The Evolution and Arrest of a Turbulent Stratified Oceanic Bottom Boundary Layer over a Slope: Downslope Regime

Abstract

The dynamics of a stratified oceanic bottom boundary layer (BBL) over an insulating, sloping surface depend critically on the intersection of density surfaces with the bottom. For an imposed along-slope flow, the cross-slope Ekman transport advects density surfaces and generates a near-bottom geostrophic thermal wind shear that opposes the background flow. A limiting case occurs when a momentum balance is achieved between the Coriolis force and a restoring buoyancy force in response to the displacement of stratified fluid over the slope: this is known as Ekman arrest. However, the turbulent characteristics that accompany this adjustment have received less attention. We present two estimates to characterize the state of the BBL based on the mixed layer thickness: Ha and HL. The former characterizes the steady Ekman arrested state, and the latter characterizes a relaminarized state. The derivation of HL makes use of a newly defined slope Obukhov length Ls that characterizes the relative importance of shear production and cross-slope buoyancy advection. The value of Ha can be combined with the temporally evolving depth of the mixed layer H to form a nondimensional variable H/Ha that provides a similarity prediction of the BBL evolution across different turbulent regimes. The length scale Ls can also be used to obtain an expression for the wall stress when the BBL relaminarizes. We validate these relationships using output from a suite of three-dimensional large-eddy simulations. We conclude that the BBL reaches the relaminarized state before the steady Ekman arrested state. Calculating H/Ha and H/HL from measurements will provide information on the stage of oceanic BBL development being observed. These diagnostics may also help to improve numerical parameterizations of stratified BBL dynamics over sloping topography.