A Balanced Approximation of the One-Layer Shallow-Water Equations on a Sphere
A Balanced Approximation of the One-Layer Shallow-Water Equations on a Sphere
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DOI：
10.1175/2008jas2837.1
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发表时间：
2009-06
影响因子：
3.1
通讯作者：
W. Verkley
中科院分区：
文献类型：
--
作者：
W. Verkley
摘要本文导出了球上一层浅水方程组的等效正压涡度方程的全球形式。该方程与相应的β平面形式具有相同的形式，但有一个重要的区别：位涡表达式中的拉伸（Cressman）项完全依赖于f 2，其中f是科里奥利参数。作为检查所产生的系统，线性Rossby波的动力学被认为是。它表明，这些波是相当准确的近似西传播波的第二类原始浅水方程。对于短纬向Rossby波，拉伸项中的因子f2可用常数值f0 2代替，其中f0为±45°纬度处的科里奥利参数。
Abstract A global version of the equivalent barotropic vorticity equation is derived for the one-layer shallow-water equations on a sphere. The equation has the same form as the corresponding beta plane version, but with one important difference: the stretching (Cressman) term in the expression of the potential vorticity retains its full dependence on f 2, where f is the Coriolis parameter. As a check of the resulting system, the dynamics of linear Rossby waves are considered. It is shown that these waves are rather accurate approximations of the westward-propagating waves of the second class of the original shallow-water equations. It is also concluded that for Rossby waves with short meridional wavelengths the factor f 2 in the stretching term can be replaced by the constant value f02, where f0 is the Coriolis parameter at ±45° latitude.