Influence of caudal fin rigidity on swimmer propulsion efficiency

Quantitative evaluation of the mechanical characteristics of swimming is experimentally challenging. Reproducing the experimental setting is hard due to the complexity and variability of the geometries involved. Even harder is the accurate characterization of swimming laws and precise measurement of forces and power. For robotic propulsion, an experimental study in this direction is that of [1]. Ideally, numerical simulation can contour some of these difficulties. However, only a few numerical investigations of three-dimensional swimming modes have been attempted so far [5]. Here, we use numerical simulation to study a specific aspect of fish-like swimming: the influence of caudal fin deformation on performance. Previous numerical [3] and experimental [4] studies were dedicated to the effect of pectoral fin deformation on the local flow patterns. In particular, [4] found that there exist optimal fin flexural rigidity for maximizing thrust. We evaluate performance thanks to a non-dimensional index taking into account the total mechanical power acting on the fluid, the swimmer velocity and the force exerted in the locomotion direction [6]. In this paper we quantitatively investigate the efficiency improvement obtained by a simple and local modification of the caudal swimmer deformation. We concentrate on locomotion at low Reynolds numbers, so that all the relevant scales of the phenomenon can adequately be resolved by three-dimensional simulations. The main idea is to compare the performance of a swimmer where the swimming law is a backward traveling wave of given amplitude and frequency, to a swimming mode where the fin deformation mimics that of an elastic medium