A Parameterization of Shear-Driven Turbulence for Ocean Climate Models

L. Jackson Atmospheric and Oceanic Sciences, Princeton University, Princeton, New Jersey

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R. Hallberg Geophysical Fluid Dynamics Laboratory, Princeton, New Jersey

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S. Legg Atmospheric and Oceanic Sciences, Princeton University, Princeton, New Jersey

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Abstract

This paper presents a new parameterization for shear-driven, stratified, turbulent mixing that is pertinent to climate models, in particular the shear-driven mixing in overflows and the Equatorial Undercurrent. This parameterization satisfies a critical requirement for climate applications by being simple enough to be implemented implicitly and thereby allowing the parameterization to be used with time steps that are long compared to both the time scale on which the turbulence evolves and the time scale with which it alters the large-scale ocean state.

The mixing is expressed in terms of a turbulent diffusivity that is dependent on the shear forcing and a length scale that is the minimum of the width of the low Richardson number region (Ri = N2/|uz|2, where N is the buoyancy frequency and |uz| is the vertical shear) and the buoyancy length scale over which the turbulence decays [Lb = Q1/2/N, where Q is the turbulent kinetic energy (TKE)]. This also allows a decay of turbulence vertically away from the low Richardson number region over the buoyancy scale, a process that the results show is important for mixing across a jet. The diffusivity is determined by solving a vertically nonlocal steady-state TKE equation and a vertically elliptic equilibrium equation for the diffusivity itself.

High-resolution nonhydrostatic simulations of shear-driven stratified mixing are conducted in both a shear layer and a jet. The results of these simulations support the theory presented and are used, together with discussions of various limits and reviews of previous work, to constrain parameters.

Corresponding author address: Dr. L. Jackson, GFDL, Forrestal Campus, Route 1, Princeton, NJ 08542. Email: laura.jackson@noaa.gov

Abstract

This paper presents a new parameterization for shear-driven, stratified, turbulent mixing that is pertinent to climate models, in particular the shear-driven mixing in overflows and the Equatorial Undercurrent. This parameterization satisfies a critical requirement for climate applications by being simple enough to be implemented implicitly and thereby allowing the parameterization to be used with time steps that are long compared to both the time scale on which the turbulence evolves and the time scale with which it alters the large-scale ocean state.

The mixing is expressed in terms of a turbulent diffusivity that is dependent on the shear forcing and a length scale that is the minimum of the width of the low Richardson number region (Ri = N2/|uz|2, where N is the buoyancy frequency and |uz| is the vertical shear) and the buoyancy length scale over which the turbulence decays [Lb = Q1/2/N, where Q is the turbulent kinetic energy (TKE)]. This also allows a decay of turbulence vertically away from the low Richardson number region over the buoyancy scale, a process that the results show is important for mixing across a jet. The diffusivity is determined by solving a vertically nonlocal steady-state TKE equation and a vertically elliptic equilibrium equation for the diffusivity itself.

High-resolution nonhydrostatic simulations of shear-driven stratified mixing are conducted in both a shear layer and a jet. The results of these simulations support the theory presented and are used, together with discussions of various limits and reviews of previous work, to constrain parameters.

Corresponding author address: Dr. L. Jackson, GFDL, Forrestal Campus, Route 1, Princeton, NJ 08542. Email: laura.jackson@noaa.gov

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