| Инд. авторы: | Bell N.K., Grebenev V.N., Medvedev S.B., Nazarenko S.V. |
| Заглавие: | Self-similar evolution of Alfven wave turbulence |
| Библ. ссылка: | Bell N.K., Grebenev V.N., Medvedev S.B., Nazarenko S.V. Self-similar evolution of Alfven wave turbulence // Journal of Physics A: Mathematical and Theoretical. - 2017. - Vol.50. - Iss. 43. - Art.435501. - ISSN 1751-8113. - EISSN 1751-8121. |
| Внешние системы: | DOI: 10.1088/1751-8121/aa8bd9; РИНЦ: 31079556; SCOPUS: 2-s2.0-85031013963; WoS: 000412212200001; |
| Реферат: | eng: We study self-similar solutions of the kinetic equation for MHD wave turbulence derived in (Galtier S et al 2000 J. Plasma Phys. 63 447-88). Motivated by finding the asymptotic behaviour of solutions for initial value problems, we formulate a nonlinear eigenvalue problem comprising in finding a number x ∗such that the self-similar shape function f(η)would have a power-law asymptotic η-x∗ at low values of the self-similar variable η and would be the fastest decaying positive solution at η → ∞. We prove that the solution f(η)of this problem has a tail decaying as a power-law, and not exponentially or super-exponentially. We present a relationship between the power-law exponents in the regions η → 0 and η → ∞, and an integral relation for f(η) x ∗ and . We confirm these relationships by solving numerically the nonlinear eigenvalue problem, and find that x∗ ≈ 3.80. © 2017 IOP Publishing Ltd.
|
| Ключевые слова: | numerical simulation; Alfven wave turbulence; power-law asymptotic; self-similar solution; |
| Издано: | 2017 |
| Физ. характеристика: | 435501 |
| Цитирование: | 1. Galtier S, Nazarenko S V, Newell A C and Pouquet A 2000 A weak turbulence theory for incompressible MHD J. Plasma Phys. 63 447-88
2. Nazarenko S V 2011 Wave Turbulence (Berlin: Springer)
3. Galtier S 2013 Wave turbulence in astrophysics Advances in Wave Turbulence vol 83 (New Jersey, London, Geneva: World Scientific Publishing) p 73
4. Connaughton C and Nazarenko S 2004 Warm cascade and anomalous scaling in a diffusion model of turbulence Phys. Rev. Lett. 92 044501-506
5. Connaughton C and Nazarenko S 2004 A model equation for turbulence (arXiv:physics/0304044)
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. Thalabard S, Nazarenko S V, Galtier S and Medvedev S B 2015 Anomalous spectral laws in differential models of turbulence J. Phys. A: Math. Theor. 48 285501
8. Leith C 1967 Diffusion approximation to inertial energy transfer in isotropic turbulence Phys. Fluids 10 1409
9. Zel'dovich Y B 1956 The motion of a gas under the action of short term pressure shock Sov. Phys. Acoust. 2 25-36
10. Zeldovich Ya B and Raizer Yu P 1966 Physiscs of Shock-Waves and High-Temperature Phenomena vol 2 (New York: Academic) p 157
11. Leith C E and Kraichnan R H 1972 Predictability of turbulent flows J. Atmos. Sci. 29 10411-71058
|
