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Steady states in Leith's model of turbulence
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Grebenev, V. N., Griffin, Adam, Medvedev, S. B. and Nazarenko, Sergey (2016) Steady states in Leith's model of turbulence. Journal of Physics A : Mathematical and Theoretical, 49 (36). doi:10.1088/1751-8113/49/36/365501
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Official URL: http://dx.doi.org/10.1088/1751-8113/49/36/365501
Abstract
We present a comprehensive study and full classification of the stationary solutions in Leith's model of turbulence with a generalised viscosity. Three typical types of boundary value problems are considered: Problems 1 and 2 with a finite positive value of the spectrum at the left (right) and zero at the right (left) boundaries of a wave number range, and Problem 3 with finite positive values of the spectrum at both boundaries. Settings of these problems and analysis of existence of their solutions are based on a phase–space analysis of orbits of the underlying dynamical system. One of the two fixed points of the underlying dynamical system is found to correspond to a 'sharp front' where the energy flux and the spectrum vanish at the same wave number. The other fixed point corresponds to the only exact power-law solution—the so-called dissipative scaling solution. The roles of the Kolmogorov, dissipative and thermodynamic scaling, as well as of sharp front solutions, are discussed.
| Item Type: | Journal Article | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QC Physics | ||||||||
| Divisions: | Faculty of Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Turbulent boundary layer, Viscosity | ||||||||
| Journal or Publication Title: | Journal of Physics A : Mathematical and Theoretical | ||||||||
| Publisher: | Institute of Physics Publishing Ltd. | ||||||||
| ISSN: | 1751-8113 | ||||||||
| Official Date: | 17 August 2016 | ||||||||
| Dates: |
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| Volume: | 49 | ||||||||
| Number: | 36 | ||||||||
| DOI: | 10.1088/1751-8113/49/36/365501 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||||||
| Grant number: | Grant : Fluctuation-driven phenomena and large deviations |
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