Singular Vortices on a Beta-Plane: A Brief Review and Recent Results

Abstract

Purpose. This paper briefly reviews the theory of singular vortices (SV) on a beta-plane. Methods and Results : The primary focus of the paper is on a long-term evolution of an individual SV: the governing equations and integrals of motion are given, the algorithm of numerical implementation of these equations for investigation of such an evolution is described, and the results of some numerical experiments are presented. It is shown that the vortex evolution consists of two stages. At an initial (quasi-linear) stage, the near-field radiation of Rossby waves by the vortex produces, near the vortex, a non-stationary secondary dipole – the beta-gyres – which forces the vortex to move (a cyclone drifts northwestward, an anticyclone – southwestward). At the next (nonlinear) stage, the far-field radiation of Rossby waves and self-interactions within the regular component of the motion become of importance. A singular cyclone (anticyclone) migrates slowly into the anticyclonic (cyclonic) beta-gyre; the SV and the beta-gyre form a compact vortex pair which continues to move northwestward (southwestward). As this process takes place, the cyclonic (anticyclonic) beta-gyre gradually drifts away from and ceases to affect the SV, while the SV starts to interact with the Rossby waves it radiated previously, which results in oscillations of its translation speed. The duration of the quasi-linear stage rapidly increases with an increasing intensity of the SV; for vortices of small or moderate intensity, this stage ends rapidly and gives way to the nonlinear stage. The first phenomenological description of the nonlinear stage of a singular monopole’s evolution appeared in our recent work on the dynamics of the SV on a beta-plane. Conclusions : The theory of singular vortices on a beta-plane developed here significantly broadens our understanding of the evolution and dynamics of localized geophysical vortices which play an important role in the large-scale circulation of the ocean and atmosphere.