### 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 language | English (US) |
---|---|

Pages (from-to) | 393-445 |

Number of pages | 53 |

Journal | Journal of Plasma Physics |

Volume | 63 |

Issue number | 5 |

State | Published - Jun 2000 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*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.

Research output: Contribution to journal › Article

*Journal of Plasma Physics*, vol. 63, no. 5, pp. 393-445.

}

TY - JOUR

T1 - Nonlinear and three-wave resonant interactions in magnetohydrodynamics

AU - Webb, G. M.

AU - Zakharian, A. R.

AU - Brio, Moysey

AU - Zank, G. P.

PY - 2000/6

Y1 - 2000/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0034196202&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034196202&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0034196202

VL - 63

SP - 393

EP - 445

JO - Journal of Plasma Physics

JF - Journal of Plasma Physics

SN - 0022-3778

IS - 5

ER -