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Self-similar evolution of Alfven wave turbulence

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Bell, Nicholas, Grebenev, V. N., Medvedev, Sergey and Nazarenko, Sergey (2017) Self-similar evolution of Alfven wave turbulence. Journal of Physics A: Mathematical and Theoretical, 50 (43). 435501. doi:10.1088/1751-8121/aa8bd9 ISSN 1751-8113.

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Official URL: https://doi.org/10.1088/1751-8121/aa8bd9

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Abstract

We study self-similar solutions of the kinetic equation for MHD wave
turbulence derived in [1]. Motivated by finding the asymptotic behaviour of solutions for initial value problems, we formulate a nonlinear eigenvalue problem comprising in finding a number x ∗ such that the self-similar shape function f(η) would have a powerlaw asymptotic η−x∗ at low values of the self-similar variable η and would be the fastest decaying positive solution at η → ∞. We prove that the solution f(η) of this problem has a tail decaying as a power-law, and not exponentially or super-exponentially. We present a relationship between the power-law exponents in the regions η → 0 and η → ∞, and an integral relation for f(η) and x. We confirm these relationships by solving numerically the nonlinear eigenvalue problem, and find that x ∗ ≈ 3.80.

Item Type: Journal Article
Subjects: Q Science > QC Physics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Magnetohydrodynamic waves, Turbulence
Journal or Publication Title: Journal of Physics A: Mathematical and Theoretical
Publisher: IOP Publishing Ltd
ISSN: 1751-8113
Official Date: 29 September 2017
Dates:
DateEvent
29 September 2017Published
12 September 2017Accepted
Volume: 50
Number: 43
Article Number: 435501
DOI: 10.1088/1751-8121/aa8bd9
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 3 October 2017
Date of first compliant Open Access: 29 September 2018
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
1499213[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
Symposium 2015/2016 Fluctuation-driven phenomena and large deviations[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
Symposium 2015/2016 Fluctuation-driven phenomena and large deviations[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266

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