Vertical Structure of Baroclinic Instability in a Three-Layer Quasigeostrophic Model over a Sloping Bottom

Abstract We use a three-layer quasigeostrophic 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 quasigeostrophic 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. Significance Statement Mesoscale eddies dominate ocean transient kinetic energy at time scales longer than a few days, playing a critical role in ocean dynamics, ocean biogeochemistry, and the climate system. Ocean eddies not captured by a model’s resolution are represented through parameterizations. The changing strength of an eddy with depth, an important aspect of realistic parameterizations, has been attributed to the baroclinic instability that generates the eddy. We use a three-layer model to demonstrate and explain the essential mechanics of the vertical structure of baroclinic instability and clarify the relative roles of upper-ocean mean flow, upper-ocean stratification, and sloping bottom topography. We exhibit the importance of interior ocean dynamics when studying topographic effects on vertical structure, a feature precluded by two-layer models.