| Инд. авторы: | Grebenev V.N., Nazarenko S.V., Medvedev S.B., Schwab I.V., Chirkunov Y.A. |
| Заглавие: | Self-similar solution in the Leith model of turbulence: Anomalous power law and asymptotic analysis |
| Библ. ссылка: | Grebenev V.N., Nazarenko S.V., Medvedev S.B., Schwab I.V., Chirkunov Y.A. Self-similar solution in the Leith model of turbulence: Anomalous power law and asymptotic analysis // Journal of Physics A: Mathematical and Theoretical. - 2014. - Vol.47. - Iss. 2. - Art.025501. - ISSN 1751-8113. - EISSN 1751-8121. |
| Внешние системы: | DOI: 10.1088/1751-8113/47/2/025501; РИНЦ: 21862222; SCOPUS: 2-s2.0-84891364597; WoS: 000329041500018; |
| Реферат: | eng: We consider a Leith model of turbulence (Leith C 1967 Phys. Fluids 10 1409) in which the energy spectrum obeys a nonlinear diffusion equation. We analytically prove the existence of a self-similar solution with a power-law asymptotic on the low-wavenumber end and a sharp boundary on the high-wavenumber end, which propagates to infinite wavenumbers in a finite-time t(*). We prove that this solution has a power-law asymptotic with an anomalous exponent x*, which is less than the Kolmogorov value, x* > 5/3. This is a result that was previously discovered by numerical simulations in Connaughton and Nazarenko (2004 Phys. Rev. Lett. 92 044501). We also prove the convergence to this self-similar solution of the spectrum evolving from an arbitrary finitely supported initial data as t -> t*.
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| Издано: | 2014 |
| Физ. характеристика: | 025501, с.025501 |
