A wavenumber partitioning scheme for two-dimensional statistical closures

Abstract

A technique of wavenumber partitioning that conserves both energy and enstrophy is developed for two-dimensional statistical closures. This advance facilitates the computation of energy spectra over seven wavenumber decades, a task that will clearly remain outside the realm of conventional numerical simulations for the foreseeable future. Within the context of the test-field model, the method is used to demonstrate Kraichnan's logarithmically-corrected scaling for the enstrophy inertial range and to make a quantitative assessment of the effect of replacing the physical Laplacian viscosity with an enhanced hyperviscosity.