Linear stability of buoyant convection in a horizontal layer of an electrically conducting fluid in moderate and high vertical magnetic field

Linear stability of buoyant convectiveflow in a horizontal layer of an electricallyconductingfluid is considered with reference to horizontal Bridgmansemiconductor crystal growth. Thefluid flows owing to the horizontal temperature gradient in the presence of a verticalmagnetic field. The main interest here is in the stability of theflow for a sufficiently strongmagnetic field, for the Hartmann numberHa> 10, and increasing to high values, of the order of 103–104. The Prandtl number,Pr, has been fixed atPr = 0.015. It is shown that besides the Hartmann number theinstability strongly depends on the type of the thermalboundary conditions at the horizontal walls. For thermallyconducting walls the basic temperature profile exhibits zones of unstable thermal stratification, which leads toinstabilities owing to the Rayleigh-B énard mechanism. However, the transitions between various, most unstable modes asHa increases are not trivial. For sufficiently high values ofHa, the most unstable mode consists of transverse oscillatory rolls located in the region of unstable stratification. For thermally insulating walls, the transitions are simpler, and for sufficiently highHa, the most unstable mode consists of longitudinal, steady, three-dimensional mode which is concentrated in the Hartmann layers at the horizontal boundaries. This mode has a combined dynamic-thermal origin and is owed to a strong shear in the Hartmann layers. The electricalboundary conditions do not qualitatively affec...

Source: Physics of Fluids - September 21, 2016 Category: Physics Authors: A. Hudoba, S. Molokov, S. Aleksandrova and A. Pedcenko Source Type: research