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Self-similar formation of the Kolmogorov spectrum in the Leith model of turbulence
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Nazarenko, Sergey and Grebenev, V. N. (2016) Self-similar formation of the Kolmogorov spectrum in the Leith model of turbulence. Journal of Physics A: Mathematical and Theoretical, 50 (3). 035501. doi:10.1088/1751-8121/50/3/035501 ISSN 1751-8113.
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Official URL: https://doi.org/10.1088/1751-8121/50/3/035501
Abstract
The last stage of evolution toward the stationary Kolmogorov spectrum of hydrodynamic turbulence is studied using the Leith model [1] . This evolution is shown to manifest itself as a reflection wave in the wavenumber space propagating from the largest toward the smallest wavenumbers, and is described by a self-similar solution of a new (third) kind. This stage follows the previously studied stage of an initial explosive propagation of the spectral front from the smallest to the largest wavenumbers reaching arbitrarily large wavenumbers in a finite time, and which was described by a self-similar solution of the second kind [2, 3, 4]. Nonstationary solutions corresponding to“warm cascades” characterised by a thermalised spectrum at large wavenumbers are also obtained.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Turbulence -- Hydrodynamics | ||||||
| Journal or Publication Title: | Journal of Physics A: Mathematical and Theoretical | ||||||
| Publisher: | IOP Publishing Ltd | ||||||
| ISSN: | 1751-8113 | ||||||
| Official Date: | 9 December 2016 | ||||||
| Dates: |
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| Volume: | 50 | ||||||
| Number: | 3 | ||||||
| Article Number: | 035501 | ||||||
| DOI: | 10.1088/1751-8121/50/3/035501 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Date of first compliant deposit: | 8 October 2018 | ||||||
| Date of first compliant Open Access: | 8 October 2018 | ||||||
| RIOXX Funder/Project Grant: |
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