ABC flows then and now
ABC flows then and now
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ABC 的过去和现在
DOI：
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发表时间：
2012
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通讯作者：
D. Galloway
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文献类型：
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作者：
D. Galloway
我们回顾了没有尺度分离的元胞空间周期发电机，从20世纪80年代早期关于ABC流的工作开始，该流具有规定的稳定速度场u = (A sin z + C cos y, B sin x + A cos z, C sin y + B cos x)。这些自然导致了在20世纪90年代与迈克·普罗克特（Mike Proctor）一起完成的二维时间依赖版本的工作，该版本为在流动周转时间尺度上增长的快速发电机的存在提供了强有力的数值证据。随后与Rainer Hollerbach共同对球壳几何进行了类似的计算。同样在20世纪90年代，其他研究开始考虑洛伦兹力的反作用力，当流动不是被规定，而是被允许根据上述ABC形式的强迫而演变时。产生的发电机大多是丝状的，并且在与天体物理学相关的低扩散极限下，显示出令人不安的平衡趋势，即总磁能远低于总动能。Archontis在1999年发现了一种磁性和动能几乎相等的非丝状发电机，这表明丝状发电机的不利结垢是可以克服的；这个发电机用了ABC强迫去掉了余弦。从那以后，几位作者一直在努力理解这种状况是如何产生的，但只取得了部分成功。最近，科学家们已经努力制造出这种发电机的其他例子，研究为什么Archontis的情况在很大范围的磁性普朗特数ν/η范围内是稳定的，最重要的是理解它在非常低的扩散率下的显著稳定性，而非磁性流动几乎总是不稳定的。
We review cellular space-periodic dynamos without scale separation, starting with early work in the 1980s on ABC flows with prescribed steady velocity fields u = (A sin z + C cos y, B sin x + A cos z, C sin y + B cos x). These naturally led to work done in the 1990s together with Mike Proctor on 2-D time-dependent versions which gave strong numerical evidence for the existence of fast dynamos growing on the flow turnover timescale. Similar calculations were subsequently performed for a spherical shell geometry jointly with Rainer Hollerbach. Also in the 1990s other studies began to take into account the back reaction of the Lorentz force when the flow rather than being prescribed was instead allowed to evolve in response to a forcing of the above ABC form. The dynamos that resulted were mostly filamentary and showed a disconcerting tendency to equilibrate with total magnetic energy much less than total kinetic energy in the low diffusivity limit relevant for astrophysics. The remarkable discovery by Archontis in 1999 of a non-filamentary dynamo with almost equal magnetic and kinetic energies showed that the unfavourable scalings for the filamentary case can be overcome; this dynamo used an ABC forcing with the cosines left out. Since then several authors have been struggling with partial success to understand just how this state of affairs comes about. Most recently efforts have been made to produce other examples of this type of dynamo, to investigate why the Archontis case is robust over a wide range of magnetic Prandtl numbers ν/η, and above all to understand its remarkable stability at very low diffusivities when non-magnetic flows are almost always unstable.