A Point Vortex Method Applied to Interfacial Waves

Abstract

The point vortex method can be adapted to apply to the evolution of waves on the interface between homogeneous incompressible fluids by adding equations governing the baroclinic change of point vortex strengths. It is shown that, in common with Lagrangian methods of other type, the method can fail through the growth of an instability. It is suggested that this instability, which causes waves on the scale of the inter-vortex separation to grow, is numerical and due to the distortion of the dispersion equation inherent in the replacement of the interfacial vortex sheet by an array of point vortices.