A Geostrophic Vortex over a Slope*

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Abstract
Nonlinear, quasigeostrophic, f-plane vortices in two layers over a topographic slope are considered. Scaling arguments suggest two parameters that dictate the effective strength of the slope: the first indicates the likelihood of dispersion at depth, and the second relates to baroclinic stability. If the deep flow is only weakly dispersive (weak slopes), an initially barotropic vortex can translate barotropically across the isobaths, provided the vortex scale exceeds the deformation scale. Over stronger slopes, the vortex separates into topographic waves and a stationary, surface-trapped vortex. An initially surface-trapped vortex larger than deformation scale becomes unstable over a weak slope, as it does over a flat bottom. However, a strong slope can stabilize the vortex to small perturbations, despite the large vortex scale. The effective slope parameters depend not only on topographic grade, but on vortex strength and size, and on the ambient stratification. Parameters obtained with represen... Abstract Nonlinear, quasigeostrophic, f-plane vortices in two layers over a topographic slope are considered. Scaling arguments suggest two parameters that dictate the effective strength of the slope: the first indicates the likelihood of dispersion at depth, and the second relates to baroclinic stability. If the deep flow is only weakly dispersive (weak slopes), an initially barotropic vortex can translate barotropically across the isobaths, provided the vortex scale exceeds the deformation scale. Over stronger slopes, the vortex separates into topographic waves and a stationary, surface-trapped vortex. An initially surface-trapped vortex larger than deformation scale becomes unstable over a weak slope, as it does over a flat bottom. However, a strong slope can stabilize the vortex to small perturbations, despite the large vortex scale. The effective slope parameters depend not only on topographic grade, but on vortex strength and size, and on the ambient stratification. Parameters obtained with represen...

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