Piecewise Potential Vorticity Inversion and Vortex Interaction

Abstract

Piecewise potential vorticity inversion (PPVI) aims at an interpretation of the interaction of potential vorticity (PV) anomalies q. The total flow domain D is divided into subdomains D1 and D2 with q1 and q2 as PV anomalies. PPVI estimates the height tendency in D that results if q is transported by the winds obtained by an inversion of a PV field with q = q1 in D1 and q = 0 in D2. Tests compare the actual height tendency to that obtained via PPVI. This method is applied to the interaction of vortices in quasigeostrophic shallow water, a problem generally accepted as a paradigm for PPVI. Indeed, results are excellent for vortex pairs. Combinations of more vortices, including vortex clusters akin to Rossby waves, are also exposed to tests. The utility of PPVI tendencies depends strongly on the arrangement of the vortices in that case. Very good agreement is found as well as cases with quite low skill. The reasons for this scatter are discussed and a dynamic interpretation of PPVI is proposed.