Dobler Wolfgang, Shukurov Anvar, Brandenburg Axel
Department of Mathematics, University of Newcastle, Newcastle upon Tyne, NE1 7RU, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Mar;65(3 Pt 2B):036311. doi: 10.1103/PhysRevE.65.036311. Epub 2002 Feb 21.
The self-excitation of magnetic field by a spiral Couette flow between two coaxial cylinders is considered. We solve numerically the fully nonlinear, three-dimensional magnetohydrodynamic (MHD) equations for magnetic Prandtl numbers P(m) (ratio of kinematic viscosity to magnetic diffusivity) between 0.14 and 10 and kinematic and magnetic Reynolds numbers up to about 2000. In the initial stage of exponential field growth (kinematic dynamo regime), we find that the dynamo switches from one distinct regime to another as the radial width delta(r)(B) of the magnetic field distribution becomes smaller than the separation of the field maximum from the flow boundary. The saturation of magnetic field growth is due to a reduction in the velocity shear resulting mainly from the azimuthally and axially averaged part of the Lorentz force, which agrees with an asymptotic result for the limit of P(m)<<1. In the parameter regime considered, the magnetic energy decreases with kinematic Reynolds number as Re-0.84, which is approximately as predicted by the nonlinear asymptotic theory (approximately Re(-1)). However, when the velocity field is maintained by a volume force (rather than by viscous stress) the dependence of magnetic energy on the kinematic Reynolds number is much weaker.
研究了两个同轴圆柱之间螺旋库埃特流对磁场的自激发。我们对磁普朗特数P(m)（运动粘度与磁扩散率之比）在0.14至10之间且运动和磁雷诺数高达约2000的情况，数值求解了完全非线性的三维磁流体动力学（MHD）方程。在指数磁场增长的初始阶段（运动发电机 regime），我们发现随着磁场分布的径向宽度delta(r)(B)变得小于磁场最大值与流动边界的间距，发电机从一种不同的 regime 切换到另一种 regime。磁场增长的饱和是由于速度剪切的减小，这主要是由洛伦兹力的方位角和轴向平均部分导致的，这与P(m)<<1极限情况下的渐近结果一致。在所考虑的参数 regime 中，磁能随运动雷诺数按Re - 0.84减小，这与非线性渐近理论（近似为Re(-1)）的预测大致相符。然而，当速度场由体积力（而非粘性应力）维持时，磁能对运动雷诺数的依赖性要弱得多。
