剪切发电机问题的非微扰拟线性方法
Nonperturbative quasilinear approach to the shear dynamo problem
摘要：
我们研究大规模发电机行动由于湍流中存在的线性剪切流。我们的治疗是准线性的，相当于标准的“一阶平滑近似”。然而，它是非微扰的剪切强度。本文首先利用剪切坐标变换和线性剪切流的伽利略不变性，导出了平均磁场演化的积分微分方程。我们表明，对于非螺旋湍流，平均场的横向剪切分量的时间演化不依赖于任何其他组件，除了自己，这是有效的任何伽利略不变的速度场，独立于其动力学。因此，对于剪切参数的所有阶数，在零电阻率极限下的准线性理论中，线性剪切流中的非螺旋湍流不存在剪切电流型效应。然后，我们开发了一个系统的近似的积分微分方程的情况下，当平均磁场变化缓慢的湍流相关时间。对于非螺旋湍流，所得到的偏微分方程可以再次通过在傅立叶空间中进行剪切坐标变换来求解。所得的解是剪切波的形式，用剪切坐标中的波数来标记。这些剪切波可以在早期和中期增长，但预计会在长时间内衰减。
英文摘要：
We study large-scale dynamo action due to turbulence in the presence of a linear shear flow. Our treatment is quasilinear and equivalent to the standard `first order smoothing approximation'. However it is non perturbative in the shear strength. We first derive an integro-differential equation for the evolution of the mean magnetic field, by systematic use of the shearing coordinate transformation and the Galilean invariance of the linear shear flow. We show that, for non helical turbulence, the time evolution of the cross-shear components of the mean field do not depend on any other components excepting themselves; this is valid for any Galilean-invariant velocity field, independent of its dynamics. Hence, to all orders in the shear parameter, there is no shear-current type effect for non helical turbulence in a linear shear flow, in quasilinear theory in the limit of zero resistivity. We then develop a systematic approximation of the integro-differential equation for the case when the mean magnetic field varies slowly compared to the turbulence correlation time. For non-helical turbulence, the resulting partial differential equations can again be solved by making a shearing coordinate transformation in Fourier space. The resulting solutions are in the form of shearing waves, labeled by the wavenumber in the sheared coordinates. These shearing waves can grow at early and intermediate times but are expected to decay in the long time limit.
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