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Инд. авторы: Chirkunov Y.A., Nazarenko S.V., Medvedev S.B., Grebenev V.N.
Заглавие: Invariant solutions for the nonlinear diffusion model of turbulence
Библ. ссылка: Chirkunov Y.A., Nazarenko S.V., Medvedev S.B., Grebenev V.N. Invariant solutions for the nonlinear diffusion model of turbulence // Journal of Physics A: Mathematical and Theoretical. - 2014. - Vol.47. - Iss. 18. - Art.185501. - ISSN 1751-8113. - EISSN 1751-8121.
Внешние системы: DOI: 10.1088/1751-8113/47/18/185501; РИНЦ: 24047833; РИНЦ: 24953977; SCOPUS: 2-s2.0-84937046410; WoS: 000335773700005;
Реферат: eng: We study Leith's model of turbulence represented by a nonlinear degenerate diffusion equation (Leith 1967 Phys. Fluids 10 1409–16, Connaughton and Nazarenko 2004 Phys. Rev. Lett. 92 044501–506). The model is constructed such that in the case of vanishing viscosity, there are two steady-state solutions: the Kolmogorov spectrum that corresponds to the cascade state and a thermodynamic equilibrium distribution. Using group analysis, we have obtained integral equations which describe all essentially different invariant solutions of the Leith equation with or without viscosity. The integral equations defining these solutions reveal new possibilities for analytical and numerical studies. In these equations, the presence of arbitrary constants allows one to solve them for different boundary conditions. We have proved existence and uniqueness for such boundary value problems.
Ключевые слова: group analysis; Invariant solutions; nonlinear diffusion in heterogeneous environment; turbulence; Kolmogorov spectrum;
Издано: 2014
Физ. характеристика: 185501
Цитирование: 
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