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11.
This paper considers, in the context of modeling the evolution of a protoplanetary cloud, the hydrodynamic aspects of the theory of concurrent processes of mass transfer and coagulation in a two-phase medium in the presence of shear turbulence in a differentially rotating gas–dust disk and of polydisperse solid particles suspended in a carrying flow of solid particles. The defining relations are derived for diffuse fluxes of particles of different sizes in the equations of turbulent diffusion in the gravitational field, which describe the convective transfer, turbulent mixing, and sedimentation of disperse dust grains onto the central plane of the disk, as well as their coagulation growth. A semiempirical method is developed for calculating the coefficients of turbulent viscosity and turbulent diffusion for particles of different kinds. This method takes into account the inverse effects of dust transfer on the turbulence evolution in the disk and the inertial differences between disperse solid particles. To solve rigorously the problem of the mutual influence of the turbulent mixing and coagulation kinetics in forming the gas–dust subdisk, the possible mechanisms of gravitational, turbulent, and electric coagulation in a protoplanetary disk are explored and the parametric method of moments for solving the Smoluchowski integro-differential coagulation equation for the particles' size distribution function is considered. This method takes into account the fact that this distribution belongs to a definite parametric class of distributions. 相似文献
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An attempt is made to construct a phenomenological model of turbulence as a self-organization process in an open system. The representation of a turbulized continuum in the form of a thermodynamic complex consisting of two subsystems—the subsystem of averaged motion and the subsystem of turbulent chaos, which is considered, in turn, as a conglomerate of vortex structures of different space–time scales—made it possible to obtain, by methods of nonequilibrium thermodynamics, the defining relationships for the turbulent fluxes and forces that describe most comprehensively the transport and structurization processes in such a continuum. Using two interpretations of the Kolmogorov parameter (as a quantity that describes the rate of dissipation of energy into heat and as the rate of transfer of turbulent energy in the eddy cascade), the defining relationships were found for this quantity, thereby making the thermodynamic approach self-sufficient. An introduction into the model of internal parameters of the medium, which characterize the excitation of macroscopic degrees of freedom, made it possible to describe thermodynamically the Kolmogorov cascade process and to obtain a variety of kinetic equations (of the Fokker–Planck type in the configuration space) for the functions of distribution of small-scale turbulence characteristics, including the unsteady kinetic equation for the distribution of probability of dissipation of turbulent energy. As an example, a detailed derivation of such relationships is given for the case of stationary turbulence, when a tendency toward local isotropy is observed. In view of the wide occurrence of this phenomenon in nature, one might expect that the developed approach to the problem of modeling strong turbulence will find its use in astrophysical and geophysical applications. 相似文献
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We formulate a complete system of equations of two-phase multicomponent mechanics including the relative motion of the phases, coagulation processes, phase transitions, chemical reactions, and radiation in terms of the problem of reconstructing the evolution of the protoplanetary gas-dust cloud that surrounded the proto-Sun at an early stage of its existence. These equations are intended for schematized formulations and numerical solutions of special 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, in particular, the developed turbulent motions of a coagulating gas suspension that lead to the formation of a dust subdisk, its gravitational instability, and the subsequent formation and growth of planetesimals. To phenomenologically describe the turbulent flows of disk material, we perform a Favre probability-theoretical averaging of the stochastic equations of heterogeneous mechanics and derive defining relations for the turbulent flows of interphase diffusion and heat as well as for the “relative” and Reynolds stress tensors needed to close the equations of mean motion. Particular attention is given to studying the influence of the inertial effects of dust particles on the properties of turbulence in the disk, in particular, on the additional generation of turbulent energy by large particles near the equatorial plane of the proto-Sun. We develop a semiempirical method of modeling the coefficient of turbulent viscosity in a two-phase disk medium by taking into account the inverse effects of the transfer of a dispersed phase (or heat) on the growth of turbulence to model the vertically nonuniform thermohydrodynamic structure of the subdisk and its atmosphere. 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. For steady motion when solid particles settle to the midplane of the disk under gravity, we analyze the parametric method of moments for solving the Smoluchowski integro-differential coagulation equation for the particle size distribution function. This method is based on the fact that the sought-for distribution function a priori belongs to a certain parametric class of distributions. 相似文献
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Solar System Research - In the framework of Tsallis statistics, we study the effect of medium nonextensivity on the Jeans gravitational instability criterion for a self-gravitating protoplanetary... 相似文献
15.
A. V. Kolesnichenko 《Solar System Research》2011,45(3):246-263
The problem of the influence of vortex helicity on the synergic structuring of cosmic matter in it, as well as the appearance
of the effect of negative viscosity in three-dimensional gyrotropic turbulence, were studied in the framework of the fundamental
problem of simulating the evolution of a rotating astrophysical nonmagnetic disk—in particular, the accretion disk—surrounding
the Sun at the early stage of its existence. The evolution equations for averaged vorticity and vortex helicity, as well as
rheological relations for the turbulent flow of heat and asymmetrical tensor of the turbulent stress in helical turbulence,
were obtained. The demonstrative dependence of helicity on the rotation velocity, density (temperature) gradients, and turbulent
energy of the disk gas was established. The role of helicity in the appearance of the inverse Richardson-Kolmogorov energy
cascade from small vortices to larger ones and the related process of the generation of the power-consuming macroscale coherent
vortex formations appearing in gyrotropic turbulence at high Reynolds number were discussed. The results of the numerical
experiments confirming the real existence of the inverse energy cascade in helical turbulence were analyzed. It was assumed
that the relatively long-term decay of turbulence in the solar protoplanet cloud can be due to the absence of the reflective
symmetry of the anisotropic field of the turbulent velocities with respect to its equatorial plane. As the concept of the
inverse energy cascade in three-dimensional helical turbulence is more and more reliably confirmed in numerical experiments,
accounting for this effect affecting the structure and dynamics of the astrophysical nonmagnetic disk becomes important during
its simulation. 相似文献
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Solar System Research - For the purpose of mathematical simulations of the formation processes for planetesimals in the Solar protoplanetary disk, statistical thermodynamics for nonextensive... 相似文献
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A. V. Kolesnichenko 《Solar System Research》2017,51(2):127-144
The long-time development of self-gravitating gaseous astrophysical systems (in particular, the evolution of the protoplanet accretion disk) is mainly determined by relatively fast processes of the collision relaxation of particles. However, slower dynamical processes related to force (Newton or Coulomb) interactions between particles should be included (as q-collisions) in the nonextensive kinetic theory as well. In the present paper, we propose a procedure to include the Newton self-gravity potential and the centrifugal potential in the near-equilibrium power-like q-distribution in the phase space, obtained (in the framework of nonextensive statistics) by means of the modified Boltzmann equation averaged with respect to an unnormalized distribution. We show that if the power distribution satisfies the stationary q-kinetic equation, then the said equation imposes clear restrictions on the character of the long-term force field and on the possible dependence of hydrodynamic parameters of the coordinates: it determines those parameters uniquely. We provide a thermodynamic stability criterion for the equilibrium of the nonextensive system. The results allow us to simulate the evolution of gaseous astrophysical systems (in particular, the gravitational stability of rotating protoplanet accretion disks) more adequately. 相似文献
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