任意初边值条件下浅水系统的广义Carrier-Greenspan变换
The Generalized Carrier-Greenspan Transform for the shallow water system with arbitrary initial and boundary conditions
摘要：
利用广义Carrier-Greenspan速端图变换（Rybkin et al.，2014年）。由于Carrier-Greenspan变换在线性化浅水系统时，严重地将IBV缠绕在速端图平面中，因此所有先前的解决方案都需要对IBV条件进行一些限制性假设，例如，初始速度为零，边界条件较小。对于物理空间中的任意非破缺初始条件，我们给出了速端图平面上等价IBV条件的显式公式，该公式可以很容易地用常规方法处理。我们的程序，我们称之为数据投影的方法，是基于泰勒公式，并允许我们减少转换IBV数据曲线上的速端平面上的等价数据线。我们的方法同样适用于任何倾斜的水深测量（不仅是平面海滩），而且，是完全分析的U形海湾。数值模拟结果表明，该方法具有很好的鲁棒性，可用于狭窄海湾和峡湾海啸波淹没的快速预报
英文摘要：
We put forward a solution to the initial boundary value (IBV) problem for the nonlinear shallow water system in inclined channels of arbitrary cross-section by means of the generalized Carrier-Greenspan hodograph transform (Rybkin et al., 2014). Since the Carrier-Greenspan transform, while linearizing the shallow water system, seriously entangles the IBV in the hodograph plane, all previous solutions required some restrictive assumptions on the IBV conditions, e.g., zero initial velocity, smallness of boundary conditions. For arbitrary non-breaking initial conditions in the physical space, we present an explicit formula for equivalent IBV conditions in the hodograph plane, which can readily be treated by conventional methods. Our procedure, which we call the method of data projection, is based on the Taylor formula and allows us to reduce the transformed IBV data given on curves in the hodograph plane to the equivalent data on lines. Our method works equally well for any inclined bathymetry (not only plane beaches) and, moreover, is fully analytical for U-shaped bays. Numerical simulations show that our method is very robust and can be used to give express forecasting of tsunami wave inundation in narrow bays and fjords
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