Isotropisation at small scales of rotating helically-driven turbulence

TL;DR

This paper provides numerical evidence of small-scale isotropization in rotating helical turbulence, showing the transition from helical wave dynamics to Kolmogorov spectra and the recovery of three-dimensionality at scales below the Zeman scale.

Contribution

It demonstrates how small-scale isotropization occurs in rotating helical turbulence and identifies the Zeman scale as a key transition point using high-resolution simulations.

Findings

Zeman scale is much larger than the dissipation scale.

Energy and helicity spectra follow inertial and Kolmogorov laws across scales.

Helicity spectrum breaks down at the Zeman scale, indicating 3D recovery.

Abstract

We present numerical evidence of how three-dimensionalization occurs at small scale in rotating turbulence with Beltrami (ABC) forcing, creating helical flow. The Zeman scale $\ell_{\Omega}$ at which the inertial and eddy turn-over times are equal is more than one order of magnitude larger than the dissipation scale, with the relevant domains (large-scale inverse cascade of energy, dual regime in the direct cascade of energy $E$ and helicity $H$, and dissipation) each moderately resolved. These results stem from the analysis of a large direct numerical simulation on a grid of $3072^3$ points, with Rossby and Reynolds numbers respectively equal to 0.07 and $2.7\times 10^4$. At scales smaller than the forcing, a helical wave-modulated inertial law for the energy and helicity spectra is followed beyond $\ell_{\Omega}$ by Kolmogorov spectra for $E$ and $H$. Looking at the two-dimensional slow manifold, we also show that the helicity spectrum breaks down at $\ell_{\Omega}$, a clear sign of recovery of three-dimensionality in the small scales.