Rayleigh-Bénard magnetoconvection with temperature modulation

Floquet analysis of modulated magnetoconvection in Rayleigh-Bénard geometry is performed. A sinusoidally varying temperature is imposed on the lower plate. As Rayleigh number Ra is increased above a critical value Ra_o, the oscillatory magnetoconvection begins. The flow at the onset of magnetoconvection may oscillate either subhar- monically or harmonically with the external modulation. The critical Rayleigh number Ra_o varies non-monotonically with the modulation frequency ω for appreciable value of the modulation amplitude a. The temperature modulation may either postpone or prepone the appearance of magnetoconvection. The magnetoconvective flow always oscillates harmonically at larger values of ω. The threshold Ra_o and the corresponding wavenumber k _o approach to their values for the stationary magnetoconvection in the absence of modulation (a = 0), as ω → ∞. Two different zones of harmonic instability merge to form a single instability zone with two local minima for higher values of Chandrasekhar's number Q, which is qualitatively new. We have also observed a new type of bicritical point, which involves two different sets of harmonic oscillations. The effects of variation of Q and Pr on the threshold Ra_o and critical wavenumber k _o are also investigated.