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Paper IPM / P / 13099  


Abstract:  
We generalize the method of A. M. Polyakov [Phys. Rev. E 52, 6183 (1995)] for obtaining structurefunction relations in turbulence in the stochastically forced Burgers equation, to develop structurefunction 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 structurefunction 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 thirdorder structurefunctions and their derivatives; these expressions are the analogs of the vonKarmanHowarth 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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