Thermodynamic model of MHD turbulence and some of its applications to accretion disks

Abstract

Here the basic concepts of stellar-planetary cosmogony, the problem of reconstructing the evolution of a protoplanetary gas-dust cloud by taking into account electrodynamic effects are addressed. A closed system of magnetohydrodynamic (MHD) equations of mean motion designed to model shear and convective turbulent flows in electrically conducting media in the presence of a magnetic field is derived in the approximation of single-fluid magnetohydrodynamics. These equations can be used for a numerical solution of the problems on mutually consistent modeling of powerful turbulent cosmic plasma flows in accretion disks and related coronas in which the magnetic field affects significantly the dynamics of occurring astrophysical processes. When developing the model of a conducting turbulized medium, in addition to the traditional probability-theoretic averaging of the MHD equations, we also systematically use the weighted Favre averaging. The latter allows the form of the averaged equations of motion for a compressible electrically conducting fluid and the analysis of the mechanisms for the amplification of macroscopic fields by turbulent flows to be simplified considerably. 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 and, in particular, to understand the mechanisms for the transfer of the gravitational and kinetic energies of mean motion to magnetic energy.