Ponty Y, Mininni P D, Montgomery D C, Pinton J-F, Politano H, Pouquet A
CNRS UMR6202, Laboratoire Cassiopée, Observatoire de la Côte d'Azur, BP 4229, Nice Cedex 04, France.
Phys Rev Lett. 2005 Apr 29;94(16):164502. doi: 10.1103/PhysRevLett.94.164502. Epub 2005 Apr 27.
We present a three-pronged numerical approach to the dynamo problem at low magnetic Prandtl numbers P(M). The difficulty of resolving a large range of scales is circumvented by combining direct numerical simulations, a Lagrangian-averaged model and large-eddy simulations. The flow is generated by the Taylor-Green forcing; it combines a well defined structure at large scales and turbulent fluctuations at small scales. Our main findings are (i) dynamos are observed from P(M)=1 down to P(M)=10(-2), (ii) the critical magnetic Reynolds number increases sharply with P(M)(-1) as turbulence sets in and then it saturates, and (iii) in the linear growth phase, unstable magnetic modes move to smaller scales as P(M) is decreased. Then the dynamo grows at large scales and modifies the turbulent velocity fluctuations.
我们提出了一种针对低磁普朗特数P(M)下的发电机问题的三管齐下的数值方法。通过结合直接数值模拟、拉格朗日平均模型和大涡模拟，规避了解析大范围尺度的困难。流动由泰勒-格林强迫产生；它在大尺度上结合了明确的结构，在小尺度上结合了湍流涨落。我们的主要发现是：(i) 在从P(M)=1到P(M)=10^(-2)的范围内观测到了发电机现象；(ii) 随着湍流的出现，临界磁雷诺数随P(M)^(-1)急剧增加，然后饱和；(iii) 在线性增长阶段，随着P(M)的减小，不稳定磁模向更小尺度移动。然后发电机在大尺度上增长并改变湍流速度涨落。
