Saving energy and enhancing performance are secular preoccupations shared by both nature and human beings. In animal locomotion, flapping flyers or swimmers rely on the flexibility of their wings or body to passively increase their efficiency using an appropriate cycle of storing and releasing elastic energy. Despite the convergence of many observations pointing out this feature, the underlying mechanisms explaining how the elastic nature of the wings is related to propulsive efficiency remain unclear. Here we use an experiment with a self-propelled simplified insect model allowing to show how wing compliance governs the performance of flapping flyers. Reducing the description of the flapping wing to a forced oscillator model, we pinpoint different nonlinear effects that can account for the observed behavior-in particular a set of cubic nonlinearities coming from the clamped-free beam equation used to model the wing and a quadratic damping term representing the fluid drag associated to the fast flapping motion. In contrast to what has been repeatedly suggested in the literature, we show that flapping flyers optimize their performance not by especially looking for resonance to achieve larger flapping amplitudes with less effort, but by tuning the temporal evolution of the wing shape (i.e., the phase dynamics in the oscillator model) to optimize the aerodynamics. F lying animals have long since inspired admiration and fueled the imagination of scientists and engineers. Alongside biologists studying form and function of flapping flyers in nature (1, 2), the last decade has seen an impressive quantity of studies driven by engineering groups using new techniques to develop and study artificial biomimetic flapping flyers (3, 4). The widespread availability of high-speed video and in particular the merging of experimental methods borrowed from fluid mechanics into the toolbox of the experimental biologist have permitted to elucidate various key mechanisms involved in the complex dynamics of flapping flight (see, for example, refs. 5-7).A recent field of investigation concerns the efficiency of flapping flyers, the major interrogation being about how natural systems optimize energy saving together with performance enhancement. In particular, the passive role of wing flexibility to increase flight efficiency through the bending of flapping wings has attracted a lot of attention. It is commonly agreed that this efficiency enhancement comes from the particular shape of the bent wing, which leads to a more favorable repartition of the aerodynamic forces (see refs. 8 and 9 for an extensive review). For flying animals in air, such as insects, it has been proposed (10-12) that wing inertia should play a major role in competing with the elastic restoring force, compared to the fluid loading. The mechanism governing the propulsive performance of the flapping flyer can therefore be seen at leading order as a two-step process, where the instantaneous shape of the wings is determined by a structural mechanics problem that then sets...

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.

Wing flexibility governs the flying performance of flapping-wing flyers. Here, we use a self-propelled flapping-wing model mounted on a "merry go round" to investigate the effect of wing compliance on the propulsive efficiency of the system. Our measurements show that the elastic nature of the wings can lead not only to a substantial reduction in the consumed power, but also to an increment of the propulsive force. A scaling analysis using a flexible plate model for the wings points out that, for flapping flyers in air, the time-dependent shape of the elastic bending wing is governed by the wing inertia. Based on this prediction, we define the ratio of the inertial forces deforming the wing to the elastic restoring force that limits the deformation as the elastoinertial number N(ei). Our measurements with the self-propelled model confirm that it is the appropriate structural parameter to describe flapping flyers with flexible wings.

We study the wake of a cylinder performing rotary oscillations around its axis at moderate Reynolds number. We observe that the structure of the vortex shedding is strongly affected by the forcing parameters. The forced wake is characterized by a ‘lock-in’ region where the vortices are shed at the forcing frequency and a region where the vortices can be reorganized to give a second frequency close to those observed for the unforced wake. We show that these modifications of the wake structure change the dynamic of the fluctuations downstream from the cylinder. We vary the amplitude and the frequency of the oscillations and study the consequences of these modifications on the mean flow and the global drag applied on the cylinder. We then discuss the mechanism responsible for the modification of the fluctuations and the modification of the drag coefficient.

We investigate the mechanics of thin sheets decorated by non-interacting creases. The system considered here consists in parallel folds connected by elastic panels. We show that the mechanical response of the creased structure is twofold, depending both on the bending deformation of the panels and the hinge-like intrinsic response of the crease. We show that a characteristic length scale, defined by the ratio of bending to hinge energies, governs whether the structure's response consists in angle opening or panel bending when a small load is applied. The existence of this length scale is a building block for future works on origami mechanics.

The wake of a flexible foil undergoing pitching oscillations in a low-speed hydrodynamic tunnel is used to examine the effect of chord-wise foil flexibility in the dynamical features of flapping-based propulsion. We compare the regime transitions in the wake with respect to the case of a rigid foil and show that foil flexibility inhibits the symmetry breaking of the reverse B\'enard-von K\'arm\'an wake reported in the literature. A momentum balance calculation shows the average thrust to be up to three times greater for the flexible foil than for the rigid foil. We explain both of these observations by analyzing the vortex dynamics in the very near wake.Comment: 10 page

Thiria, Goujon-Durand & Wesfreid (J. Fluid Mech. vol. 560, 2006, p. 123), it was shown that vortex shedding from a rotationally oscillating cylinder at moderate Reynolds number can be characterized by the spatial coexistence of two distinct patterns, one of which is related to the forcing frequency in the near wake and the other to a frequency close to the natural one for the unforced case downstream of this locked region. The existence and the modification of these wake characteristics were found to be strongly affected by the frequency and the amplitude of the cylinder oscillation. In this paper, a linear stability analysis of these forced regimes is performed, and shows that the stability characteristics of such flows are governed by a strong mean flow correction which is a function of the oscillation parameters. We also present experiments on the spatial properties of the global mode and on the selection of the vortex shedding frequency as a function of the forcing conditions for Re = 150. Finally, we elucidate a diagram of locked and non-locked states, for a large range of frequencies and amplitudes of the oscillation.