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.

Slippery Bottom Boundary Layers: The Loss of Energy From the General Circulation by Bottom Drag

“…Application of this approach requires knowledge of the functional form of E  , and the proper time scale for averaging, however it does offer hope for simple corrections to the average bottom drag dissipation calculated using interior velocities. Idealized modeling by Ruan et al (2019Ruan et al ( , 2021) also suggests the possibility that the true instantaneous bottom stress could be related to modeled or observed interior quantities (such as interior stratification and velocity) through the ratio of the BBL thickness to the theoretical full Ekman arrest thickness. This would allow bottom drag estimates to be corrected for the unresolved effects of partial Ekman arrest in the BBL.…”

“…Idealized modeling by Ruan et al. (2019, 2021) also suggests the possibility that the true instantaneous bottom stress could be related to modeled or observed interior quantities (such as interior stratification and velocity) through the ratio of the BBL thickness to the theoretical full Ekman arrest thickness. This would allow bottom drag estimates to be corrected for the unresolved effects of partial Ekman arrest in the BBL.…”

Note on the Bulk Estimate of the Energy Dissipation Rate in the Oceanic Bottom Boundary Layer

“…Thus, we expect the influence of stratification on the integrated dissipation rate to be small. In real ocean applications, however, stratification may pose problems in identifying the far-field flow U, especially when over a sloping bottom [22][23][24][25].…”

Control of the abyssal ocean overturning circulation by mixing-driven bottom boundary layers

“…To further complicate matters, the linear sloping Ekman layer solutions discussed above are subject to various flow instabilities which substantially modify the canonical solution. The most basic of these processes is gravitational instability, which is especially common in the case of a downwelling-favorable along-slope flow that drives a down-slope transport of buoyant waters, re sulting in convective mixing that progressively thickens the bottom boundary layer (Garrett et al, 1993;Ruan et al, 2019). Whether the linear solution is originally gravitationally stable or only becomes so after a period of convective mixing (Ruan et al, 2019), it may yet exhibit negative Er tel potential vorticity that renders it susceptible to centrifugal, symmetric, and mixed instabilities (Haine and Marshall, 1998;Garabato et al, 2019;Wenegrat et al, 2018;Wenegrat and Thomas, 2020).…”

“…The most basic of these processes is gravitational instability, which is especially common in the case of a downwelling-favorable along-slope flow that drives a down-slope transport of buoyant waters, re sulting in convective mixing that progressively thickens the bottom boundary layer (Garrett et al, 1993;Ruan et al, 2019). Whether the linear solution is originally gravitationally stable or only becomes so after a period of convective mixing (Ruan et al, 2019), it may yet exhibit negative Er tel potential vorticity that renders it susceptible to centrifugal, symmetric, and mixed instabilities (Haine and Marshall, 1998;Garabato et al, 2019;Wenegrat et al, 2018;Wenegrat and Thomas, 2020). The effect of all of these instabilities is to restratify the bottom boundary layer and pro mote exchange with these interior, enhancing watermass transformations in the BBL.…”