On the inviscid instability of certain two-dimensional vortex-type flows

Abstract

As a contribution to the breakdown phenomenon of vortices in a two-dimensional free boundary layer, this paper deals with the question whether a single cylindrical (i.e. two-dimensional) vortex can become unstable. For this reason a single vortex, as it occurs in a free boundary layer, is approximated by an axisymmetrical vortex model. The inviscid stability theory of rotating fluids is then applied to this vortex model. By general stability criteria it was found that a vortex consisting of vorticity of one sign only is stable according to the Rayleigh criterion, but, if the vorticity has an extremum value outside the axis, may become unstable with respect to cylindrical disturbances. Furthermore, stability calculations for three special types of vortex were performed. It was found that they were more unstable with respect to cylindrical disturbances than to three-dimensional ones.