Steady vortex dipoles with general profile functions

Abstract

Vortex dipoles in a two-dimensional, inviscid flow are obtained by prescribing the profile function relating the vorticity to the stream function. The profile functions used are smooth, and the solutions obtained have a smooth transition from the exterior flow to the interior of the vortex. The dipoles are nearly elliptical, and this relates this work to the ‘supersmooth’ dipoles obtained recently by Kizner & Khvoles (Regular Chaotic Dyn., vol. 9, 2004, pp. 509–518). The solutions found here are obtained by an iterative method for solving the nonlinear partial differential equation for the stream function. This iterative method is both robust and flexible. Solutions are also obtained in a β-plane, and they are shielded, as has also been found in previous work.