Lagrangian statistical theory of anisotropic MHD turbulence

We construct a Lagrangian statistical theory of spatially uniform, anisotropic, and strong turbulence of an incompressible magneto-fluid with a uniform mean magnetic field. We treat shear Alfven turbulence; that is, the perturbations of the velocity field and the magnetic field are assumed to be orthogonal to the mean magnetic field. The perturbation energies, however, need not be equiparted; our theory covers non-equipartition turbulence as well as equipartition turbulence. We show that, concerning the relaxation and energy-transfer of inertial-range eddies, the shear Alfven turbulence has the following fundamental properties: That is, relaxation of inertial-range eddies is dominated by the largest (energy-containing) eddies; energy cascades have spatially a quasi 2-dimensional nature because of the inhibition of cascades parallel to the mean field; thus, inevitably, the -3/2 power-law energy-spectra are derived. These properties are independent of whether the turbulence satisfies the energy equipartition. We, therefore, assert that they should be thought of as generic and robust natures of strong MHD turbulence.