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

Antoine Briard1, Luca Biferale2, and Thomas Gomez3,*

  • 1Sorbonne Universités, UPMC Université Paris 06, UMR 7190, Institut Jean Le Rond d'Alembert, F-75005 Paris, France
  • 2Department of Physics and INFN, University of Rome “Tor Vergata,” Via della Ricerca Scientifica 1, I-00133 Rome, Italy
  • 3Université Lille Nord de France, F-59000 Lille, France

  • *thomas.gomez@univ-lille1.fr
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Phys. Rev. Fluids 2, 102602(R) – Published 27 October, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.102602

Abstract

We study the energy transfer properties of three-dimensional homogeneous and isotropic turbulence where the nonlinear 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 quasinormal Markovian closure is derived to analyze the dynamics at very large Reynolds numbers, of order 105≤Reλ≤106. In agreement with previous findings, an inverse cascade of energy with a kinetic energy spectrum such as ∝k−5/3 is found for scales larger than the forcing one. Conjointly, a forward cascade of helicity towards larger wave numbers is obtained, where the kinetic energy spectrum scales as ∝k−7/3. By following the evolution of the closed spectral equations for a very long time and over a huge extension of scales, we found the development of a nonmonotonic shape for the front of the inverse energy flux. The asymptotic temporal scaling laws for the kinetic energy, helicity, and integral scales in both the forced and unforced cases are also determined.

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Phys. Rev. Fluids 2, 102602(R)– Published 27 October, 2017
  • Received 19 July 2017

©2017 American Physical Society

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