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Foundations of Mechanics of Heterogeneous Media for Accretion Disks

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Turbulence and Self-Organization

Part of the book series: Astrophysics and Space Science Library ((ASSL,volume 389))

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Abstract

Here attention is focused on one of the fundamental problems in astrophysics—the formation of protoplanetary accretion disks around late-type stars whose special case is the origin of the Solar system. Particular attention is given to the development of a semiempirical approach to modeling heterogeneous turbulence in the accretion disk that surrounded the proto-Sun at the early stage of its existence with the goal of reducing the number of assumptions in the models used. We formulate a complete system of equations of two-phase multicomponent mechanics by taking into account the relative motion of the phases, coagulation processes, phase transitions, chemical reactions, and radiation. Basically, it is designed for schematized formulations and numerical solution of specific model problems on mutually consistent modeling of the structure, dynamics, thermal regime, and chemical composition of the circumsolar disk at various stages of its evolution. The processes in the disk medium in the presence of the developed turbulent motions of a coagulating gas suspension are addressed that eventually contribute to the formation of a dust subdisk near the equatorial plane of the proto-Sun within the model under consideration and the emergence of hydrodynamic and then gravitational instability in it followed by the formation of dust clusters.

For an adequate phenomenological description of turbulent flows in a gas–dust disk, we perform the probability-theoretic Favre averaging of the stochastic equations of heterogeneous mechanics and derive the defining gradient relations for the turbulent interphase diffusion and heat fluxes as well as for the “relative” and Reynolds stress tensors needed to close the hydrodynamic equations of mean motion. We investigate the influence of the inertial effects of dust particles on the characteristics of turbulence in the disk, in particular, on the additional generation of turbulent energy by large particles. We propose a semiempirical method of modeling the turbulent viscosity coefficient in a two-phase disk by taking into account the inverse effects of dispersed phase and heat transport on the development of turbulence with the goal of modeling the vertically inhomogeneous thermohydrodynamic structure of the dust subdisk and the ambient gas.

For a steady motion when solid particles settle down to the central plane of the disk under gravity, we investigate a parametric method of moments for solving the Smoluchowski integro-differential coagulation equation for the particle size distribution function that is based on the a priori belonging of the sought-for distribution function to a certain parametric class of distributions. In addition, we analyze the possible regime of limiting saturation of the subdisk atmosphere by fine dust particles that is responsible for the intensification of various coagulation mechanisms in a turbulized medium. The results of this chapter open new possibilities for constructing improved (and more realistic) models of stellar-planetary cosmogony, thereby providing a new approach to solving the fundamental problem of the origin and evolution of the Solar system and planetary systems around other stars.

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Authors and Affiliations

  1. Department of Planetary Sciences and Cosmochemistry, V.I. Vernadsky Institute of Geochemistry and Analytical Chemistry Russian Academy of Sciences, Moscow, Russia

    Mikhail Ya Marov

  2. Department of Planetary Science and Aeronomy, Keldysh Institute of Applied Mathematics Russian Academy of Sciences, Moscow, Russia

    Aleksander V. Kolesnichenko

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  1. Mikhail Ya Marov
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  2. Aleksander V. Kolesnichenko
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Marov, M.Y., Kolesnichenko, A.V. (2013). Foundations of Mechanics of Heterogeneous Media for Accretion Disks. In: Turbulence and Self-Organization. Astrophysics and Space Science Library, vol 389. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5155-6_7

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