Self-adaptation and viscous selection in concentrated two-dimensional vortex dipoles

In this Letter we deal with 2D direct numerical simulations of concentrated vortex dipoles. We show that various initial dipolar vorticity distributions evolve towards a specific family of dipoles parametrized by the dipole aspect ratio a/b, where a is the radius of the vortices based on the vorticity polar moment in half a plane and b is the separation between the vortex centroids. This convergence is achieved through viscous effects. The considered Reynolds numbers Re= Γ/v are Re= 3000 and Re= 15000. Moreover, all the dipoles of this family are quasi-steady solutions of the Euler equations. Their scatter plots and drift velocities are given for a/b<03.