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 Rao, 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 Rao 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 Rao and the corresponding wavenumber ko 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 Rao and critical wavenumber ko are also investigated.

中文翻译：

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Rayleigh-Bénard 磁对流与温度调制

执行瑞利-贝纳几何中调制磁对流的 Floquet 分析。下板上施加正弦变化的温度。随着瑞利数 Ra 增加到临界值 Rao 以上，振荡磁对流开始。磁对流开始时的流动可能与外部调制发生次谐波或谐波振荡。临界瑞利数 Rao 随调制频率 ω 非单调变化，以获得可观的调制幅度 a 值。温度调制可以推迟或提前出现磁对流。磁对流总是在较大的 ω 值处谐波振荡。在没有调制 (a = 0) 的情况下，阈值 Rao 和相应的波数 ko 接近它们的固定磁对流值，因为 ω → ∞。两个不同的谐波不稳定区域合并形成一个不稳定区域，该不稳定区域具有两个局部最小值，用于更高的钱德拉塞卡数 Q 值，这是新的质量。我们还观察到了一种新型的双临界点，它涉及两组不同的谐波振荡。还研究了 Q 和 Pr 的变化对阈值 Rao 和临界波数 ko 的影响。这涉及两组不同的谐波振荡。还研究了 Q 和 Pr 的变化对阈值 Rao 和临界波数 ko 的影响。这涉及两组不同的谐波振荡。还研究了 Q 和 Pr 的变化对阈值 Rao 和临界波数 ko 的影响。