Thermodynamic description of a developed turbulence at the registration of coherent vortex structures

A. V. Kolesnichenko

Matematičeskoe modelirovanie, Tome 16 (2004) no. 9, pp. 92-126

Résumé

The thermodynamic approach to build-up of phenomenological macroscopic model of a developed turbulence in compressible fluid is considered at the registration of nonlinear cooperative processes, happening in her. The insert in model of a gang of variates as interior parameters of a subsystem of turbulent chaos, has enabled to receive by methods of statistical nonequilibrium thermodynamics the Fokker–Planck equation in configurational space. This equation is intended for definition of time changes of a density function of conditional probability of structural parameters concerning to cascade process of bucking of widescale vortexes and temperature inhomogeneities, and also for the analysis of Markovian stochastic processes of transition from one stationary disequilibriums in other as a result of series loss of stability at change of driving parameters. The alternate method to examination of mechanisms of similar transition, founded on the stochastic differential equation simultaneously surveyed, intimately bound with the output kinetic equation (and the given connection is traced in paper). The cardinal problem of the developed approach is parsed – an opportunity of existence asymptotically of inconvertible stationary – disequilibrium of a subsystem of turbulent chaos. The nonequilibrium thermodynamic potential for interior coordinates extending a known relation Boltzmann–Planck for equilibrium states on stationary-disequilibrium of representing band is offered and is rotined, that he is Lyapunov function for such states. The connection between an interior alternation in an inertial interval of gauges and fluctuations of energy of a dissipation was surveyed.