A phenomenological treatment of rotating turbulence

The strong similarity between the magnetohydrodynamic (MHD) turbulence and initially isotropic turbulence subject to rotation is noted. We then apply the MHD phenomenologies of Kraichnan and Matthaeus and Zhou to rotating turbulence. When the turbulence is subject to a strong rotation, the energy spectrum is found to scale as E(k) = C_Omega (Omega epsilon)^1/2 k^-2, where Omega is the rotation rate, k is the wavenumber, and epsilon is the dissipation rate. This spectral form is consistent with a recent letter by Zeman. However, here the constant C_Omega is found to be related to the Kolmogorov constant and is estimated in the range 1.22-1.8 for the typical values of the latter constant. A `rule'' that relates spectral transfer times to the eddy turnover time and the time scale for decay of the triple correlations is deduced. A hypothesis for the triple correlation decay rate leads to the spectral law which varies between the `-5/3'' (without rotation) and `-2'' laws (with strong rotation). For intermediate rotation rates, the spectrum varies according to the value of a dimensionless parameter that measures the strength of the rotation wavenumber k_Omega =(Omega^3/epsilon)^1/2 relative to the wavenumber k. An eddy viscosity is derived with an explicit dependence on the rotation rate.