Exact decomposition of the kinetic helicity flux in homogenous turbulence*

In homogeneous turbulence,  the relative contributions of different physical mechanisms to the energy cascade can be quantified by an exact decomposition of the energy flux (P. Johnson, Phys. Rev. Lett., 124, 104501 (2020), J. Fluid Mech. 922, A3(2021)). We extend the formalism to the transfer of kinetic helicity across scales and quantify the contributions of different physical effects in the inertial range. All sub-fluxes transfer helicity from large to small scales. About 50% of the mean flux is due to the scale-local deformation of vortices into vortex sheets in a way that the vorticity deformation tensor aligns with the strain rate tensor and a strain-vorticity coupling with the deformation of resolved-scale vorticity. We derive an exact relation between these effects, asserting that the mean contribution of the former is three times larger than that of the latter.  Scale non-local effects account for the remaining 50%, with approximate equipartition between scale-nonlocal versions of the two aforementioned effects and the alignment of resolved-scale vorticity strain with small-scale vorticity.