Properties of Hall-MHD Turbulence at Sub-Ion Scales: Spectral Transfer Analysis

Universal turbulent relaxation of fluids and plasmas by the principle of vanishing nonlinear transfers

A 70-year-old problem of fluid and plasma relaxation has been revisited. A principal based on vanishing nonlinear transfer is proposed to develop a unified theory of the turbulent relaxation of neutral fluids and plasmas. Unlike previous studies, the proposed principle enables us to find the relaxed states unambiguously without going through any variational principle. The general relaxed states obtained herein are found to support naturally a pressure gradient which is consistent with several numerical studies. Relaxed states are reduced to Beltrami-type aligned states where the pressure gradient is negligibly small. According to the present theory, the relaxed states are attained in order to maximize a fluid entropy S calculated from the principles of statistical mechanics [Carnevale et al., J. Phys. A: Math. Gen. 14, 1701 (1981)10.1088/0305-4470/14/7/026]. This method can be extended to find the relaxed states for more complex flows.