Blowup as a driving mechanism of turbulence in shell models.
Phys Rev E Stat Nonlin Soft Matter Phys
; 87(5): 053011, 2013 May.
Article
em En
| MEDLINE
| ID: mdl-23767624
Since Kolmogorov proposed his phenomenological theory of hydrodynamic turbulence in 1941, the description of the mechanism leading to the energy cascade and anomalous scaling remains an open problem in fluid mechanics. Soon after, in 1949, Onsager noticed that the scaling properties in the inertial range imply nondifferentiability of the velocity field in the limit of vanishing viscosity. This observation suggests that the turbulence mechanism may be related to a finite-time singularity (blowup) of incompressible Euler equations. However, the existence of such blowup is still an open problem too. In this paper, we show that the blowup indeed represents the driving mechanism of the inertial range for a simplified (shell) model of turbulence. Here, blowups generate coherent structures (instantons), which travel through the inertial range in finite time and are described by universal self-similar statistics. The anomaly (deviation of scaling exponents of velocity moments from the Kolmogorov theory) is related analytically to the process of instanton creation using the large deviation principle. The results are confirmed by numerical simulations.
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Base de dados:
MEDLINE
Assunto principal:
Reologia
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Modelos Estatísticos
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Dinâmica não Linear
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Hidrodinâmica
Tipo de estudo:
Qualitative_research
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Risk_factors_studies
Idioma:
En
Revista:
Phys Rev E Stat Nonlin Soft Matter Phys
Assunto da revista:
BIOFISICA
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FISIOLOGIA
Ano de publicação:
2013
Tipo de documento:
Article
País de afiliação:
Brasil
País de publicação:
Estados Unidos