ON SYMMETRICAL INSTABILITIES IN OCEANIC BOTTOM BOUNDARY-LAYERS

Model studies of two-dimensional, time-dependent, wind-forced, stratif ied downwelling circulation on the continental shelf have shown that t he near-bottom offshore flow can develop time-and space-dependent fluc tuations involving spatially periodic separation and reattachment of t he bottom boundary layer and accompanying recirculation cells. Based p rimarily on the observation that the potential vorticity Pi, initially less than zero everywhere, is positive in the region of the fluctuati ons, this behavior was identified as finite amplitude slantwise convec tion resulting from a symmetric instability. To further support that i dentification, a direct stability analysis of the forced, time-depende nt, downwelling circulation would be useful, but is difficult because the instabilities develop as an integral part of the evolving flow fie ld. The objectives of the present study are I) to examine the linear s tability of a near-bottom oceanic flow over sloping topography with co nditions dynamically similar to those in the downwelling circulation a nd 2) to establish a link between the instabilities observed in the wi nd-forced downwelling problem and the results of recent theoretical st udies of bottom boundary layer behavior in stratified oceanic flows ov er sloping topography. These objectives are addressed by investigating the two-dimensional linear stability and the nonlinear behavior of th e steady, inviscid, ''arrested Ekman layer'' solution produced by tran sient downwelling in one-dimensional models of stratified how adjustme nt over a sloping bottom. A linear stability analysis shows that this solution is unstable to symmetric instabilities and confirms that a ne cessary condition for instability is Pi > 0 in the bottom layer. Numer ical experiments show that the unstable, time-dependent, nonlinear beh avior in the boundary layer involves the formation of slantwise circul ation cells with characteristics similar to those found in the wind-fo rced downwelling circulation and the development of weak stable strati fiction close to that corresponding to marginally stable conditions wi th Pi = 0.