Finite Froude and Rossby number baroclinic vortex pairs

We study the evolution of baroclinically-unstable pairs of opposite-signed vortices in a three-dimensional, continuously-stratified, rotating fluid at finite Froude and Rossby numbers. We explore how ageostophic motions affect the evolution of the vortex pairs, in particular the dynamical asymmetry these motions induce in their evolution. To set the stage, we first consider the quasi-geostrophic limit of vanishingly-small Froude and Rossby numbers, conducting a linear stability analysis of two equal-volume, vertically aligned, equal-and-opposite uniform potential vorticity vortices lying at different depths. We also briefly address their nonlinear evolution. In the quasi-geostrophic limit, there is no dynamical asymmetry: cyclonic and anticyclonic vortices (hereafter “cyclones” and “anticyclones”) are identical apart from their sense of rotation. Next, the evolution of equivalent (in isopycnal coordinates) vortex pairs, at finite Froude and Rossby number is explored. In this case, an cyclone/anticyclone asymmetry arises in the evolution of the vortex pair, due to ageostrophic effects. We show that the anticyclone typically deforms less than the cyclone. Moreover, increasing the Froude and Rossby numbers tends to favour baroclinic instabilities with lower azimuthal wavenumbers. The origin of this asymmetry is traced to two contributing factors. First, the displacement of isopycnals means that two vortices, identical in isopycnal coordinates, enclose different volumes, the anticyclone being larger. Second, ageotrophic effects intensify the anticyclone relative to the cyclone. The combination of the two effects implies that the evolution of the baroclinic pair of vortices is dominated by the anticyclone.