Aquatic locomotion for self-propelled fishlike bodies and different styles of swimming

Fish swimming is an intriguing subject of interest in fluid mechanics at the border with other disciplines in the field of environmental sciences. The main complexity is given by the interaction between the fish body and the unbounded fluid domain, otherwise at rest. The theoretical approach has to consider the full body-fluid system to obtain from the exchanged internal forces the whole motion, i.e. locomotion plus recoil displacements, which define, together with the prescribed body deformation, the free swimming behavior. The impulse formulation allows for an easy calculation of the potential contribution, related to the added mass, and of the vortical contribution related to bound and released vorticity. A simple two- dimensional and non-diffusive model is adopted for the numerical simulations to generate neat results able to clarify several physical phenomena. The aim is a unified procedure for both undulatory and oscillatory swimming to obtain valid answers for cruising speed and expended energy, hence for the performance in terms of the cost of transport. The paper describes the theoretical aspects of the model within the context of the relevant literature and summarizes the more significant results obtained recently by the research group of the authors.