Bathymetry-aware parameterizations of eddy buoyancy fluxes

Baroclinic eddy restratification strongly influences the ocean's general circulation and tracer budgets, and has been routinely parameterized via the Gent-McWilliams (GM) scheme in coarse-resolution ocean climate models. These parameterizations have been improved by refinements of the GM eddy transfer coefficient using eddy-resolving simulations and theoretical developments. However, previous efforts have focused primarily on the open ocean, and the applicability of existing GM parameterization approaches to continental slopes remains to be addressed. In this study, we use a suite of eddy-resolving, process-oriented simulations to test scaling relationships between eddy mixing rates of buoyancy, mean flow properties, and topographic geometries in simulations of baroclinic turbulence over continental slopes. We focus on the case of retrograde (i.e., opposing the direction of topographic wave propagation) winds, a configuration that arises commonly around the margins of the substropical gyres.

Three types of scalings are examined, namely, the GEOMETRIC framework developed by Marshall et al. (2012), a new ``Cross-Front" (CF) scaling derived via dimensional arguments, and the mixing length theory (MLT) based scalings tested recently by Jansen et al. (2015) over a flat ocean bed. The present study emphasizes the crucial role of the local slope parameter, defined as the ratio between the topographic slope and the depth-averaged isopycnal slope, in controlling the nonlinear eddy buoyancy fluxes. It is shown that both the GEOMETRIC framework and the CF scaling can reproduce the depth-averaged eddy buoyancy transfer across steep slopes, for suitably chosen constant prefactors. To generalize these scalings across both continental slope and open ocean environments requires the introduction of prefactors that depend on the local slope parameter via empirically derived analytical functions. In contrast, the MLT-based scalings fail to quantify the cross-slope eddy buoyancy transfer when constant prefactors are adopted, but can reproduce the cross-slope eddy flux when the prefactors are adapted via empirical functions of the local slope parameter. These findings offer a basis for extending existing approaches to eddy parameterization in coarse-resolution ocean climate models.