论文标题
雷利 - 贝纳德磁反射和温度调节
Rayleigh-Bénard magnetoconvection with temperature modulation
论文作者
论文摘要
在雷利 - 纳德\几何形状中进行了调制磁反射的浮quet分析。下板的温度在有限的平均值上及时变化。由于瑞利号$ \ mathrm {ra} $是为了跨越关键值$ \ mathrm {ra} _o $ $，因此振荡性磁磁反射开始。磁反感染开始时的流量可能会通过外部调制在亚亨或谐波上振荡。关键的雷利号$ \ mathrm {ra} _o $以$ω$而异，以$ a $的可观值而变化。温度调制可能会推迟或准备磁反射的外观。磁对感染流总是在$ω$的较大值下谐波振荡。阈值$ \ mathrm {ra} _o $和相应的波数$ k_o $在没有调制的情况下，其值的固定磁反转值（$ a = 0 $），为$ω\ rightarrow \ infty $。谐波不稳定的两个不同区域合并，形成一个单个不稳定区域与两个局部最小值，以更高的chandrasekhar的数字$ \ mathrm {q} $的更高值，这是定性上新的。我们还观察到了一种新型的双向点，其中涉及两组不同的谐波振荡。还研究了$ \ mathrm {q} $和$ \ mathrm {pr} $变化对阈值$ \ mathrm {ra} _o $ $ $ $ $ $ k_o $的影响。
Floquet analysis of modulated magnetoconvection in Rayleigh-Bénard\ 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 $ω$ 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 $ω$. 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 $ω\rightarrow \infty$. 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.
