An update on the double cascade scenario in two-dimensional turbulence

TL;DR

This paper presents high-resolution simulations of two-dimensional turbulence, confirming the simultaneous existence of inverse and direct cascades with Kolmogorov laws, and analyzing finite size effects on the spectra.

Contribution

It provides the first simultaneous observation of Kolmogorov laws for both cascades in 2D turbulence at unprecedented resolution.

Findings

Inverse cascade spectrum matches Kolmogorov-Kraichnan prediction.

Inverse cascade robust against enstrophy flux variations.

Direct cascade spectrum shows finite size effects diminishing with higher resolution.

Abstract

Statistical features of homogeneous, isotropic, two-dimensional turbulence is discussed on the basis of a set of direct numerical simulations up to the unprecedented resolution $32768^2$. By forcing the system at intermediate scales, narrow but clear inertial ranges develop both for the inverse and for direct cascades where the two Kolmogorov laws for structure functions are, for the first time, simultaneously observed. The inverse cascade spectrum is found to be consistent with Kolmogorov-Kraichnan prediction and is robust with respect the presence of an enstrophy flux. The direct cascade is found to be more sensible to finite size effects: the exponent of the spectrum has a correction with respect theoretical prediction which vanishes by increasing the resolution.