Diffusive draining and growth of eddies

Abstract

The diffusive effect on barotropic models of mesoscale eddies is addressed, using the Melnikov method from dynamical systems. Simple geometric criteria are obtained, which identify whether a given eddy grows or drains out, under a diffusive (and forcing) perturbation on a potential vorticity conserving flow. Qualitatively, the following are shown to be features conducive to eddy growth (and, thereby, stability in a specific sense): (i) large radius of curvature of the eddy boundary, (ii) potential vorticity contours more tightly packed within the eddy than outside, (iii) acute eddy pinch-angle, (iv) small potential vorticity gradient across the eddy boundary, and (v) meridional wind forcing, which increases in the northward direction. The Melnikov approach also suggests how tendrils (filaments) could be formed through the breaking of the eddy boundary, as a diffusion-driven advective process.