Viscous, Resistive Magnetorotational Modes
Viscous, Resistive Magnetorotational Modes
复制标题
粘性、电阻磁旋转模式
DOI：
10.1086/589915
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
Chi
中科院分区：
文献类型：
--
作者：
M. Pessah;Chi
我们进行了一个全面的行为分析磁旋不稳定性（MRI）在粘性，电阻等离子体。在考虑波数垂直于切变的扰动时，我们得到了描述被垂直磁场缠绕的不可压缩差分旋转背景的局部动力学的非理想磁流体动力学方程的精确非线性解。我们提供了这些粘性，电阻MRI模式的几何描述，并展示了它们的物理结构如何作为雷诺数和磁雷诺数的函数进行修改。我们证明，当考虑有限耗散效应时，除非磁普朗特数是统一的，否则速度和磁场扰动不再是正交的（如在理想MHD极限中的情况）。我们推广了以前在理想极限下发现的结果，并表明了一系列的平均雷诺兹和麦克斯韦应力的关键性质也适用于粘性，电阻性MRI。特别地，我们证明了雷诺应力总是正的，麦克斯韦应力总是负的。因此，即使存在粘度和电阻率，总平均角动量输运总是向外的。我们还发现，对于雷诺数和磁雷诺数的任何组合，磁扰动支配着角动量的能量学和输运，并且总平均能量密度是负责角动量输运的总平均应力的上界。对于任意磁雷诺数，麦克斯韦应力与雷诺应力之比、磁场能量密度与动能密度之比随雷诺数的减小而增大；在理想的MHD状态下，这两个比率达到了最低限度。本文的分析结果为在剪切箱近似下求解粘阻MHD方程的各种算法提供了新的基准。
We carry out a comprehensive analysis of the behavior of the magnetorotational instability (MRI) in viscous, resistive plasmas. We find exact, nonlinear solutions of the nonideal magnetohydrodynamic (MHD) equations describing the local dynamics of an incompressible, differentially rotating background threaded by a vertical magnetic field when disturbances with wavenumbers perpendicular to the shear are considered. We provide a geometrical description of these viscous, resistive MRI modes and show how their physical structure is modified as a function of the Reynolds and magnetic Reynolds numbers. We demonstrate that when finite dissipative effects are considered, velocity and magnetic field disturbances are no longer orthogonal (as is the case in the ideal MHD limit) unless the magnetic Prandtl number is unity. We generalize previous results found in the ideal limit and show that a series of key properties of the mean Reynolds and Maxwell stresses also hold for the viscous, resistive MRI. In particular, we show that the Reynolds stress is always positive and the Maxwell stress is always negative. Therefore, even in the presence of viscosity and resistivity, the total mean angular momentum transport is always directed outward. We also find that, for any combination of the Reynolds and magnetic Reynolds numbers, magnetic disturbances dominate both the energetics and the transport of angular momentum and that the total mean energy density is an upper bound for the total mean stress responsible for angular momentum transport. The ratios between the Maxwell and Reynolds stresses and between magnetic and kinetic energy densities increase with decreasing Reynolds numbers for any magnetic Reynolds number; the lowest limit of both ratios is reached in the ideal MHD regime. The analytical results presented here provide new benchmarks for the various algorithms employed to solve the viscous, resistive MHD equations in the shearing box approximation.