A phenomenological treatment of rotating turbulence

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Abstract
In this Brief Communication, we first note the strong similarity between the magnetohydrodynamic (MHD) turbulence and initially isotropic turbulence subject to rotation. We then applied the MHD phenomenologies of Kraichnan [Phys. Fluids 8, 1385 (1965)] and Matthaeus and Zhou [Phys. Fluids B 1, 1929 (1989)] to rotating turbulence. We deduced a ‘‘rule’’ that relates spectral transfer time to the eddy turnover time and the time scale for decay of the triple correlations. Our hypothesis on 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 wave number kΩ=(Ω3/ε)1/2 relative to the wave number k. The eddy viscosity is derived with an explicitly dependence on the rotation rate.