Temporal stability of small disturbances in MHD Jeffery-Hamel flows. (English) Zbl 1175.76061

Makinde, O. D.; Mhone, P. Y.

Comput. Math. Appl. 53, No. 1, 128-136 (2007).

Summary: The temporal development of small disturbances in magnetohydrodynamic (MHD) Jeffery-Hamel flows is investigated, in order to understand the stability of hydromagnetic steady flows in convergent/divergent channels at very small magnetic Reynolds number \(R_m\). A modified form of normal modes that satisfy the linearized governing equations for small disturbance development asymptotically far downstream is employed [A. McAlpine and P.G. Drazin, Fluid Dyn. Res. 22, No. 3, 123–138 (1998; Zbl 1051.76554)]. The resulting fourth-order eigenvalue problem which reduces to the well known Orr-Sommerfeld equation in some limiting cases is solved numerically by a spectral collocation technique with expansions in Chebyshev polynomials. The results indicate that a small divergence of the walls is destabilizing for plane Poiseuille flow while a small convergence has a stabilizing effect. However, an increase in the magnetic field intensity has a strong stabilizing effect on both diverging and converging channel geometry.

MSC:

76E25	Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
76W05	Magnetohydrodynamics and electrohydrodynamics

Keywords:

MHD Jeffery-Hamel flow; small disturbances stability; spectral method; eigenvalue problem; Orr-Sommerfeld equation

Citations:

Zbl 1051.76554

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