Jansen, Malte, Alistair Adcroft, and Sina Khani, et al., August 2019: Towards an energetically consistent, resolution aware parameterization of ocean mesoscale eddies. Journal of Advances in Modeling Earth Systems, 11(8), DOI:10.1029/2019MS001750. Abstract
A subgrid‐scale eddy parameterization is developed which makes use of an explicit eddy kinetic energy (EKE) budget and can be applied at both “non‐eddying” and “eddy permitting” resolutions. The subgrid‐scale eddies exchange energy with the resolved flow in both directions via a parameterization of baroclinic instability (based on the established formulation of Gent and McWilliams) and bi‐harmonic and negative Laplacian viscosity terms. This formulation represents the turbulent cascades of energy and enstrophy consistent with our current understanding of the turbulent eddy energy cycle. At the same time, the approach is simple and general enough to be readily implemented in ocean climate models, without adding significant computational cost.
The closure has been implemented in the Modular Ocean Model (MOM6) and tested in the “Neverworld” configuration, which employs an idealized analytically defined topography designed as a testbed for mesoscale eddy parameterizations. The parameterization performs well over a range of resolutions, seamlessly connecting non‐eddying and eddy resolving regimes.
General circulation models use subgrid‐scale (SGS) parameterizations to represent the effects of unresolved mesoscale eddies on large‐scale motions. Most of the current SGS parameterizations are based on a theoretical understanding of transient eddies, where the mean flow is a temporal average. Here, we use a spatial filtering analysis to better understand the scale‐dependent characteristics of the SGS fluxes. Specifically, we apply the filtering approach to diagnose SGS eddy volume fluxes and eddy velocity scales in a hierarchy of model configurations from a flat‐bottom channel to an idealized Southern Hemisphere. Importantly, SGS volume fluxes include significant contributions from standing meanders; unlike for transient eddies, the vertically integrated SGS volume flux does not necessarily integrate to zero. To accommodate net vertically integrated eddy fluxes, we define a SGS eddy diffusivity based on planetary potential vorticity (PV) diffusion. We diagnose the transient and standing contributions to SGS fluxes and associated effective diffusivities. In the presence of bottom topography or continental barriers the standing component of the PV diffusivity becomes dominant at large filter scales in the westerly wind region, while the transient component remains dominant in the easterly wind region. Our results suggest that the diagnosed PV diffusivity can be parameterized using mixing length theory based on a priori estimates of SGS velocity and length scales.
