Simulations and theory of mechanically driven, turbulent dynamos in spherical geometry

地球和太阳系中的大多数行星，太阳和其他恒星，星系和星系团都有磁场，这些磁场不能用永久磁化来解释。人们普遍认为这些场是由发电机效应产生的。在过去的几年里，在通过实验室实验验证某些关键理论概念方面取得了显着进展（例如，在里加、卡尔斯鲁厄、马里兰州、麦迪逊和卡达拉什）。由于使用液体钠，这些最近（和正在进行的）实验不可避免地涉及高度湍流，预计将在发电机过渡中发挥关键作用。为了更好地了解机械驱动的有界发电机中湍流的性质、作用和控制，我们计划使用现有的并行非线性MHD代码进行数值模拟，并辅以理论研究。将主要研究两种类型的流动。两者都是球形几何，都与当前的实验有关。一种是静止球形容器中两个反向旋转螺旋桨的流动，另一种是第二个同心旋转球形容器中的旋转球体（球形库埃特流动）。要解决的中心问题之一是临界磁雷诺数对流体雷诺数的依赖性。共同提案的优点是，可以合作处理一些可能有类似解决办法的基本问题。

The Earth and most of the planets in the solar system, the Sun and other stars, galaxies and galaxy clusters all have magnetic fields which cannot be explained by permanent magnetization. It is generally accepted that these fields are produced by the dynamo effect. In the last few years, remarkable progress has been achieved in validating certain key theoretical concepts via laboratory experiments (e.g., at Riga, Karlsruhe, Maryland, Madison, and Cadarache). Due to the use of liquid sodium, these recent (and ongoing) experiments inevitably involve highly turbulent flows which are expected to play a critical role in the dynamo transition. In order to better understand the nature, role, and control of turbulent flows in mechanically driven, bounded dynamos, we plan to perform numerical simulations with existing, parallel, nonlinear MHD codes, complemented by theoretical investigations. Mainly two type of flows will be studied. Both are in spherical geometry, and both are related to current experiments. One is the flow of two counter-rotating propellers in a stationary spherical vessel, the other is a rotating sphere within a second, concentric, rotating spherical container (spherical Couette flow). One of the central questions to be addressed is the dependence of the critical magnetic Reynolds number on the fluid Reynolds number. The common proposal has the advantage that some fundamental problems with possibly similar solutions can be approached cooperatively.