Ramiro Godoy-Diana

Rather than resonance, flapping wing flyers may play on aerodynamics to improve performance

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.

Transitions in the wake of a flapping foil

We study experimentally the vortex streets produced by a flapping foil in a hydrodynamic tunnel, using two-dimensional particle image velocimetry. An analysis in terms of a flapping frequency-amplitude phase space allows the identification of (i) the transition from the well-known Bénard-von Kármán (BvK) wake to the reverse BvK vortex street that characterizes propulsive wakes, and (ii) the symmetry breaking of this reverse BvK pattern giving rise to an asymmetric wake. We also show that the transition from a BvK wake to a reverse BvK wake precedes the actual drag-thrust transition and we discuss the significance of the present results in the analysis of flapping systems in nature.

A model for the symmetry breaking of the reverse Bénard–von Kármán vortex street produced by a flapping foil

The vortex streets produced by a flapping foil of span to chord aspect ratio of 4:1 are studied in a hydrodynamic tunnel experiment. In particular, the mechanisms giving rise to the symmetry breaking of the reverse Benard–von Karman (BvK) vortex street that characterizes fishlike swimming and forward flapping flight are examined. Two-dimensional particle image velocimetry (PIV) measurements in the midplane perpendicular to the span axis of the foil are used to characterize the different flow regimes. The deflection angle of the mean jet flow with respect to the horizontal observed in the average velocity field is used as a measure of the asymmetry of the vortex street. Time series of the vorticity field are used to calculate the advection velocity of the vortices with respect to the free stream, defined as the phase velocity U phase , as well as the circulation Γ of each vortex and the spacing ξ between consecutive vortices in the near wake. The observation that the symmetry-breaking results from the formation of a dipolar structure from each couple of counter-rotating vortices shed on each flapping period serves as the starting point to build a model for the symmetry-breaking threshold. A symmetry-breaking criterion based on the relation between the phase velocity of the vortex street and an idealized self-advection velocity of two consecutive counter-rotating vortices in the near wake is established. The predicted threshold for symmetry breaking accounts well for the deflected wake regimes observed in the present experiments and may be useful to explain other experimental and numerical observations of similar deflected propulsive vortex streets reported in the literature.

Passive elastic mechanism to mimic fish- muscle action in anguilliform swimming

Swimmers in nature use body undulations to generate propulsive and manoeuvring forces. The anguilliform kinematics is driven by muscular actions all along the body, involving a complex temporal and spatial coordination of all the local actuations. Such swimming kinematics can be reproduced artificially, in a simpler way, by using the elasticity of the body passively. Here, we present experiments on self-propelled elastic swimmers at a free surface in the inertial regime. By addressing the fluid–structure interaction problem of anguilliform swimming, we show that our artificial swimmers are well described by coupling a beam theory with the potential flow model of Lighthill. In particular, we show that the propagative nature of the elastic wave producing the propulsive force is strongly dependent on the dissipation of energy along the body of the swimmer.

Vortex-induced drag and the role of aspect ratio in undulatory swimmers

During cruising, the thrust produced by a self-propelled swimmer is balanced by a global drag force. For a given object shape, this drag can involve skin friction or form drag, both being well-documented mechanisms. However, for swimmers whose shape is changing in time, the question of drag is not yet clearly established. We address this problem by investigating experimentally the swimming dynamics of undulating thin flexible foils. Measurements of the propulsive performance together with full recording of the elastic wave kinematics are used to discuss the general problem of drag in undulatory swimming. We show that a major part of the total drag comes from the trailing longitudinal vortices that roll-up on the lateral edges of the foils. This result gives a comparative advantage to swimming foils of larger span thus bringing new insight to the role of aspect ratio for undulatory swimmers.

Force balance in the take-off of a pierid butterfly: relative importance and timing of leg impulsion and aerodynamic forces

SUMMARY Up to now, the take-off stage has remained an elusive phase of insect flight that was relatively poorly explored compared with other maneuvers. An overall assessment of the different mechanisms involved in force production during take-off has never been explored. Focusing on the first downstroke, we have addressed this problem from a force balance perspective in butterflies taking off from the ground. In order to determine whether the sole aerodynamic wing force could explain the observed motion of the insect, we have firstly compared a simple analytical model of the wing force with the acceleration of the insects center of mass estimated from video tracking of the wing and body motions. Secondly, wing kinematics were also used for numerical simulations of the aerodynamic flow field. Similar wing aerodynamic forces were obtained by the two methods. However, neither are sufficient, nor is the inclusion of the ground effect, to predict faithfully the body acceleration. We have to resort to the leg forces to obtain a model that best fits the data. We show that the median and hind legs display an active extension responsible for the initiation of the upward motion of the insects body, occurring before the onset of the wing downstroke. We estimate that legs generate, at various times, an upward force that can be much larger than all other forces applied to the insects body. The relative timing of leg and wing forces explains the large variability of trajectories observed during the maneuvers.

