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Xiaozhou Ruan and Raffaele Ferrari

Abstract

Turbulent mixing across density surfaces transforms abyssal ocean waters into lighter waters and is vital to close the deepest branches of the global overturning circulation. Over the last 20 years, mixing rates inferred from in situ microstructure profilers and tracer release experiments (TREs) have provided valuable insights in the connection between small-scale mixing and large-scale ocean circulation. Problematically, estimates based on TREs consistently exceed those from collocated in situ microstructure measurements. These differences have been attributed to a low bias in the microstructure estimates that can miss strong, but rare, mixing events. Here we demonstrate that TRE estimates can suffer from a high bias, because of the approximations generally made to interpret the data. We first derive formulas to estimate mixing from the temporal growth of the second moment of a tracer patch by extending Taylor’s celebrated formula to account for both density stratification and variations in mixing rates. The formulas are validated with tracers released in numerical simulations of turbulent flows and then used to discuss biases in the interpretation of TREs based estimates and how to possibly overcome them.

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Xiaozhou Ruan and Andrew F. Thompson

Abstract

Oceanic boundary currents over the continental slope exhibit variability with a range of time scales. Numerical studies of steady, along-slope currents over a sloping bathymetry have shown that cross-slope Ekman transport can advect buoyancy surfaces in a bottom boundary layer (BBL) so as to produce vertically sheared geostrophic flows that bring the total flow to rest: a process known as buoyancy shutdown of Ekman transport or Ekman arrest. This study considers the generation and evolution of near-bottom flows due to a barotropic, oscillating, and laterally sheared flow over a slope. The sensitivity of the boundary circulation to changes in oscillation frequency ω, background flow amplitude, bottom slope, and background stratification is explored. When ω/f ≪ 1, where f is the Coriolis frequency, oscillations allow the system to escape from the steady buoyancy shutdown scenario. The BBL is responsible for generating a secondary overturning circulation that produces vertical velocities that, combined with the potential vorticity (PV) anomalies of the imposed barotropic flow, give rise to a time-mean, rectified, vertical eddy PV flux into the ocean interior: a “PV pump.” In these idealized simulations, the PV anomalies in the BBL make a secondary contribution to the time-averaged PV flux. Numerical results show the domain-averaged eddy PV flux increases nonlinearly with ω with a peak near the inertial frequency, followed by a sharp decay for ω/f > 1. Different physical mechanisms are discussed that could give rise to the temporal variability of boundary currents.

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Xiaozhou Ruan and Jörn Callies

Abstract

To close the abyssal overturning circulation, dense bottom water has to become lighter by mixing with lighter water above. This diapycnal mixing is strongly enhanced over rough topography in abyssal mixing layers, which span the bottom few hundred meters of the water column. In particular, mixing rates are enhanced over mid-ocean ridge systems, which extend for thousands of kilometers in the global ocean and are thought to be key contributors to the required abyssal water mass transformation. To examine how stratification and thus diabatic transformation is maintained in such abyssal mixing layers, this study explores the circulation driven by bottom-intensified mixing over mid-ocean ridge flanks and within ridge-flank canyons. Idealized numerical experiments show that stratification over the ridge flanks is maintained by submesoscale baroclinic eddies and that stratification within ridge-flank canyons is maintained by mixing-driven mean flows. These restratification processes affect how strong a diabatic buoyancy flux into the abyss can be maintained, and they are essential for maintaining the dipole in water mass transformation that has emerged as the hallmark of a diabatic circulation driven by bottom-intensified mixing.

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Xiaozhou Ruan, Andrew F. Thompson, and John R. Taylor

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: H a and H L. The former characterizes the steady Ekman arrested state, and the latter characterizes a relaminarized state. The derivation of H L makes use of a newly defined slope Obukhov length L s that characterizes the relative importance of shear production and cross-slope buoyancy advection. The value of H a can be combined with the temporally evolving depth of the mixed layer H to form a nondimensional variable H/H a that provides a similarity prediction of the BBL evolution across different turbulent regimes. The length scale L s 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/H a and H/H L 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.

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XIAOZHOU RUAN, ANDREW F. THOMPSON, and JOHN R. TAYLOR

Abstract

The influence of a sloping bottom and stratification on the evolution of an oceanic bottom boundary layer (BBL) in the presence of a mean flow is explored. As a complement to an earlier study (Ruan et al. 2019) examining Ekman arrest in a downslope regime, this paper describes turbulence and BBL dynamics during Ekman arrest in the upslope regime. In the upslope regime, an enhanced stratification develops in response to the upslope Ekman transport and suppresses turbulence. Using a suite of large-eddy simulations, we show that the BBL evolution can be described in a self-similar framework based on a non-dimensional number X/Xa. This non-dimensional number is defined as the ratio between the lateral displacement of density surfaces across the slope X and a displacement Xa required for Ekman arrest; the latter can be predicted from external parameters. Additionally, the evolution of the depth-integrated potential vorticity is considered in both upslope and downslope regimes. The PV destruction rate in the downslope regime is found to be twice the production rate in the upslope regime, using the same definition for the bottom mixed layer thickness. It is shown that this asymmetry is associated with the depth scale over which turbulent stresses are active. These results are a step towards improving parameterizations of BBL properties and evolution over sloping topography in coarse-resolution ocean models.

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