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Weak turbulence in two-dimensional magnetohydrodynamics

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Tronko, N., Nazarenko, Sergey and Galtier, S. (2013) Weak turbulence in two-dimensional magnetohydrodynamics. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Volume 87 (Number 3). Article number 033103. doi:10.1103/PhysRevE.87.033103

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Official URL: http://dx.doi.org/10.1103/PhysRevE.87.033103

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Abstract

A weak wave turbulence theory is developed for two-dimensional (2D) magnetohydrodynamics. We derive and analyze the kinetic equation describing the three-wave interactions of pseudo-Alfvén waves. Our analysis is greatly helped by the fortunate fact that in 2D the wave kinetic equation is integrable. In contrast with the three-dimensional case, in 2D the wave interactions are nonlocal. Another distinct feature is that strong derivatives of spectra tend to appear in the region of small parallel (i.e., along the uniform magnetic field direction) wave numbers leading to a breakdown of the weak-turbulence description in this region. We develop a qualitative theory beyond weak turbulence describing subsequent evolution and formation of a steady state.

Item Type: Journal Article
Divisions: Faculty of Science > Mathematics
Journal or Publication Title: Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
Publisher: American Physical Society
ISSN: 1539-3755
Official Date: 2013
Dates:
DateEvent
2013Published
Volume: Volume 87
Number: Number 3
Page Range: Article number 033103
DOI: 10.1103/PhysRevE.87.033103
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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