Bayliss R A, Forest C B, Nornberg M D, Spence E J, Terry P W
Department of Physics, University of Wisconsin-Madison, 1150 University Ave., Madison, Wisconsin 53706, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Feb;75(2 Pt 2):026303. doi: 10.1103/PhysRevE.75.026303. Epub 2007 Feb 5.
The role of turbulence in current generation and self-excitation of magnetic fields has been studied in the geometry of a mechanically driven, spherical dynamo experiment, using a three-dimensional numerical computation. A simple impeller model drives a flow that can generate a growing magnetic field, depending on the magnetic Reynolds number Rm=micro0sigmaVa and the fluid Reynolds number Re=Vanu of the flow. For Re<420, the flow is laminar and the dynamo transition is governed by a threshold of Rmcrit=100, above which a growing magnetic eigenmode is observed that is primarily a dipole field transverse to the axis of symmetry of the flow. In saturation, the Lorentz force slows the flow such that the magnetic eigenmode becomes marginally stable. For Re>420 and Rm approximately 100 the flow becomes turbulent and the dynamo eigenmode is suppressed. The mechanism of suppression is a combination of a time varying large-scale field and the presence of fluctuation driven currents (such as those predicted by the mean-field theory), which effectively enhance the magnetic diffusivity. For higher Rm, a dynamo reappears; however, the structure of the magnetic field is often different from the laminar dynamo. It is dominated by a dipolar magnetic field aligned with the axis of symmetry of the mean-flow, which is apparently generated by fluctuation-driven currents. The magnitude and structure of the fluctuation-driven currents have been studied by applying a weak, axisymmetric seed magnetic field to laminar and turbulent flows. An Ohm's law analysis of the axisymmetric currents allows the fluctuation-driven currents to be identified. The magnetic fields generated by the fluctuations are significant: a dipole moment aligned with the symmetry axis of the mean-flow is generated similar to those observed in the experiment, and both toroidal and poloidal flux expulsion are observed.
利用三维数值计算，在机械驱动的球形发电机实验的几何结构中，研究了湍流在磁场的当前产生和自激发中的作用。一个简单的叶轮模型驱动一种流动，这种流动可以产生不断增强的磁场，这取决于流动的磁雷诺数Rm = μ₀σVa和流体雷诺数Re = Va/ν。对于Re < 420，流动是层流状态，发电机转变由临界雷诺数Rmcrit = 100的阈值控制，高于该阈值时，可观察到一个不断增强的磁本征模，它主要是一个垂直于流动对称轴的偶极场。在饱和状态下，洛伦兹力使流动变慢，使得磁本征模变得接近稳定。对于Re > 420且Rm约为100时，流动变为湍流，发电机本征模受到抑制。抑制机制是时变的大尺度场和波动驱动电流（如平均场理论所预测的那些电流）的共同作用，这有效地增强了磁扩散率。对于更高的Rm，发电机再次出现；然而，磁场结构通常与层流发电机不同。它由一个与平均流对称轴对齐的偶极磁场主导，这显然是由波动驱动电流产生的。通过对层流和湍流施加一个弱的轴对称种子磁场，研究了波动驱动电流的大小和结构。对轴对称电流进行欧姆定律分析可以识别波动驱动电流。波动产生的磁场是显著的：产生了一个与平均流对称轴对齐的偶极矩，类似于实验中观察到的情况，并且同时观察到了环形和极向通量的排斥。
