Mathematics – Probability
Scientific paper
Jun 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008sosyr..42..226k&link_type=abstract
Solar System Research, Volume 42, Issue 3, pp.226-255
Mathematics
Probability
Scientific paper
Within the framework of the main problem of cosmogony related to the reconstruction of the evolution of the protoplanetary gas-dust cloud that surrounded the proto-Sun at an early stage of its existence, we have derived a closed system of magnetohydrodynamic equations for the scale of mean motion in the approximation of single-fluid magnetohydrodynamics designed to model the shear and convective turbulent flows of electrically conducting media in the presence of a magnetic field. These equations are designed for schematized formulations and the numerical solution of special problems to interconsistently model intense turbulent flows of cosmic plasma in accretion disks and associated coronas, in which the magnetic field noticeably affects the dynamics of astrophysical processes. In developing the model of a conducting turbulized medium, apart from the conventional probability-theoretical averaging of the MHD equations, we systematically use the weighted Favre averaging. The latter allows us to considerably simplify the writing of the averaged equations of motion for a compressible fluid and the analysis of the mechanisms of macroscopic field amplification by turbulent flows. To clearly interpret the individual components of the plasma and field-energy balance, we derive various energy equations that allow us to trace the possible energy conversions from one form into another, in particular, to understand the transfer mechanisms of the gravitational and kinetic energies of the mean motion into magnetic energy. Special emphasis is placed on the method for obtaining the closure relations for the total (with allowance made for the magnetic field) kinetic turbulent stress tensor in an electrically conducting medium and the turbulent electromotive force (or the so-called magnetic Reynolds tensor). This method also makes it possible to analyze the constraints imposed on the turbulent transport coefficients by the entropy growth condition. As applied to the problem of numerically simulating the structure and evolution of a protoplanetary accretion disk differentially rotating around the proto-Sun, we suggest a technique for modeling the turbulent transport coefficients, in particular, the coefficient of kinematic turbulent viscosity that allows us to take into account the magnetic field effect and the inverse effect of the heat transfer on the development of turbulence in a rotating electrically conducting disk. Our study is ultimately aimed at improving several representative hydrodynamic models of natural cosmic turbulized media, including the birth of stars from the diffuse medium of gas-dust clouds, the formation of accretion disks, and the subsequent accumulation of planetary systems. It is a continuation of the stochastic-thermodynamic approach to the synergetic description of the turbulence of astrophysical and geophysical systems that we have developed in a series of papers (Kolesnichenko, 2003; 2004; 2005; Kolesnichenko and Marov, 2006; 2007; Marov and Kolesnichenko, 2002; 2006).
Kolesnichenko Aleksander V.
Ya Marov Mikhail
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