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13 - Nonlinear Aspects

Published online by Cambridge University Press:  15 July 2019

Bernard Roberts
Affiliation:
University of St Andrews, Scotland
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Summary

Nonlinear aspects of wave propagation are investigated. Special attention is given to magnetic slabs and tubes, deriving the Benjamin-Ono equation for the slow mode in a slab and the Leibovich-Roberts equation for the slow mode in a tube. Soliton solutions are obtained and illustrated under various solar conditions. The role of Whitham’s equation is explored. Dissipative effects are also added, and shown to lead to the Benjamin-Ono-Burgers equation. Approximate solutions are given and illustrated for solar conditions. The roles of viscous and thermal damping of weakly nonlinear slow waves (sound waves) are also explored, and the effect of gravity is examined. Both standing waves and propagating waves are looked at. Finally, the nonlinear kink mode is presented.

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Publisher: Cambridge University Press
Print publication year: 2019

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  • Nonlinear Aspects
  • Bernard Roberts, University of St Andrews, Scotland
  • Book: MHD Waves in the Solar Atmosphere
  • Online publication: 15 July 2019
  • Chapter DOI: https://doi.org/10.1017/9781108613774.014
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  • Nonlinear Aspects
  • Bernard Roberts, University of St Andrews, Scotland
  • Book: MHD Waves in the Solar Atmosphere
  • Online publication: 15 July 2019
  • Chapter DOI: https://doi.org/10.1017/9781108613774.014
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Nonlinear Aspects
  • Bernard Roberts, University of St Andrews, Scotland
  • Book: MHD Waves in the Solar Atmosphere
  • Online publication: 15 July 2019
  • Chapter DOI: https://doi.org/10.1017/9781108613774.014
Available formats
×