Energy and enstrophy transfer in numerical simulations of two-dimensional turbulence

Abstract

Numerical simulations of statistically steady two-dimensional (2-D) turbulence are analyzed to determine the relative importance of the types of wave-vector triad interactions that transfer energy and enstrophy in the both the energy and enstrophy inertial ranges. In the enstrophy inertial range, it is found (in agreement with previous studies [J. Fluid Mech. 72, 305 (1975); Phys. Fluids A 2, 1529 (1990)]) that the important triads (i.e., those associated with the highest transfer rates) are typically very elongated. On the average, nearly all of the enstrophy transfer within these triads is directed from the intermediate to the largest wave-number mode (i.e., downscale transfer). Energy, too, is transferred downscale in this manner, but is also transferred upscale due to the interaction of the intermediate with the smallest wave-number mode of the triad, resulting in no net flux of energy in the enstrophy inertial range. Analysis of the geometry of the important triads indicates they are not of similar shapes at all scales, and that the enstrophy transferring triads generally consist of one wave vector near the scale of the energetic peak, no matter how large the other wave vectors are. In the energy inertial range, elongated triads are also important. As in the enstrophy inertial range, there is downscale transfer of energy and enstrophy due to the interaction of the intermediate with the largest wave-number mode. There is also upscale transfer of both energy and enstrophy due to a very nonlocal interaction involving the smallest wave-number modes. The result is a net upscale flux of energy and no net flux of enstrophy in the energy inertial range. Comparison of the transfer functions from the simulations with those calculated by an eddy-damped quasinormal closure show agreement in the gross functional forms, but display certain quantitative differences in integrated quantities such as total transfer into and flux past a given wave number.