Turbulent dynamo action at low magnetic Reynolds number
Turbulent dynamo action at low magnetic Reynolds number
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低磁雷诺数下的湍流发电机作用
DOI：
10.1017/s002211207000068x
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发表时间：
1970
影响因子：
3.7
通讯作者：
By H. K. Moffatt
中科院分区：
文献类型：
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作者：
By H. K. Moffatt
考虑了湍流对长度尺度L大于湍流尺度L的磁场的影响。该场没有外部源，在没有湍流的情况下，它因欧姆耗散而衰减。假设磁雷诺数Rm = u0l/λ（其中u0为均方根速度，λ为磁扩散系数）很小。结果表明，在最小的l/ l和Rm量级，各向同性湍流对大尺度场没有影响；但缺乏反射对称的湍流能够在Rm - 21阶或更大的长度尺度上放大场的傅里叶分量。对于统计性质在参照轴旋转下不变而在一点反射下不不变的湍流，表明磁场的磁能密度最初是位置的齐次随机函数，具有特别简单的谱，最终随着t−1 /2 exp （α2t/2λ3）而增加，其中α(= O(u02l))是湍流谱张量的一定线性泛函。对于初始定域场，得到了类似的结果。
The effect of turbulence on a magnetic field whose length-scale L is initially large compared with the scale l of the turbulence is considered. There are no external sources for the field, and in the absence of turbulence it decays by ohmic dissipation. It is assumed that the magnetic Reynolds number Rm = u0l/λ (where u0 is the root-mean-square velocity and λ the magnetic diffusivity) is small. It is shown that to lowest order in the small quantities l/L and Rm, isotropic turbulence has no effect on the large-scale field; but that turbulence that lacks reflexional symmetry is capable of amplifying Fourier components of the field on length scales of order Rm−2l and greater. In the case of turbulence whose statistical properties are invariant under rotation of the axes of reference, but not under reflexions in a point, it is shown that the magnetic energy density of a magnetic field which is initially a homogeneous random function of position with a particularly simple spectrum ultimately increases as t−½exp (α2t/2λ3) where α(= O(u02l)) is a certain linear functional of the spectrum tensor of the turbulence. An analogous result is obtained for an initially localized field.