Isolated potential vorticity patches in quasi-geostrophic zonal shear flows

Abstract

We consider the behavior of isolated uniform potential vorticity patches in a two-layer quasi-geostrophic model. The eddies are embedded in a zonal shear flow having uniform potential vorticity in each layer. This model illustrates many features of vortices in more complex geophysical systems. The form of steady vortex patches is determined by two opposite effects: (1) adjustment of the boundary of the vorticity patches to the deformation by the shearing zonal flow; (2) adjustment of the eddy stream function by the displacement of the boundary of the vorticity patches. The former effect is larger for smaller vorticity patches (compared with the Rossby deformation radius) where relative vorticity is strong, while the latter is more important in the case of larger vorticity patches, when vortex stretching effects are dominant. There are two transition points in the expression for the equilibrium form of the potential vorticity patches as functions of radius; one where the latter effects exceed the former for the linear shear component of the zonal flow and one for the parabolic component. The stability of the equilibrium forms is also investigated by numerical experiments using contour dynamics. It turns out that the vortex is generally unstable when its radius is larger than the transition points. A wide variety of behaviors occur, depending upon the background zonal velocity structure. Barotropic shear can tear apart the counter-rotating part of the vortex. Curvature in the flow causes the eddy to take on a triangular shape, with shedding of filaments from the peaks. Baroclinic shear can separate the upper and lower vortices and lead to propagation of the upper and lower pair in the meridional direction.