Modeling Baroclinic Instability on Curving Continental Slopes

Oceanic boundary currents often become unstable and shed eddies as they traverse bends in the continental slope, for example as observed in the Deep Western Boundary Current around the Grand Banks [Bower et al., 2009]. This goal of this study is to determine whether the potential vorticity gradient associated with curving continental slopes makes such flows intrinsically more susceptible to baroclinic/barotropic instabilities. We employ a two-layer quasi-geostrophic model in an annular channel with a sloping bottom boundary, which facilitates comparison with classical results of baroclinic instability in a straight channel [Pedlosky, 1964]. We derive necessary conditions for instability, phase speed bounds, and a semi-circle theorem, and solve the discrete eigenvalue problem for a basic state with constant azimuthal velocity and constant bottom slope. This basic state is shown to be analogous to the classic case of uniform two-layer mean flow in a straight channel [Mechoso, 1980], but the wavenumber dependence of the growth rate differs in the annular channel in that it depends on the absolute mean velocities through metric terms associated with the curvature of the slope. This leads to some qualitative changes in the stability of the flow, introducing additional unstable modes. We discuss the extension of this work to realistic currents and topographies, and its implications for the stability of ocean boundary currents in various regions.