Suppression of mesoscale eddy mixing by topographic PV gradients

Oceanic mesoscale eddy mixing plays a crucial role in the Earth’s climate system by redistributing heat, salt and carbon. For many ocean and climate models, mesoscale eddies still need to be parameterized. This is often done via an eddy diffusivity, Κ, which sets the strength of turbulent downgradient tracer fluxes. A well known effect is the modulation of Κ in the presence of background potential vorticity (PV) gradients, which suppresses cross-PV gradient mixing. Topographic slopes can induce such suppression through topographic PV gradients. However, this effect has received little attention, and topographic effects are often not included in parameterizations for Κ. In this study, we show that it is possible to describe the effect of topography on Κ analytically in a barotropic framework, using a simple stochastic representation of eddy-eddy interactions. We obtain an analytical expression for the depth-averaged Κ as a function of the bottom slope, which we validate against diagnosed eddy diffusivities from a numerical model. The obtained analytical expression can be generalized to any constant barotropic PV gradient. Moreover, the expression is consistent with empirical parameterizations for eddy diffusivity over topography from previous studies and provides a physical rationalization for these parameterizations. The new expression helps to understand how eddy diffusivities vary across the ocean, and thus how mesoscale eddies impact ocean mixing processes.