寻找最快的发电机：层流ABC流
Searching for the fastest dynamo: Laminar ABC flows
摘要：
通过对ABC流族和2种不同强迫尺度的数值模拟，研究了发电机不稳定性的增长率随磁雷诺数Rm的变化。对于在最大可用长度尺度下驱动的ABC流，发现随着磁雷诺数的增加：（a）首先在发电机中产生的流是2.5D流，其中A = B和C = 0（以及所有排列）。(b)产生发电机的第二种类型的流是A = B = 2C/5（和置换）的流。(c)最对称的流A = B = C是导致发电机的第三种流。(d)随着Rm的增加，A = B = C流不再是发电机，并从局部最大值过渡到三阶鞍点。(e)在较大的Rm下，A = B = C流重新建立其自身作为发电机，但仍然是鞍点。(f)在最大检查的Rm处，2.5D流的增长率开始降低，A = B = C流再次接近局部最大值，并且流A = B = 2C/5（和排列）导致在最大检查的Rm处具有增长率$γ~0.12$的最快发电机。对于以第二大可用长度尺度驱动的ABC流，发现（a）2.5D流A = B，C = 0（和排列）再次是导致发电机具有减小的开始的第一流。(b)最对称的流A = B = C是导致发电机的第二种流。它是并且仍然是局部最大值。(c)在较大的Rm下，流A = B = 2C/5（和排列）作为第三种流出现，导致发电机。当Rm增加时，它成为具有最大增长率的流。的增长率似乎有一些相关性的Lyaponov指数，但建设性的重新折叠的磁力线似乎同样重要，在确定的快速发电机流量。
英文摘要：
The growth rate of the dynamo instability as a function of the magnetic Reynolds number Rm is investigated by means of numerical simulations for the family of the ABC flows and for 2 different forcing scales. For the ABC flows that are driven at the largest available length scale it is found that as the magnetic Reynolds number is increased: (a) The flow that results first in dynamo is the 2.5D flow for which A=B and C=0 (and all permutations). (b) The second type of flow that results in dynamo is the one for which A=B=2C/5 (and permutations). (c) The most symmetric flow A=B=C is the third type of flow that results in dynamo. (d) As Rm is increased, the A=B=C flow stops being a dynamo and transitions from a local maximum to a third-order saddle point. (e) At larger Rm the A=B=C flow re-establishes its self as a dynamo but remains a saddle point. (f) At the largest examined Rm the growth rate of the 2.5D flows starts to decrease, the A=B=C flow comes close to a local maximum again and the flow A=B=2C/5 (and permutations) results in the fastest dynamo with growth rate $γ~0.12$ at the largest examined Rm. For the ABC flows that are driven at the second largest available length scale it is found that (a) the 2.5D flows A=B, C=0 (and permutations) are again the first flows that result in dynamo with a decreased onset. (b) The most symmetric flow A=B=C is the second type of flow that results in dynamo. It is and remains a local maximum. (c) At larger Rm the flow A=B=2C/5 (and permutations) appears as the third type of flow that results in dynamo. As Rm is increased it becomes the flow with the largest growth rate. The growth rates appear to have some correlation with the Lyaponov exponents but constructive re-folding of the field lines appears equally important in determining the fasted dynamo flow.
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