Rayleigh–Bénard magnetoconvection with temperature modulation

Abstract

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.