粘性、电阻性磁旋转模
Viscous, Resistive Magnetorotational Modes
摘要：
我们进行了全面的分析的行为的磁旋转不稳定性（MRI）的粘性，电阻等离子体。我们发现精确的，非线性的解决方案的非理想磁流体动力学（MHD）方程描述的不可压缩的，差分旋转的背景线程的垂直磁场时，被认为是波数垂直的剪切扰动的局部动态。我们提供了这些粘性，电阻MRI模式的几何描述，并显示它们的物理结构是如何修改的雷诺数和磁雷诺数的函数。我们证明，当有限耗散效应被认为是，速度和磁场扰动不再正交（因为它是在理想的MHD极限的情况下），除非磁普朗特数是统一的。我们概括了以前的结果发现在理想的极限，并表明，一系列的关键属性的平均雷诺应力和麦克斯韦应力也持有粘性，电阻MRI。特别是，我们表明，雷诺应力总是积极的和麦克斯韦应力总是负的。因此，即使存在粘性和电阻率，总的平均角动量输运总是向外的。我们还发现，对于任何组合的雷诺数和磁雷诺数，磁扰动占主导地位的能量和运输的角动量和总平均能量密度是一个上限的总平均应力负责角动量运输。对于任何磁雷诺数，麦克斯韦应力和雷诺应力之间的比率以及磁密度和动能密度之间的比率都随着雷诺数的减小而增大;在理想的MHD状态下，这两个比率都达到了最低限度。
英文摘要：
We carry out a comprehensive analysis of the behavior of the magnetorotational instability (MRI) in viscous, resistive plasmas. We find exact, non-linear solutions of the non-ideal 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 it 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 outwards. 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.
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