Vortex Evolution by Straining: Theory and Application to Cyclone/Anticyclone Asymmetry in Interior Flow Regimes

This talk addresses two questions: Why do freely evolving vortices weaken on average, even when the viscosity is very small? And why, away from vertical boundaries and under the influence of Earth's rotation and stable density stratification, do anticyclonic vortices become dominant over cyclonic ones when the Rossby number and deformation radius are finite? The context for answering these questions is the rotating, conservative, shallow-water model with Asymmetric and Gradient-Wind Balance approximations.

The controlling mechanisms are vortex weakening under straining deformation, with a weakening that is substantially greater for strong cyclones than strong anticyclones, followed by a partially, but not fully, compensating vortex strengthening during a relaxation phase dominated by Vortex Rossby Waves (VRWs) and their eddy-mean interaction with the vortex. The outcome is a net strain-induced vortex weakening that is greater for cyclones than anticyclones when the deformation radius is not large compared to the vortex radius and the Rossby number is not small. Furthermore, when the exterior strain field is sustained, the vortex has sustained changes when the deformation radius is comparable to the radius: for small Rossby number (ie the quasigeostrophic limit), vortices weaken at a relatively modest rate, but for larger Rossby number, cyclones weaken strongly and anticyclones actually strengthen strongly. The strong sustained changes at finite Rossby number and deformation radius are associated with strain-induced VRWs on the periphery of the mean vortex.

Therefore, in a complex flow, anticyclonic dominance develops over a sequence of transient mutual staining events due to the greater robustness of anticyclones and possibly to their sustained growth.