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| Paper IPM / Physic / 13099 |
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We generalize the method of A. M. Polyakov [Phys. Rev. E 52, 6183 (1995)] for obtaining structure-function relations in turbulence in the stochastically forced Burgers equation, to develop structure-function hierarchies for turbulence in three models for magnetohydrodynamics (MHD). These are the Burgers analog of MHD of A. Basu, J. K. Bhattacharjee, and S. Ramaswamy [Eur. Phys. J. B 9, 725 (1999)] in one dimension, and, in three dimensions (3D), the equations of magnetohydrodynamics (3D MHD) and the equations of 3D Hall MHD. Our study provides a convenient and unified scheme for the development of structure-function hierarchies for turbulence in a variety of coupled hydrodynamical equations. For turbulence in the three sets of MHD equations mentioned above, we obtain exact relations for third-order structure-functions and their derivatives; these expressions are the analogs of the von-Karman-Howarth relations for fluid turbulence. We compare our work with earlier studies of such relations in 3D MHD and 3D Hall MHD.
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