Ekman destabilization of inertially stable baroclinic abyssal flow on a sloping bottom

Abstract

Baroclinic abyssal currents on a sloping bottom, which are nonlinearly stable in the sense of Liapunov in the absence of dissipation, are shown to be destabilized by the presence of a bottom Ekman boundary layer for any positive value of the Ekman number. When the abyssal flow is baroclinically unstable, the dissipation acts to reduce the inviscid growth rates except near the marginal stability boundary where it acts to increase the inviscid growth rates. It is shown that when the abyssal flow is baroclinically stable, the Ekman destabilization corresponds to the kinematic wave phase velocity lying outside the range of the inertial topographic Rossby phase velocities. The transition mechanism described here might provide a dynamical bridge between the nonrotational roll-wave instability that can occur in supercritical abyssal overflows and frictionally induced destabilization in subinertial geostrophically balanced baroclinic abyssal currents. In addition, the theory presented here suggests a dissipation-induced destabilization mechanism for coastal downwelling fronts whose cross-slope potential vorticity gradient does not satisfy the necessary condition for baroclinic instability.