On Quasi-Geostrophic Turbulence: A Numerical Experiment

The results of extended integrations of a two-level, quasi-geostrophic model with Newtonian heating and dissipation in terms of surface friction, internal friction, and lateral diffusion are described. The major emphasis is on an analysis of the integrations in wavenumber space, including the calculations of spectra for available potential energy, kinetic energy, enstrophy, energy generations, conversions and dissipation, as well as the nonlinear cascades of the first three quantities. It is found that the fluxes of available potential energy and kinetic energy through the wavenumber domain are very small above planetary wavenumber n = 10, while the enstrophy flux is large and positive for 6 ≤ n ≤ 10, but decreases rapidly for n > 10. The available potential energy, the kinetic energy and the enstrophy as a function of wavenumber vary approximately as n−5, n−3 and n−1, for 10 ≤ n ≤ 20. Dimensional considerations based on a balance between the convergence of the enstrophy flux and the dissipation of enstrophy in wavenumber space is used to describe the experimental spectra for n > 10. In this analysis it is assumed that the flux of enstrophy is proportional to the product of the wavenumber and the enstrophy divided by a time scale which is related to the flux of enstrophy coming from the baroclinically active region in the wavenumber domain. Theory and experiment are compared with generally good agreement.