Spectral exponents of enstrophy cascade in stationary two-dimensional homogeneous turbulence

Abstract

Direct numerical simulations with up to ${4096}^2$ resolution are performed to address the question of universality of statistical properties of the enstrophy cascade in homogeneous two-dimensional turbulence driven by large-scale Gaussian white-in-time noise. Data with different Reynolds numbers are compared with each other. The energy spectrum is found to be very close to 1/${\mathit{k}}^3$. It is shown that the primary contribution to the enstrophy transfer function comes from wave-number triads with one small leg and two long ones, corresponding to wave numbers in the inertial range.