Quasi-geostrophic vortex equilibria
I have been studying vortex interactions for years. The pictures below illustrates equilibrium states for two vortices of uniform potential vorticity in the quasi-geostrophic regime. These are theoretical models of oceanic vortices. The colour indicate the sign of the vortices. On the left, the vortices are like-signed and are steadily rotating about the centre of the picture, while on the right, the vortices have opposite sign and are steadily translating. The cases defer from one row to another by the vertical offset between the vortices centres. The cases shown correspond to the cases where the vortices are at their closest horizontally. Note that in fact, all these states are (strongly) unstable.. For the lioke-signe interactions, the vortices would merge. A larger vortex would form near the centre while small debris and filaments would be shed away (due to conservation laws). For the opposite-sign interactions, the vortices would break into smaller vortices.
