AbstractThe stability of lens-shaped vortices is revisited in the context of an idealized Quasi-Geostrophic 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 requires higher resolution than was previously considered.We also study the non-linear evolution of lens-shaped vortices in the context of this model and present the following results. First, that 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 baroclinicly 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.
Journal of Physical Oceanography – American Meteorological Society
Published: Dec 26, 2017
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