论文标题
在存在垂直磁场的情况下，旋转对流稳定
Overstable rotating convection in presence of vertical magnetic field
论文作者
论文摘要
我们介绍了在存在垂直外部磁场的情况下对非线性旋转磁反射（RMC）的研究结果。我们专注于通过改变系统控制参数（即泰勒号（$ \ mathrm {ta} $），chandrasekhar编号（$ \ mathrm {q} $）和prandtl编号（$ \ \ m randrm {pr} $）的动力学，即泰勒号（$ \ mathrm {ta} $）（$ \ \ mathrm {pr} $）， $ 750 \ leq \ mathrm {ta} \ leq10^6 $，$ 0 <\ mathrm {q} \ leq 10^3 $和$ 0 <\ sathrm {pr} \ leq 0.5 $。为此，执行了管理方程式的三维直接数值模拟（DNS）和低维建模。指定参数空间中的广泛DNS在$ \ mathrm {ta} $，$ \ mathrm {q} $和$ \ mathrm {pr} $的情况下，在质量上显示了两个不同的发动机。在第一个中，双态性出现在一开始，在那个次临界对流和超临界对流共存，而仅在第二个中只观察到超临界对流。对低维模型的分析表明，超临界的HOPF分叉负责超临界的发作，而亚临界的干草叉分叉负责亚临界发作。还可以观察到，在开始时，亚临界对流的外观在所有三个控制参数上都有很大的依赖性$ \ mathrm {ta} $，$ \ mathrm {q} $和$ \ mathrm {pr} $。由于$ \ mathrm {pr} $，对于固定的$ \ mathrm {ta} $和$ \ mathrm {q} $而增加了亚临界对流的情况。但是，调查的最引人注目的发现是，$ \ mathrm {ta} $的增量对于固定$ \ mathrm {q} $和$ \ mathrm {pr} $反对亚临界对流，而$ \ mathrm {q} $ in $ \ \ m nath prm {prm}这与RMC报告的早期结果形成鲜明对比。
We present the results of our investigation on nonlinear overstable rotating magnetoconvection (RMC) in presence of vertical external magnetic field. We focus on the dynamics appearing near the onset of convection by varying the system control parameters, namely, the Taylor number ($\mathrm{Ta}$), the Chandrasekhar number ($\mathrm{Q}$) and the Prandtl number ($\mathrm{Pr}$) in the ranges $750\leq\mathrm{Ta}\leq10^6$, $0 < \mathrm{Q} \leq 10^3$ and $0 < \mathrm{Pr} \leq 0.5$. Three dimensional (3D) direct numerical simulations (DNS) of the governing equations and low-dimensional modeling of the system are performed for this purpose. Extensive DNS in the specified parameter space shows two qualitatively different onsets depending on $\mathrm{Ta}$, $\mathrm{Q}$ and $\mathrm{Pr}$. In the first one, bistability appears at the onset, where both subcritical and supercritical convection coexist, while only supercritical convection is observed in the second one. Analysis of the low-dimensional model reveals that a supercritical Hopf bifurcation is responsible for the supercritical onset and a subcritical pitchfork bifurcation is responsible for the subcritical onset. It is also observed that appearance of subcritical convection at the onset has strong dependence on all three control parameters $\mathrm{Ta}$, $\mathrm{Q}$ and $\mathrm{Pr}$. The scenario of subcritical convection is found to disappear as $\mathrm{Pr}$ is increased for fixed $\mathrm{Ta}$ and $\mathrm{Q}$. However, most striking findings of the investigation is that the increment in $\mathrm{Ta}$ for fixed $\mathrm{Q}$ and $\mathrm{Pr}$ opposes the subcritical convection, whereas the increment in $\mathrm{Q}$ for fixed $\mathrm{Ta}$ and $\mathrm{Pr}$ favors it. This is in sharp contrast with the earlier results reported in RMC.
