Article information

2014 , Volume 19, 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 G.G.
PhD. , Associate Professor
Position: Research Scientist
Office: Institute of computational mathematics and mathematical geophisics SB RAS
Address: 630090, Russia, Novosibirsk, Ac. Laverntiev ave., 6
Phone Office: (383) 330 89 94
E-mail: lazareva@ssd.sscc.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: 7427-5210

Medvedev 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. P. 63-73
Home| Scope| Editorial Board| Content| Search| Subscription| Rules| Contacts
ISSN 1560-7534
© 2019 Institute of Computational Technologies SB RAS