Vortex mergers in freely decaying two-dimensional turbulence

In freely decaying turbulence, a key physical mechanism is the merger of pairs of co-rotating vortices. In this talk, we parametrize the outcome of vortex interaction as affected by background shear as well as the separation, size, and strength of the vortices. In particular, we compare three descriptions of this process with substantially different complexity: a single pair of point vortices, two clouds of point vortices, and DNS of a pair of vortices advected by a background shear flow. We find that the simplest model, which can be treated semi-analytically, provides a reasonably accurate description of vortex interaction in both the point vortex cloud model and, more importantly, in DNS. Finally, we investigate the influence of viscosity on vortex pair collisions in DNS by parameterizing the characteristic length and vorticity scales of the post-merger vortex to better understand the time-scaling exponent that governs the statistics of vortices in decaying turbulence