Numerical Simulations of Buoyant Ekman Layers. Part II: Rectification in Zero-Mean, Time-Dependent Forcing, and Feedback on the Interior Flow

Abstract

The response of the turbulent buoyant bottom Ekman layer near a temperature front over uniform topography is studied here. The background stratification is variable across the slope; the upper slope is either neutrally or stably stratified at one-half of the gradient of the lower slope region. In case 1, a time-dependent, spatially uniform, along-isobath interior current with zero mean causes residual circulation across the boundary layer and net detachment of the fluid from the boundary layer. For forcing with time scales longer than the shutdown time scale [τ0 = f/(Nα)2; e.g., as defined by McCready and Rhines, where f is the Coriolis parameter, N is the Brunt? Väisälä frequency in the lower slope region, and α is the bottom slope], it is shown that the front represents an area of strong mean flow convergence and subsequent net detrainment of boundary layer fluid into the interior and is also a region of significant relative vorticity generation by the mean field. The residual circulation occurs in the stratified region. However, its direction and magnitude are subject to the order at which the downwelling and the upwelling phases occur because the lower and upper parts of the boundary layer respond differently to the two phases. The results are sensitive to the choice of background diffusivity. Tidal forcing produces significant differentiation in the results only when superimposed to the low-frequency current. The mean circulation then has much weaker downslope and along-slope components to the right of the front (i.e., seaward of the front). The strength of the detrainment at the front is found to be the same as in the low-frequency forcing case. In case 2, constant southward current causes convergence in the boundary layer, upwelling into the interior, vertical displacement of the isopycnals, and, through the thermal wind balance, a southward jet in the interior. This jet, which is the result of boundary layer dynamics and the presence of a front, could relate and explain the shelfbreak jet. As is shown here, a possible mechanism for the formation of an along-isobath jet (not just a shelfbreak jet) is the convergence in the bottom boundary layer, which, according to buoyant Ekman layer theory, may occur in the presence of one at least of the following: a front that intersects the bottom of constant inclination or constant stratification and a shelfbreak.