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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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:	Date Event 29 September 2017 Published 12 September 2017 Accepted
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 ID RIOXX Funder Name Funder ID 1499213 [EPSRC] Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266 Symposium 2015/2016 Fluctuation-driven phenomena and large deviations [EPSRC] Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266 Symposium 2015/2016 Fluctuation-driven phenomena and large deviations [EPSRC] Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266

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