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Ideal MHD Instabilities, with a Focus on the Rayleigh–Taylor and Kelvin–Helmholtz Instabilities

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Topics in Magnetohydrodynamic Topology, Reconnection and Stability Theory

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 591))

Abstract

In this chapter we focus on the magnetohydrodynamic (MHD) versions of the Rayleigh–Taylor and Kelvin–Helmholtz instabilities, taking the reader beyond the commonly presented situations to include how extra physics influences the stability of the models. After a discussion of the physical processes behind each instability we look at the general framework behind the study of ideal MHD instabilities, providing a detailed look at the derivation of the dispersion relation for a simple model. Extensions to this model are presented, including an investigation into how stability changes in the presence of a time-varying flow. Finally, we take a look at how nonlinearities develop and the role of the MHD in terms of the development of these nonlinearities.

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Acknowledgements

Andrew Hillier is supported by his STFC Ernest Rutherford Fellowship grant number ST/L00397X/2 and STFC research grant ST/R000891/1. This work used the COSMA Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This equipment was funded by a BIS National E-infrastructure capital grant ST/K00042X/1, DiRAC Operations grant ST/K003267/1 and Durham University. DiRAC is part of the UK National E-Infrastructure.

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  1. College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, UK

    Andrew Hillier

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  1. Andrew Hillier
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Correspondence to Andrew Hillier .

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Editors and Affiliations

  1. School of Mathematics and Statistics, University of Glasgow, Glasgow, UK

    David MacTaggart

  2. College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, UK

    Andrew Hillier

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Hillier, A. (2020). Ideal MHD Instabilities, with a Focus on the Rayleigh–Taylor and Kelvin–Helmholtz Instabilities. In: MacTaggart, D., Hillier, A. (eds) Topics in Magnetohydrodynamic Topology, Reconnection and Stability Theory. CISM International Centre for Mechanical Sciences, vol 591. Springer, Cham. https://doi.org/10.1007/978-3-030-16343-3_1

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  • DOI: https://doi.org/10.1007/978-3-030-16343-3_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-16342-6

  • Online ISBN: 978-3-030-16343-3

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