Suppression of Mesoscale Eddy Mixing by Topographic PV Gradients.

Oceanic mesoscale eddy mixing plays a crucial role in 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 K , which sets the strength of turbulent downgradient tracer fluxes. A well-known effect is the modulation of K 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 K. In this study, we show that it is possible to describe the effect of topography on K analytically in a barotropic framework, using a simple stochastic representation of eddy–eddy interactions. We obtain an analytical expression for the depth-averaged K 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. Significance Statement: Large oceanic "whirls," called eddies, can mix and transport ocean properties such as heat, salt, carbon, and nutrients. Mixing plays an important role for oceanic ecosystems and the climate system. In numerical simulations of Earth's climate, eddy mixing is typically represented using a simplified expression. However, an effect that is often not included is that eddy mixing is weaker over a sloping seafloor. In most areas of the ocean the bottom slope is steep enough for this effect to be significant. In this study we derive an expression for eddy mixing that accounts for oceanic bottom slopes. The present effort provides a physical basis for eddy mixing over oceanic bottom slopes, justifying their use in climate models. [ABSTRACT FROM AUTHOR]