Dynamics of vortex interactions in two-dimensional flows

The dynamics and interaction of like-signed vortex structures in two dimensional flows are investigated by means of direct numerical solutions of the two-dimensional Navier-Stokes equations. Two vortices with distributed vorticity merge when their distance relative to their radius, d/R-0l. is below a critical value, a(c).

Using the Weiss-field, a(c) is estimated for vortex patches. Introducing an effective radius for vortices with distributed vorticity, we find that 3.3 < a(c) < 3.5 independently of the vorticity distribution. The evolution of spiral vorticity filaments in the merging process is effectively producing small scale structures and the relation to the enstrophy "cascade" in developed 2D turbulence is discussed.

The influence of finite viscosity on the merging is also investigated. Additionally, we examine vortex interactions on a finite domain, and discuss the results in connection with the formation of "vortex crystals".