Scalings for Eddy Buoyancy Fluxes Across Prograde Shelf/Slope Fronts

Depth-averaged eddy buoyancy diffusivities across continental shelves and slopes are investigated using a suite of eddy-resolving, process-oriented simulations of prograde frontal currents characterized by isopycnals tilted in the opposite direction to the seafloor, a flow regime commonly found along continental margins under downwelling-favorable winds or occupied by buoyant boundary currents. The diagnosed cross-slope eddy diffusivity varies by up to three orders of magnitude, decaying from (Formula presented.) in the relatively flat-bottomed region to (Formula presented.) over the steep continental slope, consistent with previously reported suppression effects of steep topography on baroclinic eddy fluxes. To theoretically constrain the simulated cross-slope eddy fluxes, we examine extant scalings for eddy buoyancy diffusivities across prograde shelf/slope fronts and in flat-bottomed oceans. Among all tested scalings, the GEOMETRIC framework developed by D. P. Marshall et al. (2012, https://doi.org/10.1175/JPO-D-11-048.1) and a parametrically similar Eady scale-based scaling proposed by Jansen et al. (2015, https://doi.org/10.1016/j.ocemod.2015.05.007) most accurately reproduce the diagnosed eddy diffusivities across the entire shelf-to-open-ocean analysis regions in our simulations. This result relies upon the incorporation of the topographic suppression effects on eddy fluxes, quantified via analytical functions of the slope Burger number, into the scaling prefactor coefficients. The predictive skills of the GEOMETRIC and Eady scale-based scalings are shown to be insensitive to the presence of along-slope topographic corrugations. This work lays a foundation for parameterizing eddy buoyancy fluxes across large-scale prograde shelf/slope fronts in coarse-resolution ocean models.