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 ${\Omega }^{-1}$ for rapid rotation (i.e. when the rotation rate $\Omega$ 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 $\Omega$, with ${\Omega }^{-1/2}$ scaling. The turbulence amplitude is found to scale as ${\Omega }^0-{\Omega }^{-1}$ 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 ${\Omega }^{-2}-{\Omega }^{-1}$ for rapid rotation, depending on the temporal correlation of the forcing.

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Cited by in corpus (1)

• Dynamo quenching due to shear flow