Drift of individual β-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 β-plane, any non-zonal displacement of a singular vortex results in the development of a regular flow. An individual singular β-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 β-gyres is examined. Whereas the barotropic and baroclinic modes of the singular vortex are comparable in magnitudes, the baroclinic β-gyres attenuate with time, making the trajectory of the vortex close to that of a barotropic monopole on a β-plane.
Forced two layer beta-plane quasigeostrophic flow. Part I: Long-time existence and uniqueness of weak solutions
