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Low-Prandtl-number Bénard–Marangoni convection in a vertical magnetic field

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Abstract

The effect of a homogeneous magnetic field on surface-tension-driven Bénard convection is studied by means of direct numerical simulations. The flow is computed in a rectangular domain with periodic horizontal boundary conditions and the free-slip condition on the bottom wall using a pseudospectral Fourier–Chebyshev discretization. Deformations of the free surface are neglected. Two- and three-dimensional flows are computed for either vanishing or small Prandtl number, which are typical of liquid metals. The main focus of the paper is on a qualitative comparison of the flow states with the non-magnetic case, and on the effects associated with the possible near-cancellation of the nonlinear and pressure terms in the momentum equations for two-dimensional rolls. In the three-dimensional case, the transition from a stationary hexagonal pattern at the onset of convection to three-dimensional time-dependent convection is explored by a series of simulations at zero Prandtl number.

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  1. Fakultät für Maschinenbau, Technische Universität Ilmenau, Postfach 100565, 98684, Ilmenau, Germany

    Thomas Boeck

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  1. Thomas Boeck
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Correspondence to Thomas Boeck.

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Communicated by O. Zikanov

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Boeck, T. Low-Prandtl-number Bénard–Marangoni convection in a vertical magnetic field. Theor. Comput. Fluid Dyn. 23, 509–524 (2009). https://doi.org/10.1007/s00162-009-0138-1

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  • DOI: https://doi.org/10.1007/s00162-009-0138-1

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