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

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