On the symmetrization rate of an intense geophysical vortex

Abstract

Numerical models demonstrate that a broad class of geophysical vortices freely evolve toward vertically aligned, axisymmetric states. In principle, this intrinsic drive toward symmetry opposes destructive shearing by the environmental flow. This article examines the case in which a discrete vortex-Rossby-wave dominates a 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 *. Until now, the theory of resonantly damped vortex-Rossby-waves (technically quasi-modes) was formally restricted to slowly rotating vortices, which obey quasigeostrophic (QG) dynamics. This article extends the theory to rapidly rotating vortices. The 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 azimuthal 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. This article shows that a large potential vorticity gradient (of the proper sign) at the critical radius r * can suppress the RIB instability, and thereby preserve balanced flow, even at large Rossby numbers.