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 105 based on the Taylor scale. In agreement with previous findings, an
inverse cascade of energy with a kinetic energy spectrum like βkβ5/3 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 βkβ7/3. 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.Comment: 8 pages, 3 figure