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 104 m2s in the relatively flat-bottomed region to 10 m2 s 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. Plain Language Summary Understanding the future climate relies on numerical predictions from climate models. However, these models are limited in accuracy because they cannot resolve all crucial processes in the climate system due to computational resource limitations. One such process is the oceanic "mesoscale" turbulence (swirling ocean flows that are tens to hundreds of kilometers wide) across continental margins. These flows impact coastal circulation and ecosystems by mediating material exchanges between coastal and open-ocean environments. By running computer simulations that can explicitly resolve mesoscale turbulence, we show that heat transport by mesoscale flows becomes less efficient over continental margins than that in the open ocean, due to the presence of the sloping seafloor. After taking this reduced efficiency into account, we are able to predict the heat transport by mesoscale flows across continental margins by adapting established theories for the open-ocean environment. This work provides a basis for improving the performance of climate models, especially near coastal regions.