A group-kinetic theory with a closure by memory loss for modeling turbulence in the atmosphere and the oceans

Summary The principle of the group-kinetic method is elucidated. This method of renormalization serves as the basis for analyzing the spectral structure of turbulence. The spectral distributions include the Kolmogoroff lawk ^–5/3 for isotropic turbulence, the power lawk ^–1 for shear turbulence, the spectrum for stratified turbulence not in the power law form, the power lawk ^–3 for two-dimensional geostrophic turbulence, and the power lawsk ^–3,k ^–2 andk ^–5 for two-dimensional Rossby wave turbulence with uniform and differential rotations. We discuss a spectrum-dependent modeling in reference to the problems of the universal functions and parameters in the similarity theories for the atmospheric surface layer and the planetary boundary layer. A renormalization-based modeling of atmospheric turbulence is proposed.