Statistical theory of quasi-geostrophic turbulence.

Abstract

Within the context of statistical homogeneity, the authors examine geostrophic turbulence, employing a simple, eddy-damped closure. The authors find for decaying turbulence that high wavenumbers tend toward three-dimensional isotropy, as predicted by Charney, but wavenumbers smaller than the energy peak tend toward an approximate two-dimensional state, with the crossover wavenumber near the peak energy wavenumber. The highwavenumber energy spectrum is found to be log-modified kSUB-SUB3, where k is the three-dimensional wavenumber. Analytic information for the isotropization rate at small scales as well as for the large-scale 'barotropization' is proposed. Finally, the relation of these results to the more familiar layered approximation of the equations of motion is described. (A)