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Updated: May 2, 2026

Preparation of Free-Surface Hyperbolic Water Vortices
Published on: July 28, 2023
Structure-function hierarchies and von Kármán-Howarth relations for turbulence in magnetohydrodynamical equations
Abhik Basu1, Ali Naji2, Rahul Pandit3
1Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Calcutta 700064, India.
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.
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