title: Structure-function hierarchies and von Kármán-Howarth relations for turbulence in magnetohydrodynamical equations.
abstract: 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 analogs of MHD in one dimension [ Eur. Phys. J. B 9 725 (1999)], and in three dimensions (3DMHD and 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 Kármán-Howarth relations for fluid turbulence. We compare our work with earlier studies of such relations in 3DMHD and 3D Hall MHD.
authors.affiliation: Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Calcutta 700064, India.
authors.forename: Abhik
authors.initials: A
authors.lastname: Basu
authors.affiliation: School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran.
authors.forename: Ali
authors.initials: A
authors.lastname: Naji
authors.affiliation: Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India.
authors.forename: Rahul
authors.initials: R
authors.lastname: Pandit