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Effect of Transverse Magnetic Field on Stability of Plane Poiseuille Magnetohydrodynamic Flow

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Asymptotic and transient instability in magnetohydrodynamic channel flow in the presence of a uniform wall normal magnetic field is analysed. It is found that the magnetic field affects the asymptotic instability by leading to an exponential increase in the critical Reynolds number with the magnetic field strength. The transient growth is computed using the method of Singular Value Decomposition applied to a modified Orr-Sommerfeld and modified Squire system which are derived from the Navier-Stokes and constitutive electromagnetic equations. The magnetic field leads to a damping of the transient growth and an increase in the spanwise wavenumber which gives maximum energy amplification for a given Reynolds number. It is also found to affect the shape of the optimal perturbations by leading to a decrease in the centreline velocity of the optimal wall-normal velocity perturbation.

Author(s):

Vivek Subramaniam    
Indian Institute of Technology, Madras
India

Pranav Kamat    
Indian Institute of Technology, Madras
India

Sameen A    
Indian Institute of Technology, Madras
India