A computational model of the swimming dynamics of a fish-like body in two dimensions

Abstract

The undulatory swimming of a fish-like body is investigated by using an inviscid vortex shedding model in two dimensions. The body and separated vortices from the edge of the body are described by vortex sheets. We extend the model to include the forward and lateral motions as well as the net torque on the body and develop a new numerical method for a self-propelled deforming body. The numerical computation of the model successfully demonstrates the self-propulsion of the body and the formation of pairs of anti-rotating vortices shed from the body. At the starting stage, the body accelerates rapidly and turns the angle of incidence to some degree. The forward velocity reaches an asymptotic mean with oscillations, and the lateral velocity oscillates uniformly over time. The results of the model are in agreement with previous full numerical simulations. Furthermore, we examine the effects of the recoil motions of lateral translation and rotation of a body. The wake pattern and intensity significantly differ from the constraint of the recoil motions. It is found that free swimming requires less input power and affords more efficient energetic performance than the motions without recoil and with lateral translation. A body without recoil requires a large amount of power and is energetically inefficient. This shows that both recoil motions enhance the swimming efficiency.