Abstract
We use a three-layer quasi-geostrophic model to study the effects of sloping bottom topography on baroclinic instability in an ocean-like setting. Three layers allow for an interior potential vorticity gradient, a feature that is precluded by the use of a two-layer model. Material conservation of quasi-geostrophic potential vorticity (QG PV) is expressed in terms of sloping background density interfaces, perturbations to the sloping interfaces, and the bottom slope. Linear stability analysis and numerical simulations of initial linear growth are used to demonstrate the dependence of topographic modifications to baroclinically unstable modes on background shear and stratification. Instabilities are classified according to their vertical structure, and the nature of topographic modification to baroclinically unstable modes is shown to correspond to instability type. Surface-intensified vertical shear of the background flow supports surface-intensified baroclinic instability that is less sensitive to bottom topography, compared to uniformly sheared background flow. When background shear is constant or close-to-constant, topography has a leading order effect on the vertical structure of the most baroclinically unstable mode. Upper-ocean stratification changes the lateral and vertical scales of the most unstable mode, with weaker upper-ocean stratification supporting high-wavenumber surface-intensified baroclinically unstable modes that are less sensitive to topography. We also present and assess a novel criterion that predicts the degree of surface-intensification of the fastest-growing baroclinically unstable mode using only prescribed background properties, highlighting the role of interior potential vorticity in setting the most unstable mode’s vertical structure.
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