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.. For a clear physical interpretation of the individual components of the plasma-field energy balance, we derive various energy equations that allow us to trace the possible transitions of energy from one form to another, in particular, to understand the mechanisms for the transfer of the gravitational and kinetic energies of mean motion to magnetic energy. 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.

mathematical modelling, thermodynamics of the irreversible processes, the advanced turbulence, magnetic hydrodynamics

Mathematical modelling in actual problems of science and technics