Self-similar collapse of three geophysical vortices

The self-similar collapse of three vortices is the motion of three vortices colliding at a single point at finite time. Such a motion has first been shown to exist for two-dimensional, planar, point vortices. In this paper, we show that the concept generalises naturally to three-dimensional quasi-geostrophic vortices as well as to surface quasi-geostrophic vortices. We first determine the conditions that lead to the collapse for these singular vortices. We then show how these conditions precipitate the merger of finite core vortices both in a three-dimensional quasi-geostrophic flow and in a surface quasi-geostrophic flow.