线性导模与变拓扑的Whitham-Boussinesq模型
Linear guided modes and Whitham-Boussinesq model for variable topogra
摘要：
本文研究了两个经典的线性水波问题：i）有界等截面无限直槽的简正模，ii）无界等截面区域中的纵模。这两个问题都可以使用线性化自由表面势流理论来描述，我们的目标是将文献中已知的解析解与[vargas 2016 whitham]中提出的线性波非局部Dirichlet-Neumann算子的临时但简单近似所获得的数值解进行比较。为了研究有界横截面通道中的简正模式，我们考虑特殊的对称三角形横截面，即边倾斜于$45^{\circ}$和$60^{\circ}$垂直的对称三角形，并将使用非局部Dirichlet-Neumann算子获得的模式与Lamb [1932 hydrodynamics]、Macdonald [macdonald 1893 waves]、Greenhill [greenhill 1887 wave]、Packham [packham1980small]和Groves [groves1994hamilton]。这些几何形状有倾斜的海滩边界，原则上应该限制我们的近似狄利克雷-诺依曼算子的适用性。然而，我们看到，算子对偶模给出了非常接近的结果，而对奇模，我们在边界附近有一些差异。对于在具有无限横截面的区域中的捕获纵模，我们考虑分段恒定深度剖面，并将用非局部算子模式计算的模式与Miles [miles 1972 wave]、Lin、Juang和Tsay [lin 2001 anomalous]的线性化浅水理论的已知解析解进行比较，另见[mei 2005 theory]。这是一个重要的地球物理兴趣的问题，所提出的模型是定量给出类似的结果，为最低的陷阱模式。
英文摘要：
In this article we study two classical linear water wave problems, i) normal modes of infinite straight channels of bounded constant cross-section, and ii) trapped longitudinal modes in domains with unbounded constant cross-section. Both problems can be stated using linearized free surface potential flow theory, and our goal is to compare known analytic solutions in the literature to numerical solutions obtained using an ad-hoc but simple approximation of the non-local Dirichlet-Neumann operator for linear waves proposed in [vargas2016whitham]. To study normal modes in channels with bounded cross-section we consider special symmetric triangular cross-sections, namely symmetric triangles with sides inclined at $45^{\circ}$ and $60^{\circ}$ to the vertical, and compare modes obtained using the non-local Dirichlet-Neumann operator to known semi-exact analytic expressions by Lamb [lamb1932hydrodynamics], Macdonald [macdonald1893waves] , Greenhill [greenhill1887wave], Packham [packham1980small], and Groves [groves1994hamiltonian]. These geometries have slopping beach boundaries that should in principle limit the applicability of our approximate Dirichlet-Neumann operator. We nevertheless see that the operator gives remarkably close results for even modes, while for odd modes we have some discrepancies near the boundary. For trapped longitudinal modes in domains with an infinite cross-section we consider a piecewise constant depth profile and compare modes computed with the nonlocal operator modes to known analytic solutions of linearized shallow water theory by Miles [miles1972wave], Lin, Juang and Tsay [lin2001anomalous], see also [mei2005theory]. This is a problem of significant geophysical interest, and the proposed model is shows to give quantitatively similar results for the lowest trapped modes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
