Diagnosing Subgrid Mesoscale Eddy Fluxes With and Without Topography

Abstract

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. In this work, 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 0. 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.