The relevance of recoil and free swimming in aquatic locomotion

The study of the free swimming of undulating bodies in an otherwise quiescent fluid has always encountered serious difficulties for several reasons. When considering the full system, given by the body and the unbounded surrounding fluid, the absence of external forces leads to a subtle interaction problem dominated, at least at steady state conditions, by the equilibrium of strictly related internal forces, e.g. thrust and drag, under the forcing of a prescribed deformation. A major complication has been dictated by the recoil motion induced by the non linear interactions, which may find a quite natural solution when considering as unknowns the velocity components of the body center of mass. A simplified two-dimensional model in terms of impulse equations has been used and a fruitful separation of the main contributions due to added mass and to vorticity release is easily obtained. As main results we obtain either the mean locomotion speed and the oscillating recoil velocity components which have a large effect on the overall performance of free swimming. Several constrained gaits are considered to highlight the relevance of recoil for realizing graceful and efficient trajectories and to analyze its potential means for active control.