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Linear global stability of a flow past a sphere under a streamwise magnetic field

Published online by Cambridge University Press:  30 August 2023

Xiao-Lin Zheng ,
Jun-Hua Pan Open the ORCID record for Jun-Hua Pan [Opens in a new window]  and
Ming-Jiu Ni Open the ORCID record for Ming-Jiu Ni [Opens in a new window]
Xiao-Lin Zheng
Affiliation:
School of Engineering Science, University of Chinese Academy of Sciences, Beijing 101408, PR China
Jun-Hua Pan
Affiliation:
School of Engineering Science, University of Chinese Academy of Sciences, Beijing 101408, PR China
Ming-Jiu Ni*
Affiliation:
School of Engineering Science, University of Chinese Academy of Sciences, Beijing 101408, PR China
*
†Email address for correspondence: mjni@ucas.ac.cn
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Abstract

The global linear stability analysis for the magnetohydrodynamic liquid metal flow past an insulated sphere subjected to a constant streamwise magnetic field is investigated in the range of the Reynolds number $Re\leq 400$ and the interaction number $N\leq 40$ coupled with direct numerical simulations, where $N$ stands for strength of the electromagnetic force. The stability of the steady axisymmetric base flow to independent time-azimuthal modes is discussed. Five critical curves associated with various wake transitions are obtained in the $\{Re, N\}$ phase diagram. These critical curves reveal the stabilising effect of a weak magnetic field, the destabilising effect of a strong magnetic field and re-stabilising effect of a much stronger magnetic field. To explore the impact of the magnetic field on flow instability, a sensitivity analysis utilizing an adjoint method is performed for the first regular bifurcation. Sensitivity functions of growth rate to base-flow modifications and Lorentz force are defined to identify the region that has the most significant influence on flow instability, such as the recirculation region responsible for the stabilising effect at a weak magnetic field and the shear layer region responsible for the destabilising effect at a strong magnetic field. Furthermore, a competition between the stabilising and shear destabilising effects of the magnetic field is discussed. This analysis provides valuable insights into the non-monotonic effect of the magnetic field on flow instability.

JFM classification

Instability: Absolute/convective instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 970 , 10 September 2023 , A16
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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Footnotes

‡

These authors contributed equally to this work and should be considered co-first authors.

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