Optimised wave perturbation for the linear instability of magnetohydrodynamics in plane Poiseuille flow

Abstract

In this work, linear stability of an electrically conductive fluid experiencing Poiseuille flow for minimum Reynolds value under a normal magnetic field is analysed using the Chebyshev collocation method. The neutral curves of linear instability are derived by utilising Qualitat and Zuverlassigkeit (QZ) method. Instability of the magnetohydrodynamics for plane Poiseuille flow is introduced by solving the generalised Orr–Sommerfeld equation to determine the growth rates, wave number and spatial shapes of the eigenmodes. To solve linear problems, we use numerical methods which help us at each time step of the simulation, uncoupled by physical processes, which can improve the computational performance. This article provides the stability and error analysis, presents a concise study of the Poiseuille flow, and produces computational tests to support the given theory.

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Correspondence to Muhammad Shahzad.

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Hussain, Z., Ali, M., Shahzad, M. et al. Optimised wave perturbation for the linear instability of magnetohydrodynamics in plane Poiseuille flow. Pramana - J Phys 94, 49 (2020). https://doi.org/10.1007/s12043-019-1900-6

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Keywords

  • Computational fluid dynamics
  • instability
  • magnetohydrodynamics
  • Chebyshev collocation method
  • electrically conducting fluid

PACS Nos

  • 47.10.A−
  • 47.11.−j
  • 47.20.−k
  • 47.15.−x