Multi-scale theory of rotating turbulence

Abstract

We consider turbulence induced by an arbitrary forcing and derive turbulence amplitude and turbulent transport coefficients, first by using a quasi-linear theory and then by using a multi-scale renormalisation analysis. With an isotropic forcing, the quasi-linear theory gives that the turbulent transport coefficients, both parallel and perpendicular to the rotation vector, have the asymptotic scaling $Ω^{-1}$ for rapid rotation (i.e. when the rotation rate $Ω$ is larger than the inverse of the correlation time of the forcing and the diffusion time), while the renormalisation analysis suggests a weaker dependence on $Ω$, with $Ω^{-1/2}$ scaling. The turbulence amplitude is found to scale as $Ω^0 - Ω^{-1}$ in the rapid rotation limit depending on the property of the forcing. In the case of an anisotropic forcing, we find that non-diffusive fluxes of angular momentum scale as $Ω^{-2} - Ω^{-1}$ for rapid rotation, depending on the temporal correlation of the forcing.