Bifurcation contrasts between plane Poiseuille flow and plane Magnetohydrodynamic flow

  • Benjamin Tocher

Student thesis: Doctoral ThesisDoctor of Philosophy

Abstract

The stability characteristics of an incompressible viscous pressure-driven flow of an electrically
conducting fluid between two parallel boundaries in the presence of a transverse magnetic field are compared and contrasted with those of Plane Poiseuille flow (PPF).
Assuming that the outer regions adjacent to the fluid layer are perfectly electrically insulating,
the appropriate boundary conditions are applied. The eigenvalue problems are then
solved numerically to obtain the critical Reynolds number Rec and the critical wave number
ac in the limit of small Hartmann number (M) range to produce the curves of marginal stability. The non-linear two-dimensional travelling waves that bifurcate by way of a Hopf bifurcation from the neutral curves are approximated by a truncated Fourier series in the
streamwise direction. Two and three dimensional secondary disturbances are applied to
both the constant pressure and constant flux equilibrium solutions using Floquet theory as this is believed to be the generic mechanism of instability in shear flows. The change in shape of the undisturbed velocity profile caused by the magnetic field is found to be the dominant factor. Consequently the critical Reynolds number is found to increase rapidly with increasing M so the transverse magnetic field has a powerful stabilising effect on this type of flow.
Date of Award2013
Original languageEnglish
SupervisorSotos Generalis (Supervisor)

Keywords

  • plane Poiseuille flow
  • Reynolds number
  • Hartmann number
  • travelling waves
  • secondary solutions
  • Fourier series
  • Chebyshev series
  • Floquet theory

Cite this

Bifurcation contrasts between plane Poiseuille flow and plane Magnetohydrodynamic flow
Tocher, B. (Author). 2013

Student thesis: Doctoral ThesisDoctor of Philosophy