Three-dimensional MHD dynamo simulation

为了解决发电机作为地球和行星磁性起源机制的问题，我们进行了三维MHD发电机仿真。到目前为止，我们发现边界层的发展依赖于Ekman数，当速度场具有无滑移边界条件时，边界层内的小尺度现象占主导地位。因此，要想得到可靠的MHD发电机仿真结果，必须对边界层的影响进行评估。在1998年和1999年，我们开发了一种新的发电机模拟计算机代码，并将其结果与我们以前的代码进行了比较，表明我们的新代码是有效的。然后，我们对代码进行了修改，以适应并行计算。2000年，我们作为国际团体参加了发电机基准试验。结果表明，我们的计算结果与其他研究人员的结果一致，因此我们的计算机代码与国外研究人员开发的其他代码一样有效。结果表明，径向粗空间分辨率对速度场模式的漂移率影响较大。换句话说，当我们检查数值计算结果时，最重要的是保证边界层有足够的分辨率。假设的圆柱体在其赤道处与内核相切并平行于旋转轴，称为切线圆柱体，它也是边界层。这一层的作用在防滑边界条件下显得尤为突出。切向圆柱内部，当瑞利数较小时，流动并不剧烈，但当瑞利数较高时，对流运动变得活跃，这一特征对磁场产生和变化的机理有很大影响。作为未来的工作，我们应该尝试理解瑞利数对切圆柱内部动力学的依赖关系

Aiming at solving a dynamo problem as a mechanism of the origin of Earth and planetary magnetism, we have performed three-dimensional MHD dynamo simulation. So far, we have found that boundary layers develop depending on the Ekman number and in the layer small-scale phenomena are dominant, when a non-slip boundary condition is given to the velocity field. Therefore, we must evaluate the effect of boundary layers if we want to obtain reliable results of MHD dynamo simulation. In 1998 and 1999, we developed a new computer code for dynamo simulation and compared its results with those derived from our previous code and showed that our new code is valid. Then we modified this code so as to cope with parallel computing. In 2000, we have participated the dynamo benchmark test as an international group attempt. As a result, our results were found to agree with the others and therefore our computer code is as effective as the other codes developed by oversea researchers. From our results, we could find that crude spatial resolution in the radial direction greatly affects the drift rate of the velocity filed pattern. In other words, it is the most important to assure enough resolution in the boundary layers when we examine the results of numerical computation. A hypothetical cylinder, which is tangent to the inner core at its equator and parallel to the rotation axis, is called a tangent cylinder, which is also a boundary layer. The effect of this layer becomes prominent for the non-slip boundary condition. Inside the tangent cylinder, the flow is not violent when the Rayleigh number is small, but for a high Rayleigh number, convective motion becomes active, Such a feature has a great influence on the mechanism of magnetic field creation and variation. As a future work, we should try to under stand the dependence of the Rayleigh number on dynamics inside the tangent cylinder