Centrifugal and Symmetric Instability during Ekman Adjustment of the Bottom Boundary Layer

Jacob O Wenegrat,Leif N Thomas

doi:10.1175/jpo-d-20-0027.1

Abstract

AbstractFlow along isobaths of a sloping lower boundary generates an across-isobath Ekman transport in the bottom boundary layer. When this Ekman transport is down the slope it causes convective mixing—much like a downfront wind in the surface boundary layer—destroying stratification and potential vorticity. In this manuscript we show how this can lead to the development of a forced centrifugal or symmetric instability regime, where the potential vorticity flux generated by friction along the boundary is balanced by submesoscale instabilities that return the boundary layer potential vorticity to zero. This balance provides a strong constraint on the boundary layer evolution, which we use to develop a theory that explains the evolution of the boundary layer thickness, the rate at which the instabilities extract energy from the geostrophic flow field, and the magnitude and vertical structure of the dissipation. Finally, we show using theory and a high-resolution numerical model how the presence of centrifugal or symmetric instabilities alters the time-dependent Ekman adjustment of the boundary layer, delaying Ekman buoyancy arrest and enhancing the total energy removed from the balanced flow field. Submesoscale instabilities of the bottom boundary layer may therefore play an important, largely overlooked, role in the energetics of flow over topography in the ocean.

Highlights

The ocean bottom boundary layer (BBL) over sloping topography often has a structure reminiscent of a surface mixed layer front, with isopycnals that slope downward from the interior toward the topography (Fig. 1)
This Ekman buoyancy flux has been shown to modify the surface boundary layer in a wide variety of ways, one of the most consequential of which is through the generation of symmetric instability (SI), a fast-growing submesoscale instability associated with 2D overturning circulations in the cross-front plane (Stone 1966; Haine and Marshall 1998)
In the surface boundary layer the convective layer depth is generally defined as the location where the total vertical buoyancy flux is zero (TF10), in our simulations we find that this definition does not usefully partition the boundary layer into regions with distinct dynamics

Summary

Introduction

The ocean bottom boundary layer (BBL) over sloping topography often has a structure reminiscent of a surface mixed layer front, with isopycnals that slope downward from the interior toward the topography (Fig. 1). Following the same basic evolution, a downslope Ekman flow develops rapidly at the beginning of the simulation, generating a growing BBL that is associated with reduced stratification and low PV (Fig. 5) In this run f (f 1 ›y/›x^) , 0, indicative of centrifugal instability (Haine and Marshall 1998). In the surface boundary layer the convective layer depth is generally defined as the location where the total vertical buoyancy flux is zero (TF10), in our simulations we find that this definition does not usefully partition the boundary layer into regions with distinct dynamics The reason for this can be seen clearly by decomposing the slope-normal buoyancy flux by acrossslope wavenumber (Fig. 9b).

EBFs hw0b0

Energetics

Summary and discussion