论文标题
具有任意初始和边界条件的浅水系统的广义载体绿色转换
The Generalized Carrier-Greenspan Transform for the shallow water system with arbitrary initial and boundary conditions
论文作者
论文摘要
我们通过广义的横截面倾斜通道中的非线性浅水系统的初始边界值（IBV）问题提出了解决方案（IBV）问题（Rybkin等，2014）。由于载体绿色载体转换，同时将浅水系统线性化，并严重纠缠着Hodograph平面中的IBV，因此所有先前的解决方案都需要对IBV条件上的一些限制性假设，例如，零初始速度，边界条件的较小。对于物理空间中的任意非破坏初始条件，我们为Hodograph平面中等效的IBV条件提供了明确的公式，该公式可以通过常规方法轻松处理。我们称为数据投影方法的过程基于泰勒公式，使我们能够将Hodograph平面曲线上给出的转换的IBV数据减少到线上的等效数据。我们的方法对于任何倾斜的测深（不仅是平面海滩）也同样效果，而且对U形海湾进行了完全分析。数值模拟表明我们的方法非常强大，可用于对狭窄的海湾和峡湾中海啸淹没的明确预测
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
