Effects of a magnetic modulation on the stability of a magnetic liquid layer heated from above

The effect of a time-sinusoidal magnetic field on the onset of convection i n a horizontal magnetic fluid layer heated from above and bounded by isothe rmal non magnetic boundaries is investigated. the analysis is restricted to static and linear laws of magnetization. A first order Galerkin method is performed to reduce the governing linear system to the Mathieu equation wit h damping term. Therefore, the Floquet theory is used to determine the conv ective threshold for the free-free and rigid-rigid cases. With an appropria ted choice of the ratio of the magnetic and gravitational forces, we show t he possibility to produce a competition between the harmonic and subharmoni c modes at the onset of convection.