Krstulovic Giorgio, Thorner Gentien, Vest Julien-Piera, Fauve Stephan, Brachet Marc
Laboratoire de Physique Statistique de l'Ecole Normale Supérieure, Associé au CNRS et aux Universités Paris VI et VII, 24 Rue Lhomond, F-75231 Paris, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Dec;84(6 Pt 2):066318. doi: 10.1103/PhysRevE.84.066318. Epub 2011 Dec 27.
We present a numerical study of the magnetic field generated by the Taylor-Green vortex. We show that periodic boundary conditions can be used to mimic realistic boundary conditions by prescribing the symmetries of the velocity and magnetic fields. This gives insight into some problems of central interest for dynamos: the possible effect of velocity fluctuations on the dynamo threshold, and the role of boundary conditions on the threshold and on the geometry of the magnetic field generated by dynamo action. In particular, we show that an axial dipolar dynamo similar to the one observed in a recent experiment can be obtained with an appropriate choice of the symmetries of the magnetic field. The nonlinear saturation is studied and a simple model explaining the magnetic Prandtl number dependence of the super- and subcritical nature of the dynamo transition is given.
我们给出了关于泰勒 - 格林涡旋产生的磁场的数值研究。我们表明，通过规定速度场和磁场的对称性，周期性边界条件可用于模拟实际边界条件。这为发电机中一些核心问题提供了见解：速度波动对发电机阈值的可能影响，以及边界条件对阈值和发电机作用产生的磁场几何形状的作用。特别是，我们表明通过适当选择磁场的对称性，可以获得类似于最近实验中观察到的轴向偶极发电机。我们研究了非线性饱和，并给出了一个简单模型，该模型解释了发电机转变的超临界和亚临界性质对磁普朗特数的依赖性。