Large-amplitude undulatory swimming near a wall

The propulsive dynamics of a flexible undulating foil in a self-propelled swimming configuration near a wall is studied experimentally. Measurements of the swimming speed and the propulsive force are presented, together with image acquisition of the kinematics of the foil and particle image velocimetry (PIV) in its wake. The presence of the wall enhances the cruising velocity in some cases up to 25% and the thrust by a 45% , for swept angles of 160 and 240°. The physical mechanisms underlying this effect are discussed by studying the vorticity dynamics in the wake of the foil. Proper orthogonal decomposition is applied to the PIV measurements in order to analyse the kinetic energy modal distribution in the flow and to relate it to the propulsion generated by the foil.

Convective instability in inhomogeneous media: Impulse response in the subcritical cylinder wake

We study experimentally the impulse response of a cylinder wake below the critical Reynolds number of the Benard–von Karman instability. In this subcritical regime, a localized inhomogeneous region of convective instability exists which causes initial perturbations to be transiently amplified. The aim of this work is to quantify the evolution resulting from this convective instability using two-dimensional particle image velocimetry in a hydrodynamic tunnel experiment. The velocity fields allow us to describe the evolution of wave packets in terms of two control parameters: the Reynolds number and the magnitude of the imposed perturbation. The temporal evolution of energy exhibits a transient algebraic growth at short times followed by an exponential decay.

Does aquatic foraging impact head shape evolution in snakes

Evolutionary trajectories are often biased by developmental and historical factors. However, environmental factors can also impose constraints on the evolutionary trajectories of organisms leading to convergence of morphology in similar ecological contexts. The physical properties of water impose strong constraints on aquatic feeding animals by generating pressure waves that can alert prey and potentially push them away from the mouth. These hydrodynamic constraints have resulted in the independent evolution of suction feeding in most groups of secondarily aquatic tetrapods. Despite the fact that snakes cannot use suction, they have invaded the aquatic milieu many times independently. Here, we test whether the aquatic environment has constrained head shape evolution in snakes and whether shape converges on that predicted by biomechanical models. To do so, we used three-dimensional geometric morphometrics and comparative, phylogenetically informed analyses on a large sample of aquatic snake species. Our results show that aquatic snakes partially conform to our predictions and have a narrower anterior part of the head and dorsally positioned eyes and nostrils. This morphology is observed, irrespective of the phylogenetic relationships among species, suggesting that the aquatic environment does indeed drive the evolution of head shape in snakes, thus biasing the evolutionary trajectory of this group of animals.

Internal gravity waves in a dipolar wind: a wave-vortex interaction experiment in a stratified fluid

An experimental study on the interaction of the internal wave field generated by oscillating cylinders in a stratified fluid with a pancake dipole is presented. The experiments are carried out in a salt-stratified water tank with constant Brunt-Vaisala frequency (N). Experimental observations of the deformation of the wave beams owing to the interaction with the dipole are presented. When the wave and the dipole propagate horizontally in opposite directions (counterpropagating case), the phase line of the gravity wave beam steepens towards the vertical as it enters the dipolar field and it may even reach a turning point where the wave is reflected. When the dipole and the wave propagate in the same direction (copropagating case), the wave beam is bent towards the horizontal and may be absorbed by the dipole. These observations are in good agreement with a two-dimensional ray-theoretic model, even if the flow is fully three-dimensional and, the vertical shear induced by the dipole being too strong, the hypothesis of slow variation assumed in the WKB approximation is not verified. When the waves encounter a critical layer, we show by rigorous measurement that momentum is transferred to the dipole. New three-dimensional effects of the dipolar velocity field on the propagating internal waves are also discussed. In particular, focusing and refraction of a wave beam occurring because of the horizontal structure of the background dipolar flow allow us to explain some of the observed features that cannot be accounted for through the two-dimensional ray theory.