Geodesic
About new method of closure of the equations of turbulent motion of compressible heat-conducting gas
Matematičeskoe modelirovanie, Tome 24 (2012) no. 11, pp. 113-136

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This paper considers the modern approach to the thermodynamic modeling of developed turbulent flows of a compressible fluid based on the systematic application of the formalism of extended irreversible thermodynamics (EIT) that goes beyond the local equilibrium hypothesis, which is an inseparable attribute of classical nonequilibrium thermodynamics (CNT). In addition to the classical thermodynamic variables, EIT introduces new state parameters — dissipative flows and the means to obtain the respective evolutionary equations consistent with the second law of thermodynamics. The paper presents a detailed discussion of a number of physical and mathematical postulates and assumptions used to build a thermodynamic model of developed turbulence. A turbulized liquid is treated as an indiscrete continuum consisting of two thermodynamic sub-systems: an averaged motion subsystem and a turbulent chaos subsystem, where turbulent chaos is understood as a conglomerate of small-scale vortex bodies. Under the above formalism, this representation enables the construction of new models of continual mechanics to derive cause-and-effect differential equations for turbulent heat and impulse transfer, which describe, together with the averaged conservations laws, turbulent flows with transverse shear. Unlike gradient (noncausal) relationships for turbulent flows, these differential equations can be used to investigate both phenomena with history or memory, and nonlocal and nonlinear effects. Thus, within EIT, the second-order turbulence models underlying the so-called invariant modeling of developed turbulence get a thermodynamic explanation.
Keywords: turbulence of compressible gases, closure problem, extended irreversible thermodynamics. 
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     author = {A. V. Kolesnichenko},
     title = {About new method of closure of the equations of turbulent motion of compressible heat-conducting gas},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {113--136},
     publisher = {mathdoc},
     volume = {24},
     number = {11},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2012_24_11_a8/}
}
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A. V. Kolesnichenko. About new method of closure of the equations of turbulent motion of compressible heat-conducting gas. Matematičeskoe modelirovanie, Tome 24 (2012) no. 11, pp. 113-136. http://geodesic.mathdoc.fr/item/MM_2012_24_11_a8/