Numerical models demonstrate that a broad class of geophysical vortices freely evolve toward vertically aligned, horizontally axisymmetric states. In principle, this intrinsic drive toward symmetry can intensify the vortex core, and oppose destructive shearing by the environmental flow.

We examine the case in which a discrete vortex-Rossby-wave dominates the perturbation from symmetry, and symmetrization occurs by decay of the wave. The wave is damped by a resonance with the fluid rotation frequency at a critical radius, r_*. The damping rate is proportional to the radial derivative of potential vorticity at r_*. The theory of resonantly damped vortex-Rossby-waves (technically quasi-modes) was previously carried out for slowly rotating vortices, which obey quasi-geostrophic (QG) dynamics. Here, we extend the theory to rapidly rotating vortices, i.e., vortices with Rossby numbers greater than one.

Our first analysis makes use of the asymmetric balance (AB) approximation. Even at a modest Rossby number (unity), AB theory can predict damping rates that exceed extrapolated QG results by orders of magnitude. This finding is verified upon comparison of AB theory to numerical experiments, based on the primitive equations. The experiments focus on the decay of low wave-number asymmetries.

A discrete vortex-Rossby-wave can also resonate with an outward propagating inertia-buoyancy wave ("Lighthill" radiation), inducing both to grow. At large Rossby numbers, this growth mechanism can be dynamically relevant. All balance models, including AB theory, neglect inertia-buoyancy waves, and therefore ignore the possibility of a Rossby-inertia-buoyancy (RIB) instability. To accurately account for this instability, we generalize our theory of discrete vortex-Rossby-waves to a primitive equation model. However, we show that a sufficiently large potential vorticity gradient (of the proper sign) at the critical radius r_* can suppress the RIB instability, and thereby justify a balance approximation, even at large Rossby numbers.