Mean field responses in disordered systems: An example from rotating nonlinear magnetohydrodynamic

This study extends mean-field magnetohydrodynamic (MHD) theory by incorporating rotational effects, represented by the Coriolis term fk×u (where f is the Coriolis parameter, k is the unit vector along the rotation axis, and u the velocity fluctuation). The four principal mean-field tensors α(1), α(2), Γ(1), and Γ(2) are reformulated to account for rotation. Key findings show that rotation breaks symmetry, generating a nonzero Γ(1) tensor that couples mean flow and magnetic fields. The α(1) dynamo effect is modulated along the rotation axis, depending on helicity distribution. Rotation generally suppresses certain instabilities while promoting hybrid rotation magnetic field instabilities. Under weak to moderate rotation, the system exhibits a broader linear response range, indicating that rotation mitigates chaotic turbulence and stabilizes mean-field quantities (i.e., it reduces the growth rate of large-scale perturbations and broadens the range of mean-field amplitudes over which the electromotive force responds linearly). This work extends mean-field MHD to rotating systems, offering a more comprehensive framework for analyzing large-scale dynamo processes and instabilities in astrophysical and laboratory settings.