毛细-重力波模拟黑洞炸弹入门
A primer on the analogue black hole bomb with capillary-gravity waves
AI总结：
本文研究自由表面排水涡旋中毛细-重力波色散和粘性对模拟黑洞炸弹不稳定性的影响，揭示色散显著改变本征频率、粘性仅影响高频模式，并给出超辐射发生的环量条件和最大化不稳定性的系统条件。
摘要：
具有自由表面的排水涡旋在理论和实验中常被用作旋转黑洞模拟器。然而，大多数理论工作局限于理想化情形，其中波的色散和耗散被忽略。我们研究这些效应对模拟黑洞炸弹的影响，该不稳定性源于受限系统中旋转超辐射放大。我们揭示深水毛细-重力波的色散显著改变不稳定模式的本征频率，而粘性仅影响高频模式。此外，如果环量小于排水率的一个量级为1的倍数，超辐射不会发生，涡旋是稳定的。在具有高流速的小系统中，不稳定性达到最大，前提是涡旋与外边界之间有足够空间使第一激发态落在超辐射带宽内。本文讨论了这些结果对模拟黑洞和自由表面涡旋实验的意义。
英文摘要：
Draining vortices with a free surface are frequently employed as rotating black hole simulators, both in theory and experiments. However, most theoretical work is restricted to the idealised regime, where wave dispersion and dissipation are neglected. We investigate the role of these effects on the analogue black hole bomb, an instability resulting from rotational superradiant amplification in confined systems. We reveal that the dispersion of deep water capillary-gravity waves significantly modifies the unstable mode eigenfrequencies, whereas viscosity only affects those with high frequencies. Furthermore, if the circulation is less than an order 1 multiple of the drain rate, superradiance does not occur and the vortex is stable. The instability is maximised in small systems with high flow velocities, provided there is sufficient space between the vortex and the outer boundary for the first excited state to lie inside the superradiant bandwidth. Implications for experiments on analogue black holes and free surface vortices are discussed.
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