Magneto-Fluid Dynamic Turbulence with a Uniform Imposed Magnetic Field

Abstract

Two point correlation and spectral equations for this case are derived from the equations of fluid and electrodynamics. Solutions are obtained by assuming that the turbulent field is homogeneous and weak enough for triple correlations to be negligible. For initial conditions, it is postulated that the turbulence is initially isotropic, and that the turbulent magnetic field fluctuations are initially zero. The interaction of the mean magnetic field with the turbulent velocity field then causes magnetic field fluctuations to arise at later times. In general, the turbulent energy in the mechanical and magnetic modes tends toward equipartition for large values of time or of mean magnetic field. However, when the kinematic viscosity is much less than the electrical resistivity (or magnetic diffusivity), as for liquid metals, equipartition is not approached before the turbulence is damped out by the mean magnetic field.