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arXiv 1610.01616astro-ph.HEphysics.flu-dyn
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局部几何中的弱非线性磁转不稳定性

The weakly nonlinear magnetorotational instability in a local geometry

S. E. Clark, Jeffrey S. Oishi

摘要:

磁旋转不稳定性(MRI)是吸积盘物理学的一个基本过程,但其饱和机制仍然知之甚少。我们提出了一个多尺度分析的非理想MRI在弱非线性制度-也就是说,当最不稳定的MRI模式有一个增长率渐近接近零从上面。在这里,我们发展我们的理论在一个地方,笛卡尔渠道。我们的结果证实了Umurhan等人(2007)的发现,即扰动振幅遵循Ginzburg-Landau方程。我们进一步发现,当考虑双极扩散的影响时,具有剪切周期边界条件的局部MRI系统将出现Ginzburg-Landau方程。饱和方位角速度和垂直磁场的详细力平衡表明,即使当扩散效应是重要的,通过减少背景剪切和重排和加强背景垂直磁场的组合过程的整体流量饱和。我们直接模拟了我们系统的金兹伯格-朗道振幅演化,并证明了我们的模型在长尺度和时间尺度上预测的斑图形成。我们比较弱非线性理论的结果,在薄间隙泰勒库埃特流的MRI的直接数值模拟。

英文摘要:

The magnetorotational instability (MRI) is a fundamental process of accretion disk physics, but its saturation mechanism remains poorly understood despite considerable theoretical and computational effort. We present a multiple scales analysis of the non-ideal MRI in the weakly nonlinear regime -- that is, when the most unstable MRI mode has a growth rate asymptotically approaching zero from above. Here, we develop our theory in a local, Cartesian channel. Our results confirm the finding by Umurhan et al. (2007) that the perturbation amplitude follows a Ginzburg-Landau equation. We further find that the Ginzburg-Landau equation will arise for the local MRI system with shear-periodic boundary conditions when the effects of ambipolar diffusion are considered. A detailed force balance for the saturated azimuthal velocity and vertical magnetic field demonstrates that even when diffusive effects are important, the bulk flow saturates via the combined processes of reducing the background shear and rearranging and strengthening the background vertical magnetic field. We directly simulate the Ginzburg-Landau amplitude evolution for our system and demonstrate the pattern formation our model predicts on long length and time scales. We compare the weakly nonlinear theory results to a direct numerical simulation of the MRI in a thin-gap Taylor Couette flow.

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