Swimming and Flying

It is known that the wake pattern observed in a cross-section behind swimming or flying animals is typically characterized by the presence of periodical vortex shed- ding. However, depending on species, propulsive wakes can differ according to their spatial ordering : symmetric (squid-like) or asymmetric (fish-like), with respect to the motion axis. We conducted a very precise experiment to analyse the role of the wake topology in the generation of propulsion. Self-propulsion is achieved by the flapping motion of two identical pitching rigid foils, separated by a distance d. By keeping the momentum input unchanged, we compared both symmetric and asymmetric flapping modes. For the entire explored range of parameters, the symmetric squid-like mode proves to be more efficient for thrust generation than the fish-like asymmetrical one. We show here that this difference is due to a pressure effect related to the ability of each wake to produce, or not, significant mixing in the near wake region.

Raspa, V. ; Godoy-Diana, R. & Thiria, B. (2013 submitted), Topology-induced effect in biomimetic propulsive wakes.

Raspa, V. ; Gaubert, C. & Thiria, B. (2012), ’Manipulating thrust wakes : A parallel with biomimetic propulsion’, EPL 97, 44008.

Many living organisms use body undulations to propulse themselves through fluids : they achieve net forward motion by propagating wave of curvature down their deformable body. In inertial regimes, the anguilliform swimming mechanism has first been addressed in pioneer study by Lighthill [J. Fluid Mech., vol 9, 305-317, 1960]. In his so called reactive model, Lighthill considered the inertial momentum redistribution caused by the undulations within the fluid and he showed that the thrust force generated through this process could be estimated from the kinematic of the tail of the swimmer alone. A vast amount of theoretical and numerical works has followed, providing the basis for a broad spectrum of applications, especially in robotic and engineering. We present here a swimmer able to propulse itself at the surface of a water tank. The set up consists in a flexible filament forced to oscillate by imposing an harmonic motion to one of its extremities (using magnetic interactions). We fully characterize its dynamics, with the objective to bring a better understanding of fluid-solid interactions in undulatory propulsion. The characteristics of the propagating wave are crucial in determining the swimming performance. Modeling the filament as a forced beam under fluid loading, we pinpoint the different elements that can account for the observed kinematic. In particular, we show that in our Reynolds number regime, a quadratic fluid dissipation term is needed to propagate passively a wave in a finite elastic beam. The order of magnitude of this term is estimated by comparing the theoretical predictions of the model against the experimental data. When injecting the prescribed body deformations into Lighthill’s model, we show that this reactive theory gives good predictions of the performance of the swimmer (its forward speed).

Ramananarivo, S. ; Thiria, B. & Godoy-Diana, R. (2013 submitted) Dynamics of an swimming elastic filament on a free surface.

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.

Ramananarivo, S. ; Godoy-Diana, R. & Thiria, B. (2011), ’Rather than resonance, flapping wing flyers may play on aerodynamics to improve performance’, Proceedings of the National Academy of Sciences (USA) 108(15), 5964-5969.

Thiria, B. & Godoy-Diana, R. (2010), ’How wing compliance drives the efficiency of self-propelled flapping flyers’, Physical Review E 82, 015303®.

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 Bénard-von Kármán vortex street that characterizes fish-like swimming and forward flapping flight are examined. Two-dimensional particle image velocimetry measurements in the mid-plane 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, as well as the circulation of each vortex and the spacing 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 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.

Godoy-Diana, R. ; Aider, J. L. & Wesfreid, J. E. (2008) Transitions in the wake of a flapping foil Physical Review E, 77 : 016308.

Godoy-Diana, R. ; Marais, C. ; Aider, J. L. & Wesfreid, J. E. (2009) A model for the symmetry breaking of the reverse Bénard-von Kármán vortex street produced by a flapping foil, Journal of Fluid Mechanics, 622 : 23-32.

Marais, C. ; Thiria, B. ; Wesfreid, J. E. & Godoy-Diana, R. (2012), ’Stabilizing effect of flexibility in the wake of a flapping foil’, Journal of Fluid Mechanics 710, 659-669.

Marais, C. (2011) Dynamique tourbillonnaire dans le sillage d’un aileron oscillant : Propulsion par ailes battantes biomimétiques. Thèse de doctorat de l’Université Denis Diderot, soutenue le 14 janvier 2011.