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

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.

8 pages, 3 figures

References in corpus (5)

• Growing condensate in two-dimensional turbulence
• Coherent structures and extreme events in rotating multiphase turbulent flows
• Helicity cascades in rotating turbulence
• Helicity statistics in homogeneous and isotropic turbulence and turbulence models
• Effects of magnetic and kinetic helicities on the growth of magnetic fields in laminar and turbulent flows by helical-Fourier decomposition