Selective control of Poiseuille-Rayleigh-Bénard instabilities by a spanwise magnetic field
Résumé
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 theoptimization of several processes involving the Poiseuille-Rayleigh-Bénard flow is achieved when the traveling T modes prevail.
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