Rayleigh-B\'enard magnetoconvection with temperature modulation

Abstract

Floquet analysis of modulated magnetoconvection in Rayleigh-B\'{e}nard\ geometry is performed. The temperature of the lower plate is varied sinusoidally in time about a finite mean. As the Rayleigh number $\mathrm{Ra}$ is made to cross a critical value $\mathrm{Ra}_o$, the oscillatory magnetoconvection begins. The flow at the onset of magnetoconvection may oscillate either subharmonically or harmonically with the external modulation. The critical Rayleigh number $\mathrm{Ra}_o$ varies non-monotonically with $\omega$ for appreciable value of $a$. The temperature modulation may either postpone or prepone the appearance of magnetoconvection. The magnetoconvective flow always oscillates harmonically at larger values of $\omega$. The threshold $\mathrm{Ra}_o$ and the corresponding wave number $k_o$ approach to their values for the stationary magnetoconvection in the absence of modulation ($a = 0$), as $\omega \rightarrow \infty$. Two different zones of harmonic instability merge to form a single instability zone with two local minima for higher values of Chandrasekhar's number $\mathrm{Q}$, 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 $\mathrm{Q}$ and $\mathrm{Pr}$ on the threshold $\mathrm{Ra}_o$ and critical wave number $k_o$ are also investigated.