Long-time magnetic and cross helicities evolution in the free decaying MHD turbulence

We re-examine the free decay of MHD turbulence at large Reynolds numbers in the framework of shell models. We study the statistical properties based on representative sample of realisations (128 realisations for each type of initial conditions) over the period of 105 large-scale turnover times. The performed simulations show that the free-decaying non-helical MHD turbulence can demonstrate two different scenarios of evolution in spite of similar initial conditions. Within the first scenario, the cross-helicity accumulation is so fast that the energy cascade vanishes before significant magnetic energy dissipates. Then the system approaches the state of maximal cross-helicity. Within the second scenario, the cascade process continues to remain active until time 104 in units of large-scale turnover time. Then the magnetic field becomes vastly helical due to magnetic helicity conservation. Thus the magnetic energy does not dissipate with kinetic energy.