Local anisotropy in incompressible magnetohydrodynamic turbulence

It is a well known fact that in the presence of a dc applied magnetic field, magnetohydrodynamic (MHD) turbulence develops spectral anisotropy from isotropic initial conditions. Typically, the reduced spectrum is steeper in the direction of the magnetic field than it is in any transverse direction. One might expect that a dc field is not essential, and it is the local mean field that is responsible. To address this issue, three-dimensional MHD pseudo-spectral incompressible relaxation simulations are performed, and structure functions computed according to whether the separation is parallel to, or transverse to, the local mean magnetic field. Correlation lengths are longer in the locally averaged magnetic field direction than in any perpendicular direction, even when the global mean magnetic field is zero. Local anisotropy is observed to be stronger in regions of strong magnetic field. A general definition of anisotropy angles and a methodology to study local anisotropy are proposed.