The Dynamics of Quasigeostrophic Lens-Shaped Vortices

Abstract

AbstractThe stability of lens-shaped vortices is revisited in the context of an idealized quasigeostrophic model. We compute the stability characteristics with higher accuracy and for a wider range of Burger numbers (Bu) than what was previously done. It is found that there are four distinct Bu regions of linear instability. Over the primary region of interest (0.1 < Bu < 10), we confirm that the first and second azimuthal modes are the only linearly unstable modes, and they are associated with vortex tilting and tearing, respectively. Moreover, the most unstable first azimuthal mode is not precisely captured by the linear stability analysis because of the extra condition that is imposed at the vortex center, and accurate calculations of the second azimuthal mode require higher resolution than was previously considered. We also study the nonlinear evolution of lens-shaped vortices in the context of this model and present the following results. First, vortices with a horizontal length scale a little less than the radius of deformation (Bu > 1) are barotropically unstable and develop a wobble, whereas those with a larger horizontal length scale (Bu < 1) are baroclinically unstable and often split. Second, the transfer of energy between different horizontal scales is quantified in two typical cases of barotropic and baroclinic instability. Third, after the instability the effective Bu is closer to unity.