A dynamical model for turbulence. VI. Two-dimensional turbulence

We apply a recent turbulence model to study 2-D turbulence. As in previous models, e.g., EDQNM, our model with a purely local transfer for both energy and enstrophy is not compatible with the conservation laws of energy and enstrophy that characterize 2-D turbulence. In contrast with previous two-point closure models that abandoned the Kolmogorovian spirit of locality, the present model satisfies both energy and enstrophy conservation laws with transfers that are local within the corresponding inertial regimes but not outside. We derive the dynamical equations governing the evolution of the spectra for energy, enstrophy, palinstrophy, and skewness. Results for both forced and unforced turbulence compare satisfactorily with DNS data.