk and tail, encounters flow that has been affected strongly by the tail movement. Thus, we hypothesize that the anterior branch may be more important for regulating position within the school, while the posterior branch may be more important for synchronizing tail movements. Our study examines functional differences in the anterior and posterior lateral line in the structure and tail synchronization of fish schools. We used a widely available aquarium fish that schools, the giant danio, Devario equipinnatus. Fish swam in a large circular tank where stereoscopic videos recordings were used to reconstruct the 3D position of each individual within the school and to track tail kinematics to quantify synchronization. For one fish in each school, we ablated using cobalt chloride either the anterior region only, the posterior region only, or the entire lateral line system. We observed that ablating any region of the lateral line system causes fish to swim in a "box" or parallel swimming formation, which was different from the diamond formation observed in normal fish. Ablating only the anterior region did not substantially reduce tail beat synchronization but ablating only the posterior region caused fish to stop synchronizing their tail beats, largely because the tail beat frequency increased dramatically. Thus, the anterior and posterior lateral line system appears to have different behavioral functions in fish. Most importantly, we showed that the posterior lateral line system played a major role in determining tail beat synchrony in schooling fish. Without synchronization, swimming efficiency decreases, which can have an impact on the fitness of the individual fish and group.

Hydrodynamic advantages of in-line schooling

Fish benefit energetically when swimming in groups, which is reflected in lower tail-beat frequencies for maintaining a given speed. Recent studies further show that fish save the most energy when swimming behind their neighbor such that both the leader and the follower benefit. However, the mechanisms underlying such hydrodynamic advantages have thus far not been established conclusively. The long-standing drafting hypothesis-reduction of drag forces by judicious positioning in regions of reduced oncoming flow-fails to explain advantages of in-line schooling described in this work. We present an alternate hypothesis for the hydrodynamic benefits of in-line swimming based on enhancement of propulsive thrust. Specifically, we show that an idealized school consisting of in-line pitching foils gains hydrodynamic benefits via two mechanisms that are rooted in the undulatory jet leaving the leading foil and impinging on the trailing foil: (i) leading-edge suction on the trailer foil, and (ii) added-mass push on the leader foil. Our results demonstrate that the savings in power can reach as high as 70% for a school swimming in a compact arrangement. Informed by these findings, we designed a modification of the tail propulsor that yielded power savings of up to 56% in a self-propelled autonomous swimming robot. Our findings provide insights into hydrodynamic advantages of fish schooling, and also enable bioinspired designs for significantly more efficient propulsion systems that can harvest some of their energy left in the flow.

Hydrodynamical effect of parallelly swimming fish using computational fluid dynamics method

Fish form schools because of many possible reasons. However, the hydrodynamic mechanism whereby the energy efficiency of fish schools is improved still remains unclear. There are limited examples of fish models based on actual swimming movements using simulation, and the movements in existing models are simple. Therefore, in this study, we analyzed the swimming behavior of Biwa salmon (Oncorhynchus sp., a salmonid fish) using image analyses and formulated its swimming motion. Moreover, computational fluid dynamics analysis was carried out using the formulated swimming motion to determine the fluid force acting on the fish body model with real fish swimming motion. The swimming efficiency of the fish model under parallel swimming was obtained from the calculated surrounding fluid force and compared for different neighboring distances. The flow field around the fish model was also examined. The swimming efficiency of two fish models swimming parallelly was improved by approximately 10% when they were separated by a distance of 0.4L, where L is the total length of the model. In addition, the flow field behind the fish body was examined under both inphase and antiphase conditions and at inter-individual distances of 0.8L and 1.2L. The apparent flow speed in the distance range of 0.5–2.0L from the midpoint of the snouts of the two individuals was lower than the swimming speed. The pressure distribution on the fish model showed an elevated pressure at the caudal fin. Interestingly, we obtained an isopleth map similar to that of a caudal peduncle. To avoid a negative thrust, the aft part of the body must be thin, as shown in the isopleth map obtained in this study.

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.