Family of propagating vortex-wave equilibria for the two-dimensional Euler equations

Abstract

A family of translating vortex equilibria for the two-dimensional Euler equations is investigated both analytically and numerically. The equilibria are comprised of a nonlinear wave propagating along an infinitely long vortical interface together with a comoving point vortex and dipole. The vortical interface separates the flow of uniform vorticity from a nontrivial irrotational flow. The analytical construction, though not an exact solution for the equilibria, is a relatively simple model having good quantitative agreement with the numerical solution well into the nonlinear regime. In the limit of small wave amplitude the analytical and numerical solutions approach those obtained using linear theory.