平面旋转层中热对流产生对称磁场
Generation of a symmetric magnetic field by thermal convection in a plane rotating layer
摘要：
我们研究数值计算磁场产生的热对流与方形周期性细胞在旋转水平层的导电流体与应力的理想导电边界的瑞利数在区间5100 \le R \le 5800。三种发电机，显然没有遇到过，提出：1）稳定和时间周期的制度，其中的流动和磁场是对称的垂直轴。在这种对称性的制度，全球α效应是微不足道的，和复杂的结构系统的振幅方程控制弱非线性稳定性的系统的扰动与大的空间和时间尺度表明，扰动很可能表现出不寻常的复杂模式的行为，在未来的工作中进行研究。2)时间周期性，其中磁场总是集中在对流层的内部，与St Pierre（1993）首次观察到的行为相反，并且通常被认为是无限导电边界的通用行为。3)一个发电机表现出混沌行为的异宿性质，其中一个样本的轨迹享有之间的周期性磁流体动力学制度和轧辊的偏移。辊是无磁性的，但在运动学上产生磁场。结果，当接近轧辊时，磁能几乎下降到零。
英文摘要：
We investigate numerically magnetic field generation by thermal convection with square periodicity cells in a rotating horizontal layer of electrically-conducting fluid with stress-free electrically perfectly conducting boundaries for Rayleigh numbers in the interval 5100\le R\le 5800. Dynamos of three kinds, apparently not encountered before, are presented: 1) Steady and time-periodic regimes, where the flow and magnetic field are symmetric about a vertical axis. In regimes with this symmetry, the global alpha-effect is insignificant, and the complex structure of the system of amplitude equations controlling weakly nonlinear stability of the system to perturbations with large spatial and temporal scales suggests that the perturbations are likely to exhibit uncommon complex patterns of behaviour, to be studied in the future work. 2) Periodic in time regimes, where magnetic field is always concentrated in the interior of the convective layer, in contrast to the behaviour first observed by St Pierre (1993) and often perceived as generic for electrically infinitely conducting boundaries. 3) A dynamo exhibiting chaotic behaviour of heteroclinic nature, where a sample trajectory enjoys excursions between a periodic magnetohydrodynamic regime and rolls. The rolls are amagnetic, but generate magnetic field kinematically. As a result, magnetic energy falls off almost to zero, while the rolls are approached.
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