The alignment of two three-dimensional quasi-geostrophic vortices

We consider the interaction between two quasi-geostrophic vortices of height-to-width aspect ratio h/r, lying at two different vertical levels. We investigate whether such structures naturally align. In the case the vortices occupy distinct yet contiguous vertical levels, such an alignment can contribute to the growth in volume of oceanic mesoscale vortices. The other growth mechanism is the merger of vortices sharing common vertical levels. We show that there exist titled equilibrium states where vortices nearly align slantwise. Most equilibria for prolate vortices ( ) are stable apart in a very narrow region of the parameter space. The instability is however normally non-destructive. Pairs of oblate vortices may also be in an unstable equilibria if they are moderately offset in the horizontal direction. In this case, the instability may result in the shedding of filamentary potentially vorticity away from the vortices. This shedding of potential vorticity may result in the further alignment of the main structures.