Singular vortices in regular flows

A review of the theory of quasigeostrophic singular vortices embedded in regular flows is presented with emphasis on recent results. The equations governing the joint evolution of singular vortices and regular flow, and the conservation laws (integrals) yielded by these equations are presented. Using these integrals, we prove the nonlinear stability of a vortex pair on the f-plane with respect to any small regular perturbation with finite energy and enstrophy. On the β-plane, a new exact steady-state solution is presented, a hybrid regular-singular modon comprised of a singular vortex and a localized regular component. The unsteady drift of an individual singular β-plane vortex confined to one layer of a two-layer fluid is considered. Analysis of the β-gyres shows that the vortex trajectory is similar to that of a barotropic monopole on the β-plane. Non-stationary behavior of a dipole interacting with a radial flow produced by a point source in a 2D fluid is examined. The dipole always survives after collision with the source and accelerates (decelerates) in a convergent (divergent) radial flow.