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 ${10}^5\le {\text{Re}}_{\lambda }\le {10}^6$. In agreement with previous findings, an inverse cascade of energy with a kinetic energy spectrum such as $\propto k^{-5/3}$ 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 $\propto k^{-7/3}$. 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.

• Received 19 July 2017

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