Can Hall effect trigger Kelvin-Helmholtz instability in sub-Alfvénic flows?

B. P. Pandey*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    6 Citations (Scopus)
    23 Downloads (Pure)

    Abstract

    In the Hall magnetohydrodynamics, the onset condition of the Kelvin-Helmholtz instability is solely determined by the Hall effect and is independent of the nature of shear flows. In addition, the physical mechanism behind the super- and sub-Alfvénic flows becoming unstable is quite different: the high-frequency right circularly polarized whistler becomes unstable in the super-Alfvénic flows whereas low-frequency, left circularly polarized ioncyclotron wave becomes unstable in the presence of sub-Alfvénic shear flows. The growth rate of theKelvin-Helmholtz instability in the super-Alfvénic case is higher than the corresponding ideal magnetohydrodynamic rate. In the sub-Alfvénic case, the Hall effect opens up a new, hitherto inaccessible (to the magnetohydrodynamics) channel through which the partially or fully ionized fluid can become Kelvin-Helmholtz unstable. The instability growth rate in this case is smaller than the super-Alfvénic case owing to the smaller free shear energy content of the flow. When the Hall term is somewhat smaller than the advection term in the induction equation, the Hall effect is also responsible for the appearance of a new overstable mode whose growth rate is smaller than the purely growing Kelvin-Helmholtz mode. On the other hand, when the Hall diffusion dominates the advection term, the growth rate of the instability depends only on the Alfvén -Mach number and is independent of the Hall diffusion coefficient. Further, the growth rate in this case linearly increases with the Alfvén frequency with smaller slope for sub-Alfvénic flows.

    Original languageEnglish
    Pages (from-to)344-353
    Number of pages10
    JournalMonthly Notices of the Royal Astronomical Society
    Volume476
    Issue number1
    DOIs
    Publication statusPublished - 1 May 2018

    Bibliographical note

    Copyright 2018 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. First published in Monthly Notices of the Royal Astronomical Society, 476(1), pp.344–353. The original publication is available at https://doi.org/10.1093/mnras/sty201. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

    Keywords

    • Earth
    • Instabilities
    • MHD
    • Protoplanetary discs
    • Sun: atmosphere
    • waves

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