Infrared Dynamics and Decay of Helicity in Homogeneous Isotropic Turbulence

The decay of helicity and its impact on kinetic energy is analyzed at very large Reynolds numbers in homogeneous isotropic turbulence lacking mirror symmetry, using the Eddy-Damped Quasi-Normal Markovian closure. A theoretical time decay exponent for helicity is derived and assessed numerically. In addition to the initial well-known slowing down of non-linear transfers, it is further shown that helicity slightly accelerates the decay of kinetic energy in Batchelor turbulence, because it decreases the \(k^4\) back transfers, which is proved analytically using non-local expansions. Finally, unlike the kinetic energy spectrum in Batchelor turbulence, the permanence of large eddies is verified for the helical spectrum.