THE RENORMALIZATION-GROUP ANALYSIS FOR THE STATISTICAL PROPERTIES OF RAPIDLY ROTATING TURBULENCE

The statistical properties for rapidly rotating turbulence are investigated using the renormalization-group method. With the renormalized perturbation, the high wavenumber velocity components are taken to be average successively. The calculations show that the renormalized viscosity, which represents the influence of the high wavenumber velocity components upon the low wavenumber velocity components, tends to zero at the limit of the rotational angular velocity Ω → ∞. It indicates that the Coriolis force will impede the nonlinear interactions among different wavenumber velocity components. At the limit Ω → ∞, the turbulent energy cascade will diminish to zero. Consequently the flow tends towards laminarization as the turbulent fluctuations disappear. The calculations also show that the space-time Fourier velocity components tend to two-dimensionalization and the spherically averaged energy spectrum have the scaling behavior E(k) ∝ k^-3 for rapidly rotating turbulence.