Abstract
Ocean mesoscale eddies strongly affect the strength and variability of large-scale ocean jets such as the Gulf Stream and Kuroshio Extension. Their spatial scales are too small to be fully resolved in many current climate models and hence their effects on the large-scale circulation need to be parametrized. Here we propose a parametrization of mesoscale eddy momentum fluxes based on large-scale flow deformation. The parametrization is argued to be suitable for use in eddy-permitting ocean general circulation models, and is motivated by an analogy between turbulence in Newtonian fluids (such as water) and laminar flow in non-Newtonian fluids. A primitive-equations model in an idealised double-gyre configuration at eddy-resolving horizontal resolution is used to diagnose the relationship between the proposed closure and the eddy fluxes resolved by the model. Favourable correlations suggest the closure could provide an appropriate deterministic parametrization of mesoscale eddies. The relationship between the closure and different representations of the Reynolds stress tensor is also described. The parametrized forcing possesses the key quasi-geostrophic turbulence properties of energy conservation and enstrophy dissipation, and allows for upgradient fluxes leading to the sharpening of vorticity gradients. The implementation of the closure for eddy-permitting ocean models requires only velocity derivatives and a single parameter that scales with model resolution.
Highlights
Ocean mesoscale eddies are found throughout the world ocean, and are observed to be especially vigorous in regions of strong western boundary jets such as the Gulf Stream and Kuroshio Extension, as well as throughout the Antarctic circumpolar current
Since many of the generation of coupled climate models will make use of eddy-permitting ocean general circulation models (GCMs), and eddy-resolving GCMs will remain too computationally expensive to be widely used in the near future, it is important to develop mesoscale eddy parametrizations that are suitable for models with eddy-permitting spatial resolutions
Fluids for which further terms in the series contribute to the stress are termed non-Newtonian, and we assume here as Porta Mana and Zanna (2014) did that retaining these further terms in the series provides a way to model the turbulent stress. This approach to parametrizing turbulence is not new (Rivlin, 1957; Crow, 1968; Lumley, 1970; Meneveau and Katz, 2000); the novelty of our study is in the application of this approach to the quasi-geostrophic turbulence that characterises oceanic mesoscale eddies, the eddy Reynolds stresses due to those eddies
Summary
Ocean mesoscale eddies are found throughout the world ocean, and are observed to be especially vigorous in regions of strong western boundary jets such as the Gulf Stream and Kuroshio Extension, as well as throughout the Antarctic circumpolar current. Porta Mana and Zanna (2014) designed an eddy parametrization by determining a function of the coarse-grained flow in a high-resolution quasi-geostrophic model that correlated well with the eddy forcing to serve as the basis for a stochastic parametrization that depends on the resolved scales Such varied approaches all attempt to represent the rectified effects of upgradient momentum fluxes and energy backscatter (i.e. upscale energy transfer). Fluids for which further terms in the series contribute to the stress are termed non-Newtonian, and we assume here as Porta Mana and Zanna (2014) did that retaining these further terms in the series provides a way to model the turbulent stress This approach to parametrizing turbulence is not new (Rivlin, 1957; Crow, 1968; Lumley, 1970; Meneveau and Katz, 2000); the novelty of our study is in the application of this approach to the quasi-geostrophic turbulence that characterises oceanic mesoscale eddies, the eddy Reynolds stresses due to those eddies.
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