On stability of the MHD flow around a cylinder in an aligned magnetic field

T. Weier¹ - G. Mutschke¹ - G. Gerbeth¹ - A. Alemany² - A. Pilaud²

¹ Research Center Rossendorf, PO Box 51 01 19, D-01314 Dresden, Germany
² Laboratoire des Ecoulements Geophysiques et Industriels, Institute de Mecanique de Grenoble (LEGI-IMG), France

Abstract
The hydrodynamic stability of the flow of an incompressible conducting fluid around a circular cylinder in a uniform magnetic field coplanar to the mean flow is investigated in the case of small magnetic Reynolds numbers. Depending on the Reynolds number the flow is investigated numerically (Re < 5000) or experimentally (5000 < < Re < 9000). The two-dimensional Navier-Stokes equation was solved numerically using a finite difference method. A critical curve in the (Re, N)-space separating stable and unstable regimes is defined by zero amplitude oscillations of lift and drag force. Additionally, a linear local stability analysis of the two-dimensional flow is done analytically. Here the cylinder wake is modelled as a Kolmogorov flow. Parameters are used to fit its shape and velocity profiles to those obtained experimentally. The linear stability curve found here considerably underestimates the stabilizing influence of the magnetic field. The reason for this might be the global nature of the instabilities as proposed in [3] for the flow without magnetic field. Experimental investigations were done for higher Reynolds numbers to verify the influence of the parallel magnetic field on the stability of the flow. It was found that the low frequency fluctuations are not damped out by an increasing magnetic field. Rather they seemed to be weakly amplified. This is supported by the results of our linear stability analysis and was already reported [11] for the inviscid case. Figs 5, refs 12.