Dynamics of two identical vortices in linear shear

The dynamics of two identical vortices in linear shear was studied both numerically and experimentally. Numerical simulations based on the technique of contour dynamics reveal that the vortex evolution in adverse shear is significantly different from that in cooperative shear. Vortices in adverse shear predominantly separate, whereas vortices in cooperative shear predominantly merge. In addition, adverse shear may destruct the vortices much in the same way as a single vortex in adverse shear, whereas cooperative shear stabilizes the vortices and thus enhances the possibility of vortex merger. The critical distance for vortex merger depends strongly on both the sign and the strength of the linear shear and, to a lesser extent, on the initial vorticity distribution. A simple vortex merger criterion is derived based on the interaction of two point vortices in linear shear. The different behavior of vortices in adverse and cooperative shear was confirmed by rotating-tank experiments.