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Anomalous spectral laws in differential models of turbulence

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Thalabard, Simon, Nazarenko, Sergey, Galtier, Sébastien and Medvedev, Sergey (2015) Anomalous spectral laws in differential models of turbulence. Journal of Physics A: Mathematical and Theoretical, 48 (28). 285501. doi:10.1088/1751-8113/48/28/285501

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Official URL: http://dx.doi.org/10.1088/1751-8113/48/28/285501

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Abstract

Differential models for hydrodynamic, passive-scalar and wave turbulence given by nonlinear first- and second-order evolution equations for the energy spectrum in the k-space were analysed. Both types of models predict formation an anomalous transient power-law spectra. The second-order models were analysed in terms of self-similar solutions of the second kind, and a phenomenological formula for the anomalous spectrum exponent was constructed using numerics for a broad range of parameters covering all known physical examples. The first-order models were examined analytically, including finding an analytical prediction for the anomalous exponent of the transient spectrum and description of formation of the Kolmogorov-type spectrum as a reflection wave from the dissipative scale back into the inertial range. The latter behaviour was linked to pre-shock/shock singularities similar to the ones arising in the Burgers equation. Existence of the transient anomalous scaling and the reflection-wave scenario are argued to be a robust feature common to the finite-capacity turbulence systems. The anomalous exponent is independent of the initial conditions but varies for for different models of the same physical system.

Item Type: Journal Article
Divisions: Faculty of Science > Mathematics
Journal or Publication Title: Journal of Physics A: Mathematical and Theoretical
Publisher: IOP Publishing Ltd
ISSN: 1751-8113
Official Date: 24 June 2015
Dates:
DateEvent
20 February 2015Submitted
28 May 2015Accepted
24 June 2015Published
Volume: 48
Number: 28
Article Number: 285501
DOI: 10.1088/1751-8113/48/28/285501
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Open Access Version:
  • ArXiv

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