由移动床产生的二维旋转水波的远海传播
On the open sea propagation of two-dimensional rotational water waves generated by a moving bed
摘要：
我们研究的传播的二维海啸波引发的海啸在公海中的存在下，风产生的电流，对应于恒定的涡度的背景流。一个适当的缩放的控制方程引入无量纲参数，特别感兴趣的是设置的线性波，只依赖于垂直运动的海床。我们使用傅里叶分析方法提取公式的功能$f$，它描述了垂直位移的水的自由表面。我们表明，结果是特别有用的物理相关的浅水区制度：在无旋的情况下，预测很好地符合一些历史海啸的观察行为。在其他情况下，静止相位原理给出了对$f$渐近行为的洞察。
英文摘要：
We study the propagation of two-dimensional tsunami waves triggered by a seaquake in the open sea in the presence of underlying wind-generated currents, corresponding to background flows of constant vorticity. A suitable scaling of the governing equations introduces dimensionless parameters, of particular interest being the setting of linear waves that only depend on the vertical movement of the sea bed. We use Fourier analysis methods to extract formulae for the function $f$ which describes the vertical displacement of the water's free surface. We show that the results are particularly useful in the physically relevant shallow-water regime: in the irrotational case the predictions fit well with the observed behaviour of some historical tsunamis. In other situations, the stationary-phase principle gives insight into the asymptotic behaviour of $f$.
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