The role of nonequilibrium phase transitions in the structurization of hydrodynamic turbulence

A. V. Kolesnichenko

Matematičeskoe modelirovanie, Tome 19 (2007) no. 1, pp. 69-94.

Résumé

The aim of this paper is to develop a continual theory of developed structurized turbulence in shear flows in a compressible fluid modeled by a superposition of two mutually penetrating continuums, where the first continuum refers to the averaged field of turbulent motion, and the second, to the turbulent spacetime chaos associated with the fine-grained fluctuation motion. Incorporating into the thermohydrodynamic description of the subsystem of turbulent chaos a set of internal stochastic coordinates $q_k$ (like the locally averaged rate of turbulent energy dissipation), which characterize the structure and temporal evolution of the vorticity of the pulsational hydrodynamic field, has made it possible to use methods of statistical nonequilibrium thermodynamics to derive stochastic differential equations for these parameters and the corresponding Fokker–Planck–Kolmogorov equations for the probability density of transition. In accordance with the modified Kolmogorov similarity theory, positive fluctuating parameters $q_k$ are believed to obey the lognormal distribution in the stationary state of chaos. The Gaussian white noise with zero memory, which provides an idealized description of the real noise of vortex chaos with a very short but still finite memory, is used to model the force effect of the noise of chaos. A general concept of the birth of coherent structures in the thermodynamically open subsystem of turbulent chaos is formulated, which attributes the formation of such structures to the phenomenon of nonequilibrium phase transitions induced by the multiplicative noise of chaos during an increase of supercriticality. The interrelation between such transitions and the process of self-organization-the development of ordered “multimolecular” formations with lower symmetry as compared to that of the initial state-is discussed. The ultimate aim of this study is to refine a number of representative hydrodynamic models of natural space environments, including the formation of galaxies and galactic clusters; the birth of stars from the diffuse medium of gas and dust clouds; the formation of accretion disks and subsequent accumulation of planetary systems, etc. The study continues the stochastically thermodynamic approach to the synergetic description of structurized turbulence in astrogeophysical systems that the author has been developing in a series of previous papers.

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