Iskakov A B, Schekochihin A A, Cowley S C, McWilliams J C, Proctor M R E
Department of Physics and Astronomy, UCLA, Los Angeles, California 90095-1547, USA.
Phys Rev Lett. 2007 May 18;98(20):208501. doi: 10.1103/PhysRevLett.98.208501. Epub 2007 May 14.
Direct numerical simulations of incompressible nonhelical randomly forced MHD turbulence are used to demonstrate for the first time that the fluctuation dynamo exists in the limit of large magnetic Reynolds number Rm>>1 and small magnetic Prandtl number Pm<<1. The dependence of the critical Rmc for dynamo on the hydrodynamic Reynolds number Re is obtained for 1 less than or similar Re less than or similar 6700. In the limit Pm<<1, Rmc is about 3 times larger than for the previously well-established dynamo at large and moderate Prandtl numbers: Rmc less than or similar 200 for Re greater than or similar 6000 compared to Rmc approximately 60 for Pm>or=1. It is not yet possible to determine numerically whether the growth rate of the magnetic energy is proportional, Rm1/2 in the limit Rm-->infinity, as it should be if the dynamo is driven by the inertial-range motions at the resistive scale.
不可压缩非螺旋随机强迫磁流体动力学湍流的直接数值模拟首次证明，波动发电机存在于大磁雷诺数Rm>>1和小磁普朗特数Pm<<1的极限情况下。对于1≤Re≤6700，得到了发电机临界Rmc对流体动力学雷诺数Re的依赖关系。在Pm<<1的极限情况下，Rmc比之前在大普朗特数和中等普朗特数下确立的发电机大约大3倍：对于Re≥6000，Rmc≤200，而对于Pm≥1，Rmc约为60。目前还无法通过数值方法确定磁能增长率在Rm→∞的极限情况下是否与Rm1/2成正比，而如果发电机是由电阻尺度下的惯性范围运动驱动，就应该是这样。
