Effective Magnetic Viscosity Due to Hydrodynamic Turbulence in a Weak Large-Scale Magnetic Field

Abstract The effective magnetic viscosity λeff is calculated in the presence of hydro-dynamic turbulence in a weak large-scale magnetic field. It is argued that λeff must be dependent on wavenumber, and that only eddies whose scale is smaller than k−1 contribute to λeff(k). λeff(k) takes on different forms in the small and large wavenumber regions. In the small wavenumber region λeff(k)~[∫~k∞dqE(q)/q2]1/2, where E(q) is the energy spectrum of turbulence; and for the Kolmogorov spectrum λeff(k)~k−4/3. In the large wavenumber region in which the Alfvén oscillations play an important role, λeff(k) is modified from that in the small wavenumber region. It is also argued that in the large wavenumber region the equipartition holds between kinetic energy and magnetic energy. Whether or not the wavenumber region can be decomposed into the two parts in practical cases is considered; in interstellar turbulence, as an example, the decomposition is well justified. The reconnection rate of magnetic fields in turbulence is also considered.