Oishi Jeffrey S, Vasil Geoffrey M, Baxter Morgan, Swan Andrew, Burns Keaton J, Lecoanet Daniel, Brown Benjamin P
Department of Physics and Astronomy, Bates College, Lewiston, ME 04240, USA.
School of Mathematics and Statistics, University of Sydney, Sydney, New South Wales 2006, Australia.
Proc Math Phys Eng Sci. 2020 Jan;476(2233):20190622. doi: 10.1098/rspa.2019.0622. Epub 2020 Jan 8.
The magnetorotational instability (MRI) occurs when a weak magnetic field destabilizes a rotating, electrically conducting fluid with inwardly increasing angular velocity. The MRI is essential to astrophysical disc theory where the shear is typically Keplerian. Internal shear layers in stars may also be MRI-unstable, and they take a wide range of profiles, including near-critical. We show that the fastest growing modes of an ideal magnetofluid are three-dimensional provided the shear rate, , is near the two-dimensional onset value, . For a Keplerian shear, three-dimensional modes are unstable above ≈ 0.10 , and dominate the two-dimensional modes until ≈ 2.05 . These three-dimensional modes dominate for shear profiles relevant to stars and at magnetic Prandtl numbers relevant to liquid-metal laboratory experiments. Significant numbers of rapidly growing three-dimensional modes remainy well past 2.05 . These finding are significant in three ways. First, weakly nonlinear theory suggests that the MRI saturates by pushing the shear rate to its critical value. This can happen for systems, such as stars and laboratory experiments, that can rearrange their angular velocity profiles. Second, the non-normal character and large transient growth of MRI modes should be important whenever three-dimensionality exists. Finally, three-dimensional growth suggests direct dynamo action driven from the linear instability.
当弱磁场使具有向内增加角速度的旋转导电流体失稳时，磁旋转不稳定性（MRI）就会发生。MRI对于天体物理盘理论至关重要，在该理论中剪切通常是开普勒式的。恒星内部的剪切层也可能是MRI不稳定的，并且它们具有广泛的分布，包括接近临界的情况。我们表明，假设剪切率 接近二维起始值 ，理想磁流体中增长最快的模式是三维的。对于开普勒剪切，三维模式在 ≈ 0.10 以上是不稳定的，并且在 ≈ 2.05 之前主导二维模式。这些三维模式在与恒星相关的剪切分布以及与液态金属实验室实验相关的磁普朗特数下占主导地位。大量快速增长的三维模式在超过2.05 时仍然存在。这些发现具有三个重要意义。首先，弱非线性理论表明，MRI通过将剪切率推至其临界值而饱和。对于诸如恒星和实验室实验等能够重新排列其角速度分布的系统，这种情况可能会发生。其次，只要存在三维性，MRI模式的非正规特性和大的瞬态增长就应该很重要。最后，三维增长表明由线性不稳定性驱动的直接发电机作用。
