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Weak turbulence in two-dimensional magnetohydrodynamics

TitleWeak turbulence in two-dimensional magnetohydrodynamics
Publication TypeJournal Article
Year of Publication2013
AuthorsTronko, N, Nazarenko, SV, Galtier, S
JournalPhysical Review EPhysical Review E
Date PublishedMarch 1, 2013
ISBN Number1063-651X
KeywordsMagnetohydrodynamics, Magnetohydrodynamics and electrohydrodynamics, Magnetohydrodynamics and plasmas, Turbulence simulation and modeling

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.

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