ENERGY-TRANSFER IN ROTATING TURBULENCE

The influence of rotation on the spectral energy transfer of homogeneo us turbulence is investigated in this paper. Given the fact that linea r dynamics, e.g, the inertial waves regime found in an RDT (rapid dist ortion theory) analysis, cannot affect a homogeneous isotropic turbule nt flow, the study of nonlinear dynamics is of prime importance in the case of rotating flows. Previous theoretical (including both weakly n onlinear and EDQNM theories), experimental and DNS (direct numerical s imulation) results are collected here and compared in order to give a self-consistent picture of the nonlinear effects of rotation on turbul ence. The inhibition of the energy cascade, which is linked to a reduc tion of the dissipation rate, is shown to be related to a damping of t he energy transfer due to rotation. A model for this effect is quantif ied by a model equation for the derivative-skewness factor, which only involves a micro-Rossby number Ro(omega) = omega'/(2 Omega) - ratio o f r.m.s. vorticity and background vorticity - as the relevant rotation parameter, in accordance with DNS and EDQNM results. In addition, ani sotropy is shown also to develop through nonlinear interactions modifi ed by rotation, in an intermediate range of Rossby numbers (Ro(L) < 1 and Ro(omega) > 1), which is characterized by a macro-Rossby number Ro (L). based on an integral lengthscale L and the micro-Rossby number pr eviously defined. This anisotropy is mainly an angular drain of spectr al energy which tends to concentrate energy in the wave-plane normal t o the rotation axis, which is exactly both the slow and the two-dimens ional manifold. In addition, a polarization of the energy distribution in this slow two-dimensional manifold enhances horizontal (normal to the rotation axis) velocity components, and underlies the anisotropic structure of the integral lengthscales. Finally a generalized EDQNM (e ddy damped quasi-normal Markovian) model is used to predict the underl ying spectral transfer structure and all the subsequent developments o f classic anisotropy indicators in physical space. The results from th e model are compared to recent LES results and are shown to agree well . While the EDQNM2 model was developed to simulate 'strong' turbulence , it is shown that it has a strong formal analogy with recent weakly n onlinear approaches to wave turbulence.