Nonlinear motion of a shallow water barotropic vortex

Abstract

Nonlinear motions of a shallow water barotropic vortex on a β plane differ substantially from the analogous linear motions. The nonlinear model described here, in which wavenumber 1-3 asymmetries interact with each other and the mean vortex, predicts that an initially completely cyclonic vortex will accelerate toward the NNW reaching a speed of 2.5 m s-1 at 48 h. During the test of the 240-h calculation, the speed varies by <0.5 m s-1 as the direction turns from NNW to NW. The vortex accelerations are in phase with temporal changes of vortex-relative angular momentum (LR). The turning of the track coincides with a transition of the wavenumber 1 asymmetry from a single dipole to a double dipole. The latter structure appears to be another orthogonal solution of the second-order radial structure equation for a neutral linear normal mode. -from Author