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Article information
2014 , Volume 19, ¹ 1, p.63-73
Grebenev V.N., Nazarenko S.V., Shvab I.V., Chirkunov Y.A., Lazareva G.G., Shtyrina O.V., Medvedev S.B.
Self-similar solution to Leith's model for the spectral density of turbulence
In this paper we study a phenomenological turbulence model suggested in [1] in which the energy spectrum obeys a nonlinear diffusion equation. This equation meets the scaling properties of the original Navier-Stokes equation and it has the Kolmogorov -5/3 cascade and the thermodynamic equilibrium as steady-state solutions. The general steady state in this model contains a nonlinear mixture of the constant-flux and thermodynamic components. As it was shown in [1] such "warm cascade" solutions describe the so-called bottleneck phenomenon of spectrum stagnation near the dissipative scale. Transient self-similar solutions describing a finite-time formation of steady cascade were investigated numerically in [1],[8] in the inviscid case with vanishing external forcing. This analysis showed a nontrivial scaling behavior and the finite time formation for the steady state cascade states. In this paper we proved the existence of the transient self-similar solutions.
[full text]
Keywords: turbulence, Kolmogorov spectr, thermodynamic equilibrium, self-similar solutions, heteroclinic orbit
Author(s):
Grebenev V N
Dr.
Position: Senior Research Scientist
Office: Institute of computational technologies SB RAS
Address: 630090, Russia, Novosibirsk, prospect Akademika Lavrentyeva, 6
Phone Office: (383)3308570
E-mail: vova@lchd.ict.nsc.ru
Nazarenko Sergey Vitalyevich
PhD.
Position: Professor
Office: Mathematics Institute University of Warwick
Address: United kingdom, Warwik, Novosibirsk, prospect Akademika Lavrentyeva, 6
Shvab I V
Office: Institute of Computational Tehcnologies SB RAS
Address: Russia, Novosibirsk, Novosibirsk, prospect Akademika Lavrentyeva, 6
E-mail: shva@ict.nsc.ru
Chirkunov Yuri Alexandrovich
Dr. , Associate Professor
Position: Professor
Office: Novosibirsk Technical University
Address: 630092, Russia, Novosibirsk, Lavrentjev avenue 6
E-mail: chrl0l@mail.ru
Lazareva Galina Gennadievna
Dr. , Correspondent member of RAS, Professor
Office: Peoples Friendship University of Russia
Address: 117198, Russia, Moscow, 6, Miklukho-Maklaya Street
E-mail: lazareva-gg@rudn.ru
Shtyrina Olga Vladimirovna
PhD.
Position: Research Scientist
Office: Institute of Computational Technologies SB RAS
Address: 633190, Russia, Novosibirsk, Larentiev aven. 6
Phone Office: (3832) 309772
E-mail: olya.shtyrina@gmail.com
SPIN-code: 7427-5210Medvedev Sergey Borisovich
Dr.
Position: Leading research officer
Office: Inctitute of Computational Technologies SB RAS
Address: 630090, Russia, Novosibirsk, Ac. Lavrentyev ave., 6
Phone Office: (383) 330-73-73
E-mail: serbormed@gmail.com
SPIN-code: 2140-1726
Bibliography link:
Grebenev V.N., Nazarenko S.V., Shvab I.V., Chirkunov Y.A., Lazareva G.G., Shtyrina O.V., Medvedev S.B. Self-similar solution to Leith's model for the spectral density of turbulence // Computational technologies. 2014. V. 19. ¹ 1. P. 63-73
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