Distinct Impacts of Topographic Versus Planetary PV Gradients on Baroclinic Turbulence

The impacts of topographic versus planetary potential vorticity (PV) gradients on fully-developed geostrophic turbulence are often treated as dynamically equivalent in theoretical understanding and parameterizations of ocean mesoscale turbulence. Using a suite of homogeneous, two-layer quasi-geostrophic (QG) turbulence simulations, we identify similarities and distinctions of topographic versus planetary PV gradients in modulating turbulent eddy energy and fluxes. We show that, while an elevated background PV gradient can suppress geostrophic turbulence, a positive (negative) bottom slope tilted in the same (opposite) direction to the background isopycnal slope barotropitizes (de-barotropizes) the turbulent energy at large scales, which contrasts with a dynamically inert planetary PV gradient in the mode-wise energy transfer. Then, in the presence of weak bottom drag, a positive slope energizes large-scale along-slope jets and limits small-scales barotropic eddies, both of which yield stronger eddy suppression effects than from a planetary PV gradient; by contrast, a negative slope hinders along-slope jet formation by enhancing the dual energy cascade cycling, which alleviates the topographic suppression on eddies. In the presence of strong bottom drag, a positive slope elevates barotropic eddy energy, which further enhances the eddy-driven fluxes; by contrast, a negative slope confines turbulent energy to the baroclinic mode, which is strongly damped, causing further weakened turbulent energy and eddy fluxes. A flow regime captured by linear QG theories also emerges as the turbulent energy cascade is jointly suppressed by negative slopes and strong bottom drag. This study provides insights into parameterizing mesoscale eddy effects over sloping bathymetry in predictive ocean models.