A closure theory for the split energy-helicity cascades in homogeneous isotropic homochiral turbulence

TL;DR

This paper develops a closure theory for homochiral turbulence, revealing inverse energy cascades and forward helicity cascades at high Reynolds numbers, with detailed spectral and flux evolution analysis.

Contribution

It introduces an adapted EDQNM closure for homochiral turbulence, providing new insights into energy and helicity cascades at very high Reynolds numbers.

Findings

Inverse energy cascade with $k^{-5/3}$ spectrum

Forward helicity cascade with $k^{-7/3}$ spectrum

Non-monotonic energy flux front development

Abstract

We study the energy transfer properties of three dimensional homogeneous and isotropic turbulence where the non-linear transfer is altered in a way that helicity is made sign-definite, say positive. In this framework, known as homochiral turbulence, an adapted eddy-damped quasi-normal Markovian (EDQNM) closure is derived to analyze the dynamics at very large Reynolds numbers, of order $10^5$ based on the Taylor scale. In agreement with previous findings, an inverse cascade of energy with a kinetic energy spectrum like $\propto k^{-5/3}$ is found for scales larger than the forcing one. Conjointly, a forward cascade of helicity towards larger wavenumbers is obtained, where the kinetic energy spectrum scales like $\propto k^{-7/3}$. By following the evolution of the closed spectral equations for a very long time and over a huge extensions of scales, we found the developing of a non monotonic shape for the front of the inverse energy flux. The very long time evolution of the kinetic energy and integral scale in both the forced and unforced cases is analyzed also.