Abstract
In magnetohydrodynamic turbulence, the classical theory by Kraichnan and Iroshnikov based on dimensional analysis gives a linear dependence of the exponents ζp = p/4 of the structure functions for the Elsässer variables z± = u ± B. This linear behavior contradicts observations of MHD turbulence in the solar wind, where anomalous scaling was found similar as in hydrodynamic turbulence. Since the experimentally observed scaling can not yet be derived by analytical theories, one is dependent also on numerical simulations. As an alternative to direct numerical simulations we present a stochastic approach that recently was introduced for two-dimensional hydrodynamic flows. Finally, we discuss the applicability of operator-product expansions on a direct cascade in strongly turbulent systems.
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