Selective control of Poiseuille-Rayleigh-Benard instabilities by a spanwise magnetic field

作者：Fakhfakh W^*; Kaddeche S; Henry D; Ben Hadid H

来源：Physics of Fluids, 2010, 22(3): 034103.

DOI：10.1063/1.3327287

The stability of a pressure driven flow in an electrically conducting fluid heated from below and subjected to a spanwise constant magnetic field is investigated through a linear stability analysis. The numerical calculations show that such a magnetic field only affects the longitudinal stationary modes (L), which are stabilized, and has no effect on the transverse traveling modes (T). A direct consequence is the expansion of the domain where the transverse traveling (T) modes prevail. This expansion is controlled by the strength of the spanwise magnetic field, expressed through the Hartmann number (Ha, ratio of magnetic to viscous dissipation forces). Moreover, when Ha exceeds a limiting value depending on the Prandtl number, the (T) modes become the only dominant modes in the whole Re range. Particular attention was dedicated to the oblique modes (O) corresponding to fully three-dimensional disturbances in order to verify that they never become the dominant modes when the magnetic field is applied, similarly to what was found without magnetic field. From a practical point of view, these results could be of a great interest since it is known that the optimization of several processes involving the Poiseuille-Rayleigh-Benard flow is achieved when the traveling (T) modes prevail.

• 出版日期2010-3