由跨剪切流的边界入流驱动的不稳定性：吸积盘中规避瑞利稳定性判据的一种途径？
Instability driven by boundary inflow across shear: a way to circumvent Rayleigh's stability criterion in accretion disks?
AI总结：
本文通过简化模型识别出“边界入流不稳定性”的最小要素，揭示入流携带涡量穿过内部剪切可破坏离心稳定旋转流，并讨论其对吸积盘的潜在意义。
摘要：
我们研究了最近由 Gallet 等人（2010）以及 Ilin 和 Morgulis（2013）讨论的二维不稳定性，该不稳定性是在离心稳定的旋转流上施加径向横流时出现的。通过找到一个更简单的直线型不稳定性示例——一个受剪切的半平面，我们确定了该不稳定性的最小要素，并阐明了入流/出流边界的失稳/稳定效应。该不稳定性——在此命名为“边界入流不稳定性”——属于临界层类型，其中该临界层要么位于入流壁面处且增长率为 $O(\sqrt{\eta})$（如 Ilin 和 Morgulis 2013 所发现），要么位于流动内部且增长率为 $O(\eta\log 1/\eta)$，其中 $\eta$ 度量（较小的）入流与切向流之比。该不稳定性对旋转剖面的变化具有鲁棒性，即使对于那些非常瑞利稳定的剖面也是如此，并且对加入更多物理因素（如粘性、三维性和可压缩性）也具有鲁棒性，但对入流边界上切向速度场所施加的边界条件敏感。只要涡量在入流边界处不被固定，该不稳定性似乎是普遍存在的，并通过入流将边界处存在的涡量平流输运穿过内部剪切区来起作用。发现到二维状态的主分岔和到三维状态的次分岔都是超临界的。假设吸积流仅由分子粘性驱动，因此 $\eta=O(Re^{-1})$，该不稳定性对吸积盘并非立即相关，因为临界阈值为 $O(Re^{-2/3})$，且入流边界条件更可能是无应力而非无滑移。然而，本文的分析确实突显了进入盘的质量若携带涡量，则有可能扰乱轨道流动。
英文摘要：
We investigate the 2D instability recently discussed by Gallet et al. (2010) and Ilin \& Morgulis (2013) which arises when a radial crossflow is imposed on a centrifugally-stable swirling flow. By finding a simpler rectilinear example of the instability - a sheared half plane, the minimal ingredients for the instability are identified and the destabilizing/stabilizing effect of inflow/outflow boundaries clarified. The instability - christened `boundary inflow instability' here - is of critical layer type where this layer is either at the inflow wall and the growth rate is $O(\sqrtη)$ (as found by Ilin \& Morgulis 2013), or in the interior of the flow and the growth rate is $O(η\log 1/η)$ where $η$ measures the (small) inflow-to-tangential-flow ratio. The instability is robust to changes in the rotation profile even to those which are very Rayleigh-stable and the addition of further physics such as viscosity, 3-dimensionality and compressibility but is sensitive to the boundary condition imposed on the tangential velocity field at the inflow boundary. Providing the vorticity is not fixed at the inflow boundary, the instability seems generic and operates by the inflow advecting vorticity present at the boundary across the interior shear. Both the primary bifurcation to 2D states and secondary bifurcations to 3D states are found to be supercritical. Assuming an accretion flow driven by molecular viscosity only so $η=O(Re^{-1})$, the instability is not immediately relevant for accretion disks since the critical threshold is $O(Re^{-2/3})$ and the inflow boundary conditions are more likely to be stress-free than non-slip. However, the analysis presented here does highlight the potential for mass entering a disk to disrupt the orbiting flow if this mass flux possesses vorticity.
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