The presence of magnetic fields in many astrophysical objects is due to dynamo action, whereby a part of the kinetic energy is converted into magnetic energy. A turbulent dynamo that produces magnetic field structures on the same scale as the turbulent flow is known as the fluctuation dynamo. We use numerical simulations to explore the nonlinear, statistically steady state of the fluctuation dynamo in driven turbulence. We demonstrate that as the magnetic field growth saturates, its amplification and diffusion are both affected by the back-reaction of the Lorentz force upon the flow. The amplification of the magnetic field is reduced due to stronger alignment between the velocity field, magnetic field, and electric current density. Furthermore, we confirm that the amplification decreases due to a weaker stretching of the magnetic field lines. The enhancement in diffusion relative to the field line stretching is quantified by a decrease in the computed local value of the magnetic Reynolds number. Using the Minkowski functionals, we quantify the shape of the magnetic structures produced by the dynamo as magnetic filaments and ribbons in both kinematic and saturated dynamos and derive the scalings of the typical length, width, and thickness of the magnetic structures with the magnetic Reynolds number. We show that all three of these magnetic length scales increase as the dynamo saturates. The magnetic intermittency, strong in the kinematic dynamo (where the magnetic field strength grows exponentially) persists in the statistically steady state, but intense magnetic filaments and ribbons are more volume-filling.

中文翻译：

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PrM≥1时波动发电机的饱和机理

在许多天体物体中，磁场的存在是由于发电机的作用，因此一部分动能被转换成磁能。产生与湍流相同规模的磁场结构的湍流发电机被称为波动发电机。我们使用数值模拟来探索驱动湍流中波动发电机的非线性统计稳态。我们证明，随着磁场的增长饱和，其放大和扩散都受到洛伦兹力对流的反作用的影响。磁场的放大由于速度场，磁场和电流密度之间更强的对齐而降低。此外，我们确认，由于磁场线的拉伸较弱，放大率会降低。相对于磁力线拉伸的扩散增强通过减小磁性雷诺数的局部值来量化。使用Minkowski泛函，我们可以量化由发电机产生的磁性结构的形状，包括运动学和饱和动力学中的磁丝和带，并用雷诺数得出磁性结构的典型长度，宽度和厚度的比例。 。我们显示，随着发电机的饱和，所有这三个磁性长度尺度都会增加。在运动发电机中很强的磁间歇性（磁场强度呈指数增长）在统计稳定状态下持续存在，但是强磁丝和磁条充满了更多的体积。