2D vortex interaction in a non-uniform flow

In a two-dimensional incompressible fluid, we study the interaction of two like-signed Rankine vortices embedded in a steady shear/strain flow. The numerical results of vortex evolutions are compared with the analytical results for point vortices. We show the existence of vortex equilibria, and of merger for initial distances larger than those without external flow. The evolutions depend on the initial orientation of the vortices in the external flow.