The dependence of Rossby wave breaking on the vertical structure of the polar vortex

The three-dimensional structure of wave propagation and breaking on the edge of polar vortices is examined using a multilayer quasigeostrophic model, with piecewise constant potential vorticity (PV) in each layer. The linear propagation of waves up the edge of a vortex is found to be sensitive to vertical variations in the vortex structure, with reduced propagation if the PV or area of the vortex increases with height; this reduction is dramatic for a cylindrical vortex with increasing PV. The characteristics of the nonlinear evolution and wave breaking is examined using high-resolution contour dynamics simulations and is also found to be sensitive to the vertical structure of the vortex. The amplitude of the forcing required for wave breaking to occur is larger for baroclinic vortices (with PV or area increasing with height) than for barotropic vortices. For cylindrical vortices with PV increasing with height the variation of wave breaking with forcing amplitude is qualitatively different from that of a barotropic vortex. Wave breaking occurs in the upper layers for only a limited, intermediate range of forcing amplitudes: there is no wave breaking in upper layers for weak forcing and for large forcing there is only wave breaking at the bottom of the vortex (i.e., the wave breaking is more vertically confined than for a barotropic vortex). For vortices with both PV and area increasing with height there is again a regime with wave breaking in the upper layers for weak amplitude forcing. However,the characteristics of the filaments produced by the wave breaking in upper layers is different from that in the barotropic case, with the filaments rolling up into a series of small vortices.