Stability of a coupled body–vortex system

Abstract

This paper considers the dynamics of a rigid body interacting with point vortices in a perfect fluid. The fluid velocity is obtained using the classical complex variables theory and conformal transformations. The equations of motion of the solid–fluid system are formulated in terms of the solid variables and the position of the point vortices only. These equations are applied to study the dynamic interaction of an elliptic cylinder with vortex pairs because of its relevance to understanding the swimming of fish in an ambient vorticity field. Two families of relative equilibria are found: moving Föppl equilibria; and equilibria along the ellipse's axis of symmetry (the axis perpendicular to the direction of motion). The two families of relative equilibria are similar to those present in the classical problem of flow past a fixed body, but their stability differs significantly from the classical ones.