Mesoscale eddies (30–100km in scale) dominate the ocean kinetic energy at subinertial frequencies, yet their spatial scales are too fine to be resolved in ocean global models with a horizontal resolution of 1° (~100km). Climate models thus rely on parametrizations for turbulent fluxes, often empirically based.
Due to the Earth’s rapid rotation and the thin-layer geometry of the oceans, oceanic flows are predominantly quasi-horizontal and exhibit characteristics of two-dimensional turbulence, as described by Kraichnan, Leith, and Batchelor: energy is transferred from smaller to larger scales, reinforcing large coherent structures through an inverse cascade process. In a first part, we investigate the effective diffusivity of two-dimensional turbulent flows: how strong is the turbulent transport of a passive tracer that possesses a large-scale inhomogeneous distribution ? A detailed study of the inverse cascade in 2D Navier-Stokes turbulence highlights the significant role of coherent vortices in setting both the effective diffusivity and the large-scale properties of the flow. We introduce a model where these vortices organize into a vortex gas. The model provides scaling laws, validated against direct numerical simulations, that challenge the assumption of scale invariance of the inverse cascade. This approach establishes a direct connection between 2D Navier-Stokes dynamics and the quasi-2D baroclinic instability models that describe mesoscale oceanic turbulence. Indeed, the physical-space description of the inverse cascade allows for a formal mapping between two quasi-geostrophic models of baroclinic instability, leading to a minimal framework capturing the universal features of their turbulent transport.