Compensating Behavior and Constancy of Normalized Energy Transfers in Hall Magnetohydrodynamic Turbulence∗)

Using a dissipation-scale adaptive, wavelet-like shell decomposition method and normalization by dissipation-scale characteristics, we found a novel sustaining behavior of self-similarity in the quadratic energy transfer process in freely decaying, fully developed, homogeneous and isotropic turbulences of an incompressible Hall magnetohydrodynamic medium. The process is associated with the relative reduction of nonlinear energy transfer in the dissipation range, which was reported in our previous study [K. Araki and H. Miura, Plasma Fusion Res. 8, 2401137 (2013)]. Gradual reductions in energy transfers by fluid advection and the Hall-term effect are compensated by enhancement of energy transfers due to mutual interactions between velocity and magnetic fields, i.e. between the Lorentz force effect and magnetic induction. This sustaining behavior suggests that coupling between velocity and magnetic fields may be crucial, even when linear dispersive waves aroused by a uniform background magnetic field are absent.