Nonlinear and three-wave resonant interactions in magnetohydrodynamics

G. M. Webb, A. R. Zakharian, Moysey Brio, G. P. Zank

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

Hamiltonian and variational formulations of equations describing weakly nonlinear magnetohydrodynamic (MHD) wave interactions in one Cartesian space dimension are discussed. For wave propagation in uniform media, the wave interactions of interest consist of (a) three-wave resonant interactions in which high-frequency waves may evolve on long space and time scales if the wave phases satisfy the resonance conditions; (b) Burgers self-wave steepening for the magnetoacoustic waves, and (c) mean wave field effects, in which a particular wave interacts with the mean wave field of the other waves. The equations describe four types of resonant triads: slow-fast magnetoacoustic wave interaction, Alfven-entropy wave interaction, Alfven-magnetoacoustic wave interaction, and magnetoacoustic-entropy wave interaction. The formalism is restricted to coherent wave interactions. The equations are used to investigate the Alfven-wave decay instability in which a large-amplitude forward propagating Alfven wave decays owing to three-wave resonant interaction with a backward-propagating Alfven wave and a forward-propagating slow magnetoacoustic wave. Exact solutions of the equations for Alfven-entropy wave interactions are also discussed.

Original languageEnglish (US)
Pages (from-to)393-445
Number of pages53
JournalJournal of Plasma Physics
Volume63
Issue number5
StatePublished - Jun 2000

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wave interaction
magnetohydrodynamics
magnetoacoustic waves
magnetohydrodynamic waves
interactions
entropy
magnetoacoustics
decay
wave propagation
formalism
formulations

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics

Cite this

Webb, G. M., Zakharian, A. R., Brio, M., & Zank, G. P. (2000). Nonlinear and three-wave resonant interactions in magnetohydrodynamics. Journal of Plasma Physics, 63(5), 393-445.

Nonlinear and three-wave resonant interactions in magnetohydrodynamics. / Webb, G. M.; Zakharian, A. R.; Brio, Moysey; Zank, G. P.

In: Journal of Plasma Physics, Vol. 63, No. 5, 06.2000, p. 393-445.

Research output: Contribution to journalArticle

Webb, GM, Zakharian, AR, Brio, M & Zank, GP 2000, 'Nonlinear and three-wave resonant interactions in magnetohydrodynamics', Journal of Plasma Physics, vol. 63, no. 5, pp. 393-445.
Webb, G. M. ; Zakharian, A. R. ; Brio, Moysey ; Zank, G. P. / Nonlinear and three-wave resonant interactions in magnetohydrodynamics. In: Journal of Plasma Physics. 2000 ; Vol. 63, No. 5. pp. 393-445.
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