排水浴缸涡对浅水波的散射
Scattering of surface shallow water waves on a draining bathtub vortex
摘要：
在线性近似下，我们研究了长波对中心有排水沟的浅水盆地中轴对称流的散射。这个经典问题可以看作是旋转黑洞上的波散射模型。对于低频解析解导出来描述两个纯位扰动（表面重力波），扰动与非零位涡。对于中等频率，这样的解决方案得到数值和图示。结果表明，扰动动力学过程有两个过程，即中心涡对入射重力波的散射和位涡激发的重力波的发射。讨论了它们联合行动的一些方面。
英文摘要：
In the linear approximation we study long wave scattering on an axially symmetric flow in a shallow water basin with a drain in the center. This classical problem can be considered as a model of wave scattering on a rotating black hole. For the low frequencies analytic solutions are derived to describe both pure potential perturbations (surface gravity waves), and perturbations with nonzero potential vorticity. For moderate frequencies such solutions are obtained numerically and illustrated graphically. It is shown that there are two processes governing the dynamics of perturbations, namely, the scattering of incident gravity waves by central vortex, and the emission of gravity waves stimulated by the potential vorticity. Some aspects of their joint action are discussed.
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