Remark on the Mean Energy of the Fluctuating Magnetic Field in Mean‐field Magnetohydrodynamics

Abstract

Abstract A relation between the mean square of the fluctuating magnetic field, B′ , and the square of the mean magnetic field, B̄ , is derived for the case of homogeneous isotropic turbulence. The second order correlations approximation is used under the assumption that the space and time scales L̄ and T̄ of the mean field are large compared with the scales L and T of the fluctuations. B OCHNER 's theorem manifests itself as a guarantee for the ratio B̄′ 2 |B̄ 2 to be non‐negative.