剪切系统中$α$涨落产生的大尺度磁场
Generation of large-scale magnetic fields due to fluctuating $α$ in shearing systems
摘要：
我们探讨了剪切流中大规模磁场的增长，由于螺旋度波动与有限的相关时间，通过研究的Kraichnan-Moffatt模型的零均值随机波动的$α$参数的发电机理论。利用一阶光滑近似和$α$统计量的伽利略不变性，导出了大尺度磁场演化的线性积分微分方程。这使得能够构建在剪切速率$S$和$α$ -相关时间$τ_α$中无扰动的模型。在简要回顾了可精确解的白噪声极限的显著特征之后，我们考虑了小但非零的$τ_α$的情况。当大尺度磁场缓慢变化时，其演化服从一个偏微分方程。我们提出了大规模磁场的指数增长率的模态解和条件，其驱动程序是Kraichnan扩散率，莫法特漂移，剪切和非零相关时间。特别令人感兴趣的是发电机行动时，$α$ -波动是弱的，即当Kraichnan扩散是积极的。我们表明，在没有莫法特漂移，剪切不引起增长的解决方案。但剪切和莫法特漂移共同作用，可以驱动大规模的发电机行动与增长率$γ\propto |S|$。
英文摘要：
We explore the growth of large-scale magnetic fields in a shear flow, due to helicity fluctuations with a finite correlation time, through a study of the Kraichnan-Moffatt model of zero-mean stochastic fluctuations of the $α$ parameter of dynamo theory. We derive a linear integro-differential equation for the evolution of large-scale magnetic field, using the first-order smoothing approximation and the Galilean invariance of the $α$-statistics. This enables construction of a model that is non-perturbative in the shearing rate $S$ and the $α$-correlation time $τ_α$. After a brief review of the salient features of the exactly solvable white-noise limit, we consider the case of small but non-zero $τ_α$. When the large-scale magnetic field varies slowly, the evolution is governed by a partial differential equation. We present modal solutions and conditions for the exponential growth rate of the large-scale magnetic field, whose drivers are the Kraichnan diffusivity, Moffatt drift, Shear and a non-zero correlation time. Of particular interest is dynamo action when the $α$-fluctuations are weak; i.e. when the Kraichnan diffusivity is positive. We show that in the absence of Moffatt drift, shear does not give rise to growing solutions. But shear and Moffatt drift acting together can drive large scale dynamo action with growth rate $γ\propto |S|$.
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