Quasi-geostrophic monopoles in a sheared zonal flow: Influence of the beta-effect and variable shear

Abstract

This work builds on and continues a suite of earlier studies of the interaction between a monopole and a sheared zonal flow in the framework of a 1.5-layer quasi-geostrophic model. In Reznik and Kravtsov [Phys. Fluids 33, 116606 (2021); hereafter RK21], this problem was considered under an f-plane approximation for the case in which the dependence of the zonal velocity U¯(y) on latitude y was linear. Here, the conclusions stemming from that work are generalized for the case of a beta-plane and a variable shear of the background flow. Namely, numerical experiments with singular vortices using the algorithm of Kravtsov and Reznik [“Numerical solutions of the singular vortex problem,” Phys. Fluids 31, 066602 (2019); hereafter KR19] confirm the existence of the trapping latitude ytr, which attracts (repels) prograde (retrograde) vortices and clarifies the underlying mechanisms. Unlike in the case of a linear shear on an f-plane, the latitude ytr here does not necessarily coincide with the latitude at which the effective beta-parameter β¯=β−∂yyU¯+Rd−2U¯ vanishes (here, β denotes the derivative of the Coriolis parameter with respect to latitude and Rd is the Rossby radius of deformation). Another important difference is that in the presence of nonzero β≠0, a trapped prograde vortex exhibits a near-zonal westward drift with the zonal velocity close to the phase speed of long Rossby waves −βRd2 and the meridional velocity at least two orders of magnitude smaller than that. On the other hand, the meridional velocity of a retrograde vortex appears to be unrestricted; such a vortex can rapidly move in any direction, including the direction across the zonal current.