The evolution and arrest of a turbulent stratified oceanic bottom boundary layer over a slope: Upslope regime and PV dynamics

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  • 1 Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts
  • 2 Environmental Science and Engineering, California Institute of Technology, Pasadena, California
  • 3 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK
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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.

Corresponding author address: Xiaozhou Ruan, Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139. E-mail: xruan@mit.edu

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.

Corresponding author address: Xiaozhou Ruan, Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139. E-mail: xruan@mit.edu
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