Synergetic approach to exposition of a stationary-nonequilibrium turbulence

A. V. Kolesnichenko

Matematičeskoe modelirovanie, Tome 16 (2004) no. 1, pp. 37-66.

Résumé

The phenomenological macroscopic model of a stationary-nonequilibrium three-dimensional turbulence in compressible fluid with allowance for of nonlinear cooperative processes, happening in her designed. Representation of a turbulized continuum by the way of thermodynamic complex consisting of two subsystems – of a subsystem of an average motion and a subsystem of turbulent chaos, viewed, in turn, as conglomeration of vortex structures of different time-space gauges, has allowed to receive by methods of statistical nonequilibrium thermodynamics defining relations for turbulent flows and forces, which one fullestly feature processes of transport and self-organizing in a quasistationary case. The introduction in model of interior parameters of medium describing provoked macroscopic degrees of freedom has enabled to extend the Onzager's theory so that she featured also turbulent fluctuations concerning medial, that, in particular, has allowed to simulate by thermodynamic methods Kolmogorov cascade process and to receive the manifold kinetic equations for distribution functions of the small-scale performances of a turbulence. By virtue of abundance of a turbulent flow regime in the nature, it is possible to expect, that offered the synergeti approach to problems of model operation of a developed turbulence will find a use in different astro- and geophysical appendices.

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