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Gravitational mode calculation of basins discretized by orthogonal curvilinear grids

机译：正交曲线网格离散盆地的重力模式计算

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摘要

This paper presents a simple and straightforward method for carrying out the direct numerical solution of the eigenvalue problem associated to the homogeneous linear shallow-water equations expressed using orthogonal curvilinear coordinates, when 'adiabatic' boundary conditions apply. These equations, together with the boundary conditions, define a self-adjoint problem in the continuum. The method presented here, which is thought for calculating the 2-D theoretical gravity modes of both natural and artificial basins, relies on a change of basis of the dependent variable vector. This preliminary transformation makes it, in fact, possible to formulate two different numerical approaches which guarantee the self-adjoint property of the discrete form of the system consisting of the governing equations and the boundary conditions. The method is tested using a square and a fully circular domain, both of which allow comparisons with well-known analytical and numerical solutions. Discretizing the physical domain of a fully circular basin by a cylindrical coordinate grid makes it possible to show the actual efficiency of the method in calculating the theoretical gravity modes of basins discre-tized by a boundary-foll owing coordinate grid which allows laterally variable resolution.
机译：本文提出了一种简单明了的方法，当应用“绝热”边界条件时，可以执行与使用正交曲线坐标表示的齐次线性浅水方程相关的特征值问题的直接数值解。这些方程式与边界条件一起在连续体中定义了一个自伴问题。这里介绍的方法被认为是用于计算自然盆地和人工盆地的二维理论重力模式的方法，它依赖于因变量矢量的变化。实际上，通过这种初步的转换，可以制定两种不同的数值方法，这些方法可以保证由控制方程和边界条件组成的系统离散形式的自伴性质。使用正方形和完全圆形的域对方法进行了测试，这两种方法都可以与众所周知的分析和数值解决方案进行比较。通过圆柱坐标网格离散化完全圆形盆地的物理域，可以显示该方法在计算边界边界坐标网格离散化的盆地理论重力模式时的实际效率，该方法允许横向可变分辨率。

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