On Symmetric Instabilities in Oceanic Bottom Boundary Layers

Abstract

Model studies of two-dimensional, time-dependent, wind-forced, stratified downwelling circulation on the continental shelf have shown that the near-bottom offshore flow can develop time- and space-dependent fluctuations involving spatially periodic separation and reattachment of the bottom boundary layer and accompanying recirculation cells. Based primarily on the observation that the potential vorticity ?, initially less than zero everywhere, is positive in the region of the fluctuations, this behavior was identified as finite amplitude slantwise convection resulting from a symmetric instability. To further support that identification, a direct stability analysis of the forced, time-dependent, downwelling circulation would be useful, but is difficult because the instabilities develop as an integral part of the evolving flow field. The objectives of the present study are 1) to examine the linear stability of a near-bottom oceanic flow over sloping topography with conditions dynamically similar to those in the downwelling circulation and 2) to establish a link between the instabilities observed in the wind-forced downwelling problem and the results of recent theoretical studies of bottom boundary layer behavior in stratified oceanic flows over sloping topography. These objectives are addressed by investigating the two-dimensional linear stability and the nonlinear behavior of the steady, inviscid, ?arrested Ekman layer? solution produced by transient downwelling in one-dimensional models of stratified flow adjustment over a sloping bottom. A linear stability analysis shows that this solution is unstable to symmetric instabilities and confirms that a necessary condition for instability is ? > 0 in the bottom layer. Numerical experiments show that the unstable, time-dependent, nonlinear behavior in the boundary layer involves the formation of slantwise circulation cells with characteristics similar to those found in the wind-forced downwelling circulation and the development of weak stable stratifiction close to that corresponding to marginally stable conditions with ? = 0.