We discuss the solution of the small perturbation equations for a horizontal fluid layer heated from below with an applied magnetic field either in vertical or in horizontal direction. The field inhibits, due to the L...We discuss the solution of the small perturbation equations for a horizontal fluid layer heated from below with an applied magnetic field either in vertical or in horizontal direction. The field inhibits, due to the Lorentz force, more or less the onset of convective cellular motion. The solution of the eigenvalue problem shows that the critical Rayleigh number increases with increasing Hartmann number while the corresponding wave length decreases. Interesting analogies to solar granulation and black spot phenomena are obvious. The general influence of a horizontal magnetic field is larger than that of a vertical field. It is easy to understand this by discussing the influence of the Lorentz force on the Rayleigh -Benard convection. This result corrects earlier calculations in the literature.展开更多
文摘We discuss the solution of the small perturbation equations for a horizontal fluid layer heated from below with an applied magnetic field either in vertical or in horizontal direction. The field inhibits, due to the Lorentz force, more or less the onset of convective cellular motion. The solution of the eigenvalue problem shows that the critical Rayleigh number increases with increasing Hartmann number while the corresponding wave length decreases. Interesting analogies to solar granulation and black spot phenomena are obvious. The general influence of a horizontal magnetic field is larger than that of a vertical field. It is easy to understand this by discussing the influence of the Lorentz force on the Rayleigh -Benard convection. This result corrects earlier calculations in the literature.
