论文标题
被困的自由表面波，用于羔羊 - 俄罗斯涡流流
Trapped Free Surface Waves for a Lamb-Oseen Vortex Flow
论文作者
论文摘要
在被困的旋转岩心的游泳池中观察到了被困的表面波。为了研究这种效果，我们已经数字研究了羔羊的自由表面响应 - 对小扰动的摩塞涡流。液体的深度有限，但侧向无绑。所使用的数值方法在光谱上是准确的，并使用一种新型的非反射缓冲区区域来模拟侧面无界的流体。尽管在此流中可能会出现各种线性波，但我们将重点放在表面重力波上。我们研究了涡流方位角模式数和涡流旋转速率的函数的涡流线性模式。我们发现，在较低的旋转速率下，线性模式通过将能量辐射到远场而衰减，而在较高的旋转速率下，模式几乎变得中立稳定，并将其捕获在涡流的附近。虽然由于浴缸涡流的微小扰动而在浅水表面波中以前已经看到了被困的模式，但由于缺乏内向流动和非shallaly-water波的分散性质，此处考虑的情况在质上有所不同。我们还发现，对于缓慢的涡旋旋转速率，被困的波沿与涡旋旋转相反的方向传播，而在阈值旋转速率高于阈值的旋转速率上，Waves与流动共旋转。
Trapped surface waves have been observed in a swimming pool trapped by, and rotating around, the cores of vortices. To investigate this effect, we have numerically studied the free-surface response of a Lamb--Oseen vortex to small perturbations. The fluid has finite depth but is laterally unbounded. The numerical method used is spectrally accurate, and uses a novel non-reflecting buffer region to simulate a laterally unbounded fluid. While a variety of linear waves can arise in this flow, we focus here on surface gravity waves. We investigate the linear modes of the vortex as a function of the perturbation azimuthal mode number and the vortex rotation rate. We find that at low rotation rates, linear modes decay by radiating energy to the far field, while at higher rotation rates modes become nearly neutrally stable and trapped in the vicinity of the vortex. While trapped modes have previously been seen in shallow water surface waves due to small perturbations of a bathtub vortex, the situation considered here is qualitatively different owing to the lack of an inward flow and the dispersive nature of non-shallow-water waves. We also find that for slow vortex rotation rates, trapped waves propagate in the opposite direction to the vortex rotation, whereas, above a threshold rotation rate, waves co-rotate with the flow.
