Viscous selection of an elliptical dipole

Abstract

A theory of viscous evolution and selection of symmetric two-dimensional dipoles is suggested, based on a combination of numerical simulations and an asymptotic analysis, where the slow time scale associated with the vorticity diffusion due to viscosity is incorporated. It is shown that viscosity first brings a dipole to an intermediate asymptotic state, which is independent of the initial conditions, and then slowly takes the dipole away from this state. We demonstrate that, among the variety of possible ideal-fluid dipole solutions, viscosity going to zero selects a unique solution, which is described to high accuracy by the elliptical dipole solution with a separatrix aspect ratio of 1.037.