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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
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: |
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| 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: |
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