ANALYTICAL AND NUMERICAL APPROACHES TO STRUCTURE FUNCTIONS IN MAGNETOHYDRODYNAMIC TURBULENCE

In magnetohydrodynamic turbulence, the classical theory by Kraichnan a nd Iroshnikov based on dimensional analysis gives a linear dependence of the exponents zeta(p) = p/4 of the structure functions for the Elsa sser variables z(+/-) = u +/- B. This linear behavior contradicts obse rvations of MHD turbulence in the solar wind, where anomalous scaling was found similar as in hydrodynamic turbulence. Since the experimenta lly observed scaling can not yet be derived by analytical theories, on e is dependent also on numerical simulations. As an alternative to dir ect numerical simulations we present a stochastic approach that recent ly was introduced for two-dimensional hydrodynamic hows. Finally, we d iscuss the applicability of operator-product expansions on a direct ca scade in strongly turbulent systems.