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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:doi: 10.1088/1751-8121/aa8bd9
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Official URL: https://doi.org/10.1088/1751-8121/aa8bd9
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 | ||||||||||||
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| 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: |
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| Volume: | 50 | ||||||||||||
| Number: | 43 | ||||||||||||
| Article Number: | 435501 | ||||||||||||
| DOI: | doi: 10.1088/1751-8121/aa8bd9 | ||||||||||||
| Status: | Peer Reviewed | ||||||||||||
| Publication Status: | Published | ||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
| RIOXX Funder/Project Grant: |
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