Modification alpha formalism of Shakura–Sunyaev for the coefficient of turbulent viscosity in an astrophysical disk of finite thickness

Aleksandr Vladimirovich Kolesnichenko

doi:10.20948/prepr-2022-1-e

Abstract

In the approximation of one-fluid hydrodynamics, a closed system of Favre-averaged magneto-hydrodynamic equations is formulated, intended for the numerical simulation of compressible turbulent flows of electrically conductive media in the presence of a magnetic field. Special emphasis is paid to the method of obtaining, within the framework of irreversible thermodynamics, the constitutive relations for the turbulent flux heat and the total (kinetic plus magnetic) tensor of turbulent stresses. A new approach to modeling the coefficient of turbulent kinematic viscosity for an astrophysical disk is proposed, which takes into account the influence of an external and generated magnetic field, as well as the processes of convective heat transfer on turbulence in a stratified layer of finite thickness, and thereby modifies the Shakura–Sunyaev alpha formalism developed by for a thin disk and widely used in the astrophysical literature.

Highlights

A noticeable fraction of gas in the near-solar protoplanetary disk at the very initial stage of its evolution represents partially ionized plasma; the degree of ionization of this plasma is quite sufficient for the development of various plasma instabilities, in particular, the hydro magnetic shear instability discovered by Velikhov [Velikhov 1959]
A new approach to modeling the coefficient of turbulent kinematic viscosity for an astrophysical disk is proposed, which takes into account the influence of an external and generated magnetic field, as well as the processes of convective heat transfer on turbulence in a stratified layer of finite thickness, and thereby modifies the Shakura–Sunyaev alpha formalism developed by for a thin disk and widely used in the astrophysical literature
As applied to the problem of the reconstruction of the evolution of the preplanetary gas–dust accretion disk, we developed in a number of papers [Kolesnichenko 2000, 2001, 2003-2005; Kolesnichenko, Marov, 2006-2008; Marov, Kolesnichenko, 2002, 2006] an approach to the solution of the problem of an adequate mathematical simulation of the turbulized disk medium taking into account the combined influence of magnetohydrodynamic effects and the effects of hydrodynamic turbulence on thedynamics and processes of heat and mass transport in the differentially rotating space gas–dust plasma, the inertial properties of the polydispersive admixture of solid particles, the processes of coagulation and radiation, and a number of additional effects occurring during turbulent plasma motion in a magnetic field

Summary

A.V. Kolesnichenko

Recommended form of bibliographic references: Kolesnichenko A.V. Modification alpha formalism of Shakura–Sunyaev for the coefficient of turbulent viscosity in an astrophysical disk of finite thickness // Keldysh Institute Preprints. 2022. Recommended form of bibliographic references: Kolesnichenko A.V. Modification alpha formalism of Shakura–Sunyaev for the coefficient of turbulent viscosity in an astrophysical disk of finite thickness // Keldysh Institute Preprints. Предложен новый подход к моделированию коэффициента турбулентной кинематической вязкости для астрофизического диска, который учитывает влияние внешнего и генерируемого магнитного поля, а также процессов конвективного переноса тепла на турбулентность в стратифицированном слое конечной толщины и тем самым модифицирует альфа формализм Шакуры–Сюняева, разработанный для тонкого диска и широко используемый в астрофизической литературе. Aleksandr Vladimirovich Kolesnichenko Modification alpha formalism of Shakura–Sunyaev for the coefficient of turbulent viscosity in an astrophysical disk of finite thickness.

Introduction

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Conclusions