Thermodynamic modelling of the magnetohydrodynamic turbulence

A closed system of magnetohydrodynamic equations of mean motion designed to model turbulent flows in electrically conducting media in the presence of a magnetic field is derived in the approximation of single-fluid magnetohydrodynamics. Particular attention is given to the method of deriving the closing relations for the total (including the magnetic field) kinetic turbulent stress tensor and the so-called magnetic Reynolds tensor within the framework of extended irreversible thermodynamics. This also allows the constraints imposed by the entropy growth condition on the turbulent transport coefficients to be analyzed. We propose a technique for modeling the turbulent transport coefficients, in particular, the kinematic turbulent viscosity, which makes it possible to take into account the influence of a magnetic field and the inverse effect of heat transfer on the development of turbulence in electrically conducting media.