| 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.
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| Ключевые слова: | group analysis; Invariant solutions; nonlinear diffusion in heterogeneous environment; turbulence; Kolmogorov spectrum; |
| Издано: | 2014 |
| Физ. характеристика: | 185501 |
| Цитирование: | 1. Leith C 1967 Diffusion approximation to inertial energy transfer in isotropic turbulence Phys. Fluids 10 1409-16
2. Connaughton C and Nazarenko S V 2004 Warm cascade and anomalous scaling in a diffusion model of turbulence Phys. Rev. Lett. 92 044501
3. Connaughton C and Nazarenko S V 2004 A model equation for turbulence arXiv:physics/0304044
4. Galtier S, Nazarenko S V, Newell A C and Pouquet A J 2000 A weak turbulence theory for incompressible magnetohydrodynamics J. Plasma Phys. 63 447-88
5. Connaughton C and Newell A C 2010 Dynamical scaling and the finite-capacity anomaly in three-wave turbulence Phys. Rev. E 81 036303
6. Grebenev V N, Nazarenko S V, Medvedev S B, Schwab I V and Chirkunov Y A 2014 Self-similar solution in Leith model of turbulence: anomalous power law and asymptotic analysis J. Phys. A: Math. Theor. 47 025501
7. Bos W J T, Connaughton C and Godeferd F 2012 Developing homogeneous isotropic turbulence Physica D 241 232-36
8. L'vov V S and Nazarenko S V 2006 Differential model for 2D turbulence JETP Lett. 83 541-5
9. Besnard D, Harlow F, Rauenzahn R and Zemach C 1996 Transport equations for the reynolds stress tensor Theor. Comput. Fluid Dyn. 8 148-64
10. Adzhemyan L T and Antonov N V 1998 Renormalization group in turbulence theory: exactly solvable Heisenberg model Theor. Math. Phys. 115 562-74
11. Chen L-Y, Goldenfeld N and Oono Y 1996 Renormalization group and singular perturbations: multiple scales, bounadry layers, and reductive perturbation theory Phys. Rev. E 54 376-94
12. Kovalev V F 2008 Renormalization-group symmetries for solutions of nonlinear boundary value problems Phys.-Usp. 51 815-30
13. Zeldovich Y B and Raizer Y P 1966 Physics of Shock-waves and High-Temperature Phenomena vol 2 (New York: Academic) p 157
14. Grundy R E 2004 Large time solution of an inhomogeneous nonlinear diffusion equation Proc. R. Soc. Lond. A 386 347-72
15. Ovsiannikov L V 1982 Group Analysis of Differential Equations (New York: Academic) p 416 xvi +
16. Chirkunov Y A and Khabirov S V 2012 The Elements of Symmetry Analysis of Differential Equations of Continuous Medium Mechanics (Novosibirsk: NSTU) p 659 (in Russian)
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