Eddy kinetic energy transport in barotropic turbulence

Eddy energy transport in rotating, barotropic turbulence is investigated using numerical simulation. Stochastic forcing is used to generate an inhomogeneous field of turbulence, and the time-mean energy profile is diagnosed. An advective-diffusive model for the transport is fit to the simulation data by requiring the model to accurately predict the observed time-mean energy distribution. Isotropic harmonic diffusion of energy is found to be an accurate model in the case of uniform, solid-body background rotation (the $f$-plane), with a diffusivity that scales reasonably well with a mixing-length law $\kappa\propto V\ell$ where $V$ and $\ell$ are `characteristic' eddy velocity and length scales. Passive tracer dynamics are added, and it is found that the energy diffusivity is $75\%$ of the tracer diffusivity. The addition of a differential background rotation with constant vorticity gradient $\beta$ leads to significant changes to the energy transport. The eddies generate and interact with a mean flow. Mean advection plus anisotropic diffusion is moderately accurate only for flows with scale separation between mean and eddies.