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.
Highlights
The undulatory motion of a body translating through a quiescent fluid is the concerned of this paper
We develop a new numerical method for the model and apply it to simulate the undulatory swimming of a fish-like body and study its dynamics and propulsive performance
Comparison of the motions with and without recoil We examine the effects of lateral translation and rotation, which are the relevant recoil motions accompanying the swimming generated by its shape deformation
Summary
The undulatory motion of a body translating through a quiescent fluid is the concerned of this paper. Theoretical studies on fish swimming used an inviscid analysis to examine the force acting on the body. Lighthill[3,4] proposed an elongated-body theory to analyze the effect of added mass of fluid as it accelerates owing to the undulatory body motion. Wu5,6 developed the linearized potential-flow theory by considering vortex shedding in addition to the inertial forces from added mass. While these seminal works provide insight into the swimming mechanism, they overestimate the thrust and efficiency on realistic fish-like motions.[7,8]
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