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1 International Journal of Applied Mechanics and Engineering

1 2008

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The evolution of three-dimensional perturbations in a magnetohydrodynamic couette flow

Balagondar P. M., Vijayalakshmi A. R.

International Journal of Applied Mechanics and Engineering

2008

Vol. 13, no 3

627-638

The evolution of three-dimensional disturbances in a magnetohydrodynamic Couette flow is investigated using the initial-value problem approach. The general solution to the linearized equations governing three-dimensional disturbances is obtained by using two-dimensional Fourier transformation and other transformations rather than the traditional normal mode approach. The governing stability equation is solved using both the Fourier method and perturbation method. In the Fourier approach, the stability equation is reduced to Mathieu's equation and a periodic solution is obtained. Perturbation solution is obtained for small values of Alfvén velocity. Here Green's function method is employed to obtain the time evolution of linearized disturbances. A measure of disturbance energy is obtained in the case of square wave pulse for velocity and the magnetic field. The time evolution of the three-dimensional disturbances is obtained in terms of the two Green's function representations, one in the form of a Fourier sine series and the other in the form of sine hyperbolic functions representing the energy of a single component and the total energy of a single component. It is shown graphically that the total energy and the sum of first five components of energy are similar but are of different magnitudes.