The interaction of two baroclinic geostrophic vortices on the β–plane

The interaction of two anticyclonic baroclinic vortices on the β–plane is studied, taking into account the effects of vortex–vortex advection and the radiation of barotropic Rossby waves. Quasi–geostrophic dynamics is assumed in each of the two layers and the vortices are represented by delta–function anomalies in the upper–layer potential vorticity. The vortices are strong (i.e. their swirl velocities are large compared with the long baroclinic Rossby wave speed), but are sufficiently widely separated so that the advection of one vortex due to another is of the same order as the meridional drift caused by Rossby wave radiation. Centre of mass arguments are used to demonstrate that the velocity of a vortex is due to the sum of (a) advection due to the other vortex and (b) drift due to wave radiation.The far–field structure of the Rossby wave wake of two zonally aligned vortices (i.e. they have zero meridional displacement relative to each other) is found as a function of their relative position enabling the total drag on the centre of mass to be found. The drag and subsequent meridional drift of each vortex due to the wave radiation alone is then deduced. Equilibria are found in which the vortices have the same southward and westward drift, thus preserving their zonal alignment. Depending on the vortex separation distance, the equilibrium configuration may have meridional drift significantly different from that of a single vortex by itself. For example, when the ratio of the upper–layer depth to bottom–layer depth is 0.4, the meridional drift may be as little as 35% or as much as 117% of the single–vortex drift speed. The stability of the equilibria as a function of the vortex separation distance is found.