A Study of Mechanism of the Energy Distribution in the MHD Turbulence at Low Magnetic Reynolds Numbers

The motion of a conducting fluid with an externally-applied magnetic field at the low magnetic Reynolds number is important in Magnetohydrodynamic (MHD) applications. For example, magnetic field is applied to control turbulent flow in the manufacturing process of the industrial products. The characteristic of the MHD turbulence is the anisotropic energy dumping. In order to understand the characteristic, we focus on different behavior of the diagonal components of the Reynolds stresses. The purpose of our study is show the process of energy distribution in the MHD turbulence at low magnetic Reynolds number using the transport equation for the Reynolds stresses. We take the case of homogeneous turbulence in a conducting fluid which is exposed to a uniform external magnetic field. In order to elucidate the anisotropic process, it is important to understand the characteristic of the Lorentz force. In this study, we clarify it and derive the transport equation for the Reynolds stresses, which is based on the characteristic. We show the mechanism of anistropic energy transfer in the physical space and the cause of the difference in the diagonal component of the Reynolds stresses.