Stability of momentumless wakes

The caudal fin of swimming animals can be modelled as a thrust-producing flapping foil. When considered alone, such a foil produces on average a jet wake with a positive net momentum. It has been argued that the instability characteristics of these averaged wakes are linked to the propulsion efficiency of swimming animals. Here, we reconsider this question by taking into account both the thrust and the drag exerted on a self-propelled swimming body. To do so, we study the stability of a family of momentumless wakes, constructed as the Oseen approximation of a force doublet moving at constant velocity. By performing a local stability analysis, we first show that these wakes undergo a transition from absolute to convective instability. Then, using the time stepper approach by integrating the linearised Navier–Stokes system, we investigate the global stability and reveal the influence of a non-parallel base flow as well as the role of the locally absolutely unstable upstream region in the wake. Finally, to complete the global scenario, we address the nonlinear evolution of the wake disturbance. These results are then discussed in the context of aquatic locomotion. According to the present stability results, and assuming the Oseen approximation whose validity has been assessed only for moderate Reynolds number, the momentumless wake of aquatic animals is generally stable, whereas the corresponding thrust part is unstable. It is therefore essential to consider all forces exerted on a self-propelled animal when discussing its wake stability and its propulsion efficiency.

Evaluation on Leading Order Vortex Decay behind an Aircraft Using an Analytical Model

A theoretical model in this article which is used to evaluate leading order vortex decay behind an aircraft, is presented. This model is then applied to two important problems. The first evaluates safety separation distances for the super class of aircraft exemplified by the Airbus A380. The second evaluates the swirl parameter which is shown to decay to a sufficiently lowlevel that short-wave instabilities are likely to be instigated. The model uses the Oseen approximation,which assumes that in the far-field the ratio of the perturbed velocity to the aircraft velocity is small, and developed from recent publications by the first author. The atmospheric turbulence is incorporated into the model by using effective viscosity.