Aerofoil-vortex in a rotational and strained field

Abstract

We show that a plane region (vortex) of uniform vorticity ω 0 and whose boundary shape is a certain aerofoil is a steady solution of a free-boundary value problem involving the angular velocity and the strain rates of order not exceeding 3 as bifurcation parameters. We also determine the stability of such steady states. Classical results, in this direction, of Kirchhofif and Love are obtained here as special cases.