On the validity of a nonlocal approach for MHD turbulence

The phenomenology of magnetohydrodynamic (MHD) turbulence proposed by R. H. Kraichnan, and its consequences for energy spectra and energy decay laws i n the high Reynolds number self-similar regime, are first reviewed. After r ecalling the exact relationships for MHD derived in the spirit of the so-ca lled "4/5" law of Kolmogorov, such laws are used to compute intermittency e xponents for statistically steady MHD flows in two space dimensions. These exponents are evaluated both for the structure functions of order p built o n the physical variables-velocity v and magnetic field b, or their combinat ion, through the Elsasser variables z(+/-) = v +/- b-and for the flux varia bles Y-p(+/-)(r) = [[delta z(L)(-/+)(r)(delta z(i)(+/-)(r))(2)](p/3)], wher e L denotes the longitudinal components of the fields. There are indication s that these nonlinear fluxes scale in a manner similar to that of noncondu cting fluids, whereas the physical v, b, z(+/-) fields are more intermitten t than in the neutral fluid case. (C) 1999 American Institute of Physics. [ S1070-6631(99)01608-6].