Two-layer quasi-geostrophic singular vortices embedded in a regular flow. Part 2. Steady and unsteady drift of individual vortices on a beta-plane

摘要

Drift of individual beta-plane vortices confined to one layer of a two-layer fluid under the rigid-lid condition is considered. For this purpose, the theory of two-layer quasi- geostrophic singular vortices is employed. On a beta-plane, any non-zonal displacement of a singular vortex results in the development of a regular flow. An individual singular P-plane vortex cannot be steady on its own: the vortex moves coexisting with a regular flow, be the drift steady or not. In this paper, both kinds of drift of a singular vortex are considered. A new steady exact solution is presented, a hybrid regular-singular modon. This hybrid modon consists of a dipole component and a circularly symmetric rider. The dipole is regular, and the rider is a superposition of the singular vortex and a regular circularly symmetric field. The unsteady drift of a singular vortex residing in one of the layers is considered under the condition that, at the initial instant, the regular field is absent. The development of barotropic and baroclinic regular beta-gyres is examined. Whereas the barotropic and baroclinic modes of the singular vortex are comparable in magnitudes, the baroclinic beta-gyres attenuate with time, making the trajectory of the vortex close to that of a barotropic monopole on a beta-plane.