Dynamo theory describes the magnetic field induced by the rotating, convecting and electrically conducting fluid in a celestial body. The classical ABC-flow model represents fast dynamo action, required to sustain such a magnetic field. In this letter, Lagrangian coherent structures (LCSs) in the ABC-flow are detected through Finite-time Lyapunov exponents (FTLE). The flow skeleton is identified by extracting intersections between repelling and attracting LCSs. For the case A = B = C = 1, the skeleton structures are made up from lines connecting two different types of stagnation points in the ABC-flow. The corresponding kinematic ABC-dynamo problem is solved using a spectral method, and the distribution of cigar-like magnetic structures visualized. Inherent links are found to exist between LCSs in the ABC-flow and induced magnetic structures, which provides insight into the mechanism behind the ABC-dynamo.

中文翻译：

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运动型ABC发电机中的流动和磁结构

发电机理论描述了由天体中的旋转，对流和导电流体感应的磁场。经典的ABC流动模型代表维持这种磁场所需的快速发电机作用。在这封信中，通过有限时Lyapunov指数（FTLE）检测了ABC流中的拉格朗日相干结构（LCS）。通过提取排斥和吸引LCS之间的交点来识别流骨架。对于A = B = C= 1，骨架结构由连接ABC流中两种不同类型的停滞点的线组成。使用频谱方法解决了相应的运动学ABC发电机问题，并可视化了雪茄状磁性结构的分布。发现内在联系存在于ABC流中的LCS与感应磁结构之间，这提供了对ABC发电机背后机制的了解。