Scalings for eddy buoyancy transfer across continental slopes under retrograde winds

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 via 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 buoyancy diffusivity, 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 subtropical gyres. Three types of scalings are examined, namely, the GEOMETRIC framework developed by Marshall a al. (2012), a new Cross-Front (CF) scaling derived via dimensional arguments, and the mixing length theory (MLT)-based scalings tested recently by Jansen a 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. Both the GEOMETRIC framework and the CF scaling can reproduce the depth-averaged eddy buoyancy transfer across alongshore-uniform continental slopes, for suitably chosen constant prefactors. Generalization of 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 eddy buoyancy transfer across alongshore-uniform continental slopes 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. Application of these scalings in prognostic ocean simulations also depends on an accurate representation of standing eddies associated with the topographic corrugations of the continental slope. These findings offer a basis for extending existing approaches to parameterizing transient eddies, and call for future efforts to parameterize standing eddies in coarse-resolution ocean climate models.