Umurhan O M, Menou K, Regev O
Department of Physics, Technion-Israel Institute of Technology, Haifa, Israel.
Phys Rev Lett. 2007 Jan 19;98(3):034501. doi: 10.1103/PhysRevLett.98.034501.
We show by means of a perturbative weakly nonlinear analysis that the axisymmetric magnetorotational instability (MRI) of a viscous, resistive, incompressible rotating shear flow subject to a background vertical magnetic field in a thin channel gives rise to a Ginzburg-Landau equation for the disturbance amplitude. For small magnetic Prandtl number (P(m)), the saturation amplitude is proportional square root P(m) and the resulting momentum transport scales as R(-1), where R is the hydrodynamic Reynolds number. Simplifying assumptions, such as linear shear base flow, mathematically expedient boundary conditions, and continuous spectrum of the vertical linear modes, are used to facilitate this analysis. The asymptotic results are shown to comply with numerical calculations using a spectral code. They suggest that the transport due to the nonlinearly developed MRI may be very small in experimental setups with P(m)<<1.
我们通过微扰弱非线性分析表明，在薄通道中，受背景垂直磁场作用的粘性、有电阻、不可压缩旋转剪切流的轴对称磁旋转不稳定性（MRI）会产生一个关于扰动幅度的金兹堡 - 朗道方程。对于小磁普朗特数（P(m)），饱和幅度与P(m)的平方根成正比，并且由此产生的动量输运尺度为R(-1)，其中R是流体动力学雷诺数。为便于此分析，采用了一些简化假设，如线性剪切基流、数学上方便的边界条件以及垂直线性模式的连续谱。渐近结果表明与使用谱代码的数值计算相符。结果表明，在P(m) << 1的实验装置中，由非线性发展的MRI引起的输运可能非常小。
