On the role of added mass and vorticity release for self-propelled aquatic locomotion

Abstract

Aquatic locomotion of a deformable body from rest up to its asymptotic speed is given by the unsteady motion which is produced by a series of periodic reactions dictated by the body configuration and by the style of swimming. The added mass plays a crucial role, not only for the initial burst, but also along each manoeuvre, to accelerate the surrounding fluid for generating the kinetic energy and to enable vortex shedding in the wake. The estimate of these physical aspects has been largely considered in most theoretical models, but not sufficiently deepened in many experimental and numerical investigations. As a motivation, while the vortical structures are easily detectable from the flow field, the added mass, on the contrary, is usually embedded in the overall forcing terms. By the present impulse formulation, we are able to separate and to emphasize the role of the added mass and vorticity release to evaluate in a neat way their specific contributions. The precise identification of the added mass is also instrumental for a well-posed numerical problem and for easily readable results. As a further point, the asymptotic speed is found to be guided either by the phase velocity of the prescribed undulation and by the unavoidable recoil motion induced by the self-propelled swimming. The numerical results reported in the present paper concern simplified cases of non-diffusing vorticity and two-dimensional flow.