Instability driven by boundary inflow across shear: a way to circumvent Rayleigh’s stability criterion in accretion disks?
Instability driven by boundary inflow across shear: a way to circumvent Rayleigh’s stability criterion in accretion disks?
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由切变边界流入驱动的不稳定性：一种规避吸积盘瑞利稳定性准则的方法？
DOI：
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发表时间：
2015
影响因子：
3.7
通讯作者：
R. Kerswell
中科院分区：
文献类型：
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作者：
R. Kerswell
我们研究了Gallet等人（Phys. Fluids，第22卷，2010，034105）和Ilin & Morgulis（J. Fluid Mech.，第730卷，2013年，pp. 364-378），其在径向横流施加在离心稳定的旋流上时产生。通过找到一个简单的直线不稳定的例子-剪切半平面，最小成分的不稳定性和不稳定/稳定的流入/流出边界澄清。不稳定性-这里命名为“边界流入不稳定性”-是临界层类型，其中该层位于流入壁处并且增长率为O（\sqrt{{\it\eta}}）$（如Ilin & Morgulis（J. Fluid Mech.，第730卷，2013年，pp. 364-378）），或在流动的内部，增长率为O（{\it\eta}\log 1/{\it\eta}）$，其中${\it\eta}$测量（小）流入与切向流的比率。不稳定性是强大的旋转剖面的变化，甚至那些是非常瑞利稳定的，并增加了进一步的物理，如粘度，三维和压缩性，但敏感的边界条件施加在流入边界的切向速度场。如果涡量在入流边界处不是固定的，则不稳定性似乎是通用的，并且通过存在于边界处的穿过内部切变的入流平流涡量来操作。二维状态的一次分叉和三维状态的二次分叉都是超临界的。假设吸积流仅由分子粘性驱动，所以${\it\eta}=O（Re^{-1}）$，不稳定性与吸积盘没有直接关系，因为临界阈值是$O（Re^{-2/3}）$，流入边界条件更可能是无应力而不是无滑移。然而，这里提出的分析突出了质量进入磁盘破坏的轨道流的潜力，如果这个质量通量具有涡。
We investigate the two-dimensional (2D) instability recently discussed by Gallet et al. (Phys. Fluids, vol. 22, 2010, 034105) and Ilin & Morgulis (J. Fluid Mech., vol. 730, 2013, pp. 364–378) which arises when a radial cross-flow 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 destabilising/stabilising 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 $O(\sqrt{{\it\eta}})$ (as found by Ilin & Morgulis (J. Fluid Mech., vol. 730, 2013, pp. 364–378)), or in the interior of the flow and the growth rate is $O({\it\eta}\log 1/{\it\eta})$ , where ${\it\eta}$ 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, three-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 ${\it\eta}=O(Re^{-1})$ , 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.