The question of how individuals in a population organize when living in groups arises for systems as different as a swarm of microorganisms or a flock of seagulls. The different patterns for moving collectively involve a wide spectrum of reasons, such as evading predators or optimizing food prospection. Also, the schooling pattern has often been associated with an advantage in terms of energy consumption. In this study, we use a popular aquarium fish, the red nose tetra fish, Hemigrammus bleheri, which is known to swim in highly cohesive groups, to analyze the schooling dynamics. In our experiments, fish swim in a shallow-water tunnel with controlled velocity, and stereoscopic video recordings are used to track the 3D positions of each individual in a school, as well as their tail-beating kinematics. Challenging the widespread idea of fish favoring a diamond pattern to swim more efficiently [Weihs D (1973) Nature 241:290-291], we observe that when fish are forced to swim fast-well above their free-swimming typical velocity, and hence in a situation where efficient swimming would be favored-the most frequent configuration is the "phalanx" or "soldier" formation, with all individuals swimming side by side. We explain this observation by considering the advantages of tail-beating synchronization between neighbors, which we have also characterized. Most importantly, we show that schooling is advantageous as compared with swimming alone from an energy-efficiency perspective.fish swimming | collective dynamics | pattern formation | synchronization | energy efficiency T he dynamics of animal groups is driven by many different factors, such as foraging, social life, or survival instinct against predators (1). The collective movements are built from local interactions between the individuals constituting the group (2, 3). Apart from behavioral aspects, the benefit from schooling has often been associated with group optimization in terms of hydrodynamic resistance (4). A fish school represents a typical case of such cohesive and collaborative complex systems. The fluid dynamical mechanisms influencing the motion of fish in a school have been described in essence in the early study of Weihs (5). He demonstrated, using a 2D model, that if each fish maintains a specific position within the school, forming a diamond pattern, the hydrodynamic interactions will globally improve the swimming performance. The basic idea is that fish in a school optimize swimming by interacting constructively with the vortices shed by the local leading individuals; such constructive interactions require a precise synchronization between fish. This study has been followed by an extensive number of studies modeling or simulating fish school swimming configurations to validate Weihs' hypothesis (6-8). It has been shown that by following this strategy, fish could improve their efficiency by ∼20% (8, 9). However, the idea that a beneficial situation in terms of swimming power can be achieved for the group by maintaining a specific complex pattern remai...

In this work, we address the case of red nose tetra fish Hemigrammus bleheri swimming in groups in a uniform flow, giving special attention to the basic interactions and cooperative swimming of a single pair of fish. We first bring evidence of synchronization of the two fish, where the swimming modes are dominated by 'out-phase' and 'in-phase' configurations. We show that the transition to this synchronization state is correlated with the swimming speed (i.e. the flow rate), and thus with the magnitude of the hydrodynamic pressure generated by the fish body during each swimming cycle. From a careful spatio-temporal analysis corresponding to those synchronized modes, we characterize the distances between the two individuals in a pair in the basic schooling pattern. We test the conclusions of the analysis of fish pairs with a second set of experiments using groups of three fish. By identifying the typical spatial configurations, we explain how the nearest neighbour interactions constitute the building blocks of collective fish swimming.

This paper addresses the physical mechanism of intermittent swimming by considering the burst-and-coast regime of fish swimming at different speeds. The burst-and-coast regime consists of a cycle with two successive phases, i.e., a phase of active undulation powered by the fish muscles followed by a passive gliding phase. Observations of real fish whose swimming gait is forced in a water flume from low to high speed regimes are performed, using a full description of the fish kinematics and mechanics. We first show that fish modulate a unique intrinsic cycle to sustain the demanded speed by modifying the bursting to coasting ratio while maintaining the duration of the cycle nearly constant. Secondly, we show using numerical simulations that the chosen kinematics by correspond to optimized gaits for swimming speeds larger than 1 body length per second.

Burst-and-coast swimming is an intermittent mode of locomotion used by various fish species. The intermittent gait has been associated with certain advantages such as stabilizing the visual field, improved sensing ability, and reduced energy expenditure. We investigate burst-coast swimming in rummy nose tetra fish (Hemigrammus bleheri) using a combination of experimental data and numerical simulations. The experiments were performed in a shallow water channel where the tetra fish swam against an imposed inflow. High speed video recordings of the fish were digitized to extract the undulatory kinematics at various swimming speeds. The kinematics data were then used in Navier–Stokes simulations to prescribe the undulatory motion for three-dimensional geometrical models of the fish. The resulting steady-state speeds of the simulated self-propelled swimmers agree well with the speeds observed experimentally. We examine the power requirements for various realistic swimming modes, which indicate that it is possible to use continuous swimming gaits that require considerably less mechanical energy than intermittent burst-coast modes at comparable speeds. The higher energetic cost of burst-coast swimming suggests that the primary purpose of intermittent swimming may not be to conserve energy, but it may instead be related to a combination of other functional aspects such as improved sensing and the likely existence of a minimum tail-beat frequency. Importantly, using sinusoidal traveling waves to generate intermittent and continuous kinematics, instead of using experiment-based kinematics, results in comparable power requirements for the two swimming modes.

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In this work, we present detailed particle image velocimetry (PIV) based investigation of wake structure of a pitching airfoil. PIV measurements have been carried out for NACA0015 airfoil at Re = 2900 with reduced frequency range of 1.82-10.92 and pitching angle of 5 •. Two different wake structures (reverse Kármán shedding and deflected vortex shedding) are observed over this parameter range. The vorticity decreases substantially over a distance of two chord-lengths. The velocity profile indicates a jet-like flow downstream of the airfoil. It is shown that the jet-like flow downstream of the airfoil is however not a sufficient condition for the generation of thrust. The vortex strength is found to be invariant of the pitching frequency. Certain differences from the reported results are noted, which may be because of difference in the airfoil shape. These results can help improve understanding of the flow behavior as the low Reynolds number range is not well studied.