On the beta-drift of an initially circular vortex patch

Abstract

The nonlinear inviscid evolution of a vortex patch in a single-layer quasi-geostrophic fluid and within a background planetary vorticity gradient is examined numerically at unprecedented spatial resolution. The evolution is governed by two dimensionless parameters: the initial size (radius) of the vortex compared to the Rossby deformation radius, and the initial strength of the vortex compared to the variation of the planetary vorticity across the vortex. It is found that the zonal speed of a vortex increases with its strength. However, the meridional speed reaches a maximum at intermediate vortex strengths. Both large and weak vortices are readily deformed, often into elliptical and tripolar shapes. This deformation is shown to be related to an instability of the instantaneous vorticity distribution in the absence of the planetary vorticity gradient β.

The extremely high numerical resolution employed reveals a striking feature of the flow evolution, namely the generation of very sharp vorticity gradients surrounding the vortex and extending downstream of it in time. These gradients form as the vortex forces background planetary vorticity contours out of its way as it propagates. The contours close to the vortex swirl rapidly around the vortex and homogenize, but at some critical distance the swirl is not strong enough and, instead, a sharp vorticity gradient forms. The region inside this sharp gradient is called the ‘trapped zone’, though it shrinks slowly in time and leaks. This leaking occurs in a narrow wake called the ‘trailing front’, another zone of sharp vorticity gradients, extending behind the vortex.