Rossby-inertia-bouyancy instability in baroclinic vortices (formerly paper P2.15)

We extend the theory of vortex Rossby (VR) waves undergoing inertia-bouyancy (IB) wave emission to geophysical cyclones with baroclinic vertical structures. We consider both monotonic cyclones, where the potential vorticity (PV) decays monotonically with distance from the vortex center, and “single-peak” cyclones, where the PV reaches a single maximum away from the vortex center. We focus on large Rossby number vortices that are three-dimensional, with wind fields modeled after tropical cyclones, and satisfy hydrostatic and gradient wind balance; the ambient fluid in the far field has constant Brunt-Väisällä frequency.

The anelastic equations in cylindrical coordinates are solved as an eigenvalue problem. For the monotonic cyclone, the dependence of the growth rate of Rossby-inertia-bouyancy (RIB) waves on the radial and vertical PV gradient is studied. Consistent with barotropic theories, the growth rate increases with increasing PV gradient. RIB modes are robust as long as the minimum in the radial PV gradient is sufficiently far from the vortex center to support a VR wave. The radial and vertical structure of the RIB modes differs from those in barotropic vortices. These differences are discussed through a WKB analysis of VR and IB waves. The “single-peak” cyclone is dominated by classical barotropic instabilities if the peak is 1) sufficiently strong and 2) far enough away from the vortex center to allow a VR wave to ride the “inner” PV gradient. If these two conditions are not met and/or the “outer” PV gradient is sufficiently strong, the dominant instability is a RIB mode.

The nonlinear saturation of the RIB modes and the end state reached by the vortex is examined using a fully nonlinear model (WRF).