Desingularized propagating vortex equilibria

Abstract

Abstract. The correction to the propagation velocity of point vortex equilibria caused by allowing the vortices to have finite core size is calculated. A matched asymptotic expansion in the small parameter ✏, given by the ratio of the core size to the dimension of the equilibrium configuration, is carried out. The resulting velocity correction is found to be of order ✏ 4 and arises from the interaction of second-and third-order terms in the inner expansion, which are themselves forced by the strain and strain derivatives of the outer field.