Haugen Nils Erland L, Brandenburg Axel, Dobler Wolfgang
Department of Physics, The Norwegian University of Science and Technology, Høyskoleringen 5, N-7034 Trondheim, Norway.
Phys Rev E Stat Nonlin Soft Matter Phys. 2004;70(1 Pt 2):016308. doi: 10.1103/PhysRevE.70.016308. Epub 2004 Jul 26.
Nonhelical hydromagnetic forced turbulence is investigated using large scale simulations on up to 256 processors and 1024(3) mesh points. The magnetic Prandtl number is varied between 1/8 and 30, although in most cases it is unity. When the magnetic Reynolds number is based on the inverse forcing wave number, the critical value for dynamo action is shown to be around 35 for magnetic Prandtl number of unity. For small magnetic Prandtl numbers we find the critical magnetic Reynolds number to increase with decreasing magnetic Prandtl number. The Kazantsev k(3/2) spectrum for magnetic energy is confirmed for the kinematic regime, i.e., when nonlinear effects are still unimportant and when the magnetic Prandtl number is unity. In the nonlinear regime, the energy budget converges for large Reynolds numbers (around 1000) such that for our parameters about 70% is in kinetic energy and about 30% is in magnetic energy. The energy dissipation rates are converged to 30% viscous dissipation and 70% resistive dissipation. Second-order structure functions of the Elsasser variables give evidence for a k(-5/3) spectrum. Nevertheless, the three-dimensional spectrum is close to k(-3/2), but we argue that this is due to the bottleneck effect. The bottleneck effect is shown to be equally strong both for magnetic and nonmagnetic turbulence, but it is far weaker in one-dimensional spectra that are normally studied in laboratory turbulence. Structure function exponents for other orders are well described by the She-Leveque formula, but the velocity field is significantly less intermittent and the magnetic field is more intermittent than the Elsasser variables.
利用在多达256个处理器和1024(3)个网格点上进行的大规模模拟，对非螺旋磁流体强迫湍流进行了研究。磁普朗特数在1/8到30之间变化，不过在大多数情况下它等于1。当磁雷诺数基于反向强迫波数时，对于磁普朗特数为1的情况，发电机作用的临界值显示约为35。对于小磁普朗特数，我们发现临界磁雷诺数随着磁普朗特数的减小而增加。在运动学区域，即非线性效应仍不重要且磁普朗特数为1时，证实了磁能的Kazantsev k(3/2)谱。在非线性区域，对于大雷诺数（约1000）能量收支收敛，使得对于我们的参数，约70%为动能，约30%为磁能。能量耗散率收敛到30%的粘性耗散和70%的电阻耗散。埃尔萨塞尔变量的二阶结构函数为k(-5/3)谱提供了证据。然而，三维谱接近k(-3/2)，但我们认为这是由于瓶颈效应。结果表明，瓶颈效应在磁湍流和非磁湍流中同样强烈，但在实验室湍流中通常研究的一维谱中要弱得多。其他阶次的结构函数指数可以很好地用谢 - 勒维克公式描述，但速度场的间歇性明显小于埃尔萨塞尔变量，而磁场的间歇性则更强。
