Shallow water modeling in spherical coordinates: equation formulation, numerical implementation, and application
Shallow water modeling in spherical coordinates: equation formulation, numerical implementation, and application
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球坐标系中的浅水建模：方程公式、数值实现和应用
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
R. Luettich
中科院分区：
文献类型：
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作者：
R. Kolar;W. G. Gray;J. Westerink;R. Luettich
一类地表水模型是通过对微尺度质量和动量平衡进行深度平均而获得的浅水模型。将浅水模型应用于大规模问题（数千公里量级）需要使用球坐标。传统上，球坐标中的平衡定律是通过简单地扩展标准深度平均方程中的空间算子来导出的。然而，方程本身基于假设的平面，因此推导和解释之间存在不一致。在本文中，提出了一种在深度平均过程中正确考虑地球曲率的方法。该推导产生了连续性和动量平衡中的新项，我们将其称为曲率项。尺度分析评估各项的大小。结果表明，当垂直速度较小（即至少为 4 倍）时，连续性平衡中的曲率项可忽略不计。
One class of surface water models is the shallow water models obtained by depth-averaging the microscale mass and momentum balances. Application of shallow water models to large scale problems (on the order of 1000's of km) requires the use of spherical coordinates. Traditionally, balance laws in spherical coordinates are derived by simply expanding the spatial operators in the standard depth-averaged equations. However, the equations themselves are based on an assumed planar surface so that an inconsistency exists between the derivation and the interpretation. In this article, a method is presented that properly accounts for the curvature of the Earth during the depth-averaging procedure. The derivation gives rise to new terms in both the continuity and momentum balances, terms that we refer to as curvature terms. A scaling analysis evaluates the magnitude of the terms. It is shown that the curvature term in the continuity balance is insignificant when the vertical velocity is small, i.e., at least four ...