Normal Modes of the Shallow Water Equations for Zonal Wavenumber Zero
Normal Modes of the Shallow Water Equations for Zonal Wavenumber Zero
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零纬向波数浅水方程的正规模态
DOI：
10.2151/jmsj1965.61.4_479
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发表时间：
1983
影响因子：
3.1
通讯作者：
Yosuke Shigehisa
中科院分区：
文献类型：
--
作者：
Yosuke Shigehisa
讨论了与非纬向本征解性质一致的拉普拉斯潮汐方程的纬向对称地转本征解的构造。我们推导了一个微分方程，它定义了在拉普拉斯位势潮汐方程中，当纬向波数趋于零时，在极限情况下纬向波数为零的地转本征解。这些特征解与非零纬向波数的对应解相似。在Lamb参数*=0和*= *的特殊情况下，对于非零波数，相关本征解的性质分别与Haurwitz波和赤道波的性质密切对应。结果表明，正a（包括*=0）的本征解集构成了纬向对称地转势及其相关地转风的完备集。
The construction of zonally symmetric geostrophic eigensolutions to Laplace's tidal equations which have properties consistent with those of the nonzonal eigensolutions is discussed. We have derived a differential equation which defines geostrophic eigensolutions for zonal wave number zero in the limit as the zonal wave number tends to zero in Laplace's tidal equation for geopotential. These eigensolutions are similar to the counterparts for non-zero zonal wave number. In special cases of Lamb's parameter *=0 and *= *, the properties of the associated eigensolutions closely correspond to those of Haurwitz waves and equatorial waves, respectively, for non-zero wave number. It is shown that the set of eigensolutions for positive a (including *=0) forms a complete set for zonally symmetric geopotential and the associated geostrophic wind.