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, 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 varies non-monotonically with the modulation frequency for appreciable value of the modulation amplitude . The temperature modulation may either postpone or prepone the appearance of magnetoconvection. The magnetoconvective flow always oscillates harmonically at larger values of . The threshold Ra and the corresponding wavenumber approach to their values for the stationary magnetoconvection in the absence of modulation ( = 0), as  → ∞. Two different zones of harmonic instability merge to form a single instability zone with two local minima for higher values of Chandrasekhar's number , 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 and Pr on the threshold Ra and critical wavenumber are also investigated.