ANALYTICAL AND PHENOMENOLOGICAL STUDIES OF ROTATING TURBULENCE

A framework, which combines mathematical analysis, closure theory, and phenomenological treatment, is developed to study the spectral transf er process in turbulent flows that are subject to rotation. First, we outline a mathematical procedure that is particularly appropriate for problems with two disparate time scales. The approach that is based on the Green's method leads to the Poincare velocity variables and the P oincare transformation when applied to rotating turbulence. The effect s of the rotation are now conveniently included in the momentum equati on as the modifications to the convolution of nonlinear term. The Poin care transformed equations are used to obtain a time-dependent Taylor- Proudman theorem valid in the asymptotic limit when the nondimensional parameter mu = Omega t --> infinity (Omega is the rotation rate and t is the time). The ''split'' of the energy transfer in both direct and inverse directions is established. Second, we apply the Eddy-Damped-Q uasinormal-Markovian (EDQNM) closure to the Poincare transformed Euler /Navier-Stokes equations. This closure leads to expressions for the sp ectral energy transfer. In particular, a unique triple velocity decorr elation time is derived with an explicit dependence on the rotation ra te. This provides an important input for applying the phenomenological treatment of Zhou [Phys. Fluids 7, 2092 (1995)]. In order to characte rize the relative strength of rotation, another nondimensional number, a spectral Rossby number, which is defined as the ratio of rotation, and turbulence time scales, is introduced. Finally, the energy spectru m and the spectral eddy viscosity are deduced. (C) 1996 American Insti tute of Physics.