Abstract

We compare the classical mean-field dynamo model proposed by Steenbeck, Krause, and Rädler to describe the generation of large-scale magnetic fields and the Kazantsev model that describes the small-scale dynamo in an unbounded homogeneous and isotropic flow. We consider the subcritical regime of small magnetic Reynolds numbers whereby there is no rapid generation. The same regime can also be understood as a process in which the small-scale generation is stopped due to its intrinsic mechanisms. Within both approaches we examine what distinguishes the spectra of the linear and nonlinear processes under the suppression of hydrodynamic (kinetic) helicity or, in other words, compare the alpha-quenchings. We check whether averaging the induction equation over scales larger than the velocity field correlation length leads to the loss of any features in the spectrum near the dissipative scale. We study the various types of dynamo stabilization using which seems more justified physically than the standard alpha-quenching, but more difficult within large-scale models containing limited information about the random velocity field. In particular, we compare the integral suppression whereby the total energy is conserved and the spectral suppression that suggests the conservation of energy and helicity in each spectral shell without assuming their redistribution over the spectrum.

中文翻译：

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均场发电机模型中水动力螺旋抑制的小规模分析

摘要

我们比较了Steenbeck，Krause和Rädler提出的描述平均磁场生成的经典平均场发电机模型，以及描述无界均质和各向同性流中的小规模发电机的Kazantsev模型。我们考虑了小雷诺数的亚临界状态，因此没有快速产生。相同的机制也可以理解为由于其内在机制而停止小规模发电的过程。在这两种方法中，我们研究了在流体动力学（动力学）螺旋抑制作用下，线性和非线性过程的光谱之间有何区别，或者换句话说，比较了α猝灭。我们检查在大于速度场相关长度的尺度上平均归纳方程是否会导致耗散尺度附近频谱中的任何特征丢失。我们研究了各种类型的发电机稳定，使用这些发电机在物理上似乎比标准的α猝灭更为合理，但在包含有关随机速度场的有限信息的大规模模型中，难度更大。特别是，我们比较了保留总能量的积分抑制和建议在每个光谱壳中保留能​​量和螺旋度的光谱抑制，而不假设它们在光谱上的重新分布。但是在包含关于随机速度场的有限信息的大规模模型中，难度更大。特别是，我们比较了保留总能量的积分抑制和建议在每个光谱壳中保留能​​量和螺旋度的光谱抑制，而不假设它们在光谱上的重新分布。但是在包含关于随机速度场的有限信息的大规模模型中，难度更大。特别是，我们比较了保留总能量的积分抑制和建议在每个光谱壳中保留能​​量和螺旋度的光谱抑制，而不假设它们在光谱上的重新分布。