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*.
Издано:	2014
Физ. характеристика:	025501, с.025501