Merger criterion for two vortices in 3d quasi-geostrophic flow

In this study we examine the interaction between two like-signed quasi-geostrophic vortices containing different uniform potential vorticity. The interaction depends on 6 parameters: the potential vorticity ratio between the two vortices, their volume ratio, their individual height-to-width aspect ratio, their vertical offset and their horizontal separation distance. We first calculate equilibrium states using an asymptotic approach which models the vortices as ellipsoids and then determine their linear stability. It is found that two vortices can merge at farther distances when one has stronger potential vorticity than the other. This tells us that interaction between vortices having significantly different potential vorticity may be more destructive, for a given separation distance. Most of the vortex interactions for the considered parameter space are in the partial-merger regime (where the largest vortex grows in volume) and this happens between vortices of similar po! tential vorticity.