Interaction of two equal vortices on a β plane

The interaction of two equal vortices under the influence of a gradient of background vorticity (β) is studied numerically and experimentally. If the initial shape and vorticity distribution of the vortices is fixed, two parameters determine the evolution: the normalized intercentroid distance d*=d/R, where R is the radius of the vortex; and the normalized gradient of background vorticity β*=βR/ω, where ω is the peak vorticity of the vortex. Alternate ways of identifying regimes of behavior in the parameter plane (d*,β*) are presented. These are applied to numerical simulations of interaction of vortices with steplike, steep and smooth vorticity profiles. It is found that the critical distance for merger decreases with increasing β* for all vortex types, and that vortices with smooth vorticity profile are the most merger-prone vortices. Laboratory experiments were done in a rotating water tank with a flat sloping bottom providing the β effect. The vortices produced have a smooth vorticity profile and show the same behavior observed in the simulations, except that, as a result of viscous effects, the critical merger distance is shifted towards larger values of d*.