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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 ISSN 1751-8113.

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Official URL: http://dx.doi.org/10.1088/1751-8113/49/36/365501

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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, Engineering and Medicine > 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:
DateEvent
17 August 2016Published
25 August 2016Accepted
1 April 2016Submitted
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
Date of first compliant deposit: 25 August 2016
Date of first compliant Open Access: 25 August 2016
Funder: Engineering and Physical Sciences Research Council (EPSRC)
Grant number: Grant : Fluctuation-driven phenomena and large deviations

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