On the normal modes of Laplace's tidal equations for zonal wavenumber zero
On the normal modes of Laplace's tidal equations for zonal wavenumber zero
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关于纬向波数为零的拉普拉斯潮汐方程的简正模态
DOI：
10.3402/tellusa.v44i1.14940
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发表时间：
1992
期刊：
影响因子：
2
通讯作者：
A. Kasahara
中科院分区：
文献类型：
--
作者：
H. Tanaka;A. Kasahara
拉普拉斯潮汐方程的简正模（称为Hough调和函数）对于纬向波数m > 0是完备的，因此，经向和纬向速度分量以及重力位可以表示为一系列Hough调和函数。然而，对应于m = 0的Hough谐波是不完整的，因为第二类简正模式具有全部零频率。为了满足正交基函数的需要，Kasahara和Shigehisa构造了m = 0时拉普拉斯潮汐方程的两组不同的旋转模式，分别称为K模式和S模式。在这项研究中，我们比较了K-和S-模式的能量比和结构之间的特征差异。从FGGE IIIb再分析的大气数据的纬向平均分量分别投影到K-和S-模式，除了重力模式。我们发现，K-模式表示捕获的大部分观察到的带状能量与几个条款，而S-模式表示需要许多条款。K-模式系列收敛速度比S-模式系列，特别是在所观察到的纬向场的小垂直尺度分量。沿着讨论了投射在K-和S-模态上的能量谱之间的差异，并考虑了每一组能量谱作为纬向大气运动展开函数的优点。DOI：10.1034/j.1600-0870.1992.00003.x
Normal modes of Laplace's tidal equations, referred to as Hough harmonics, are complete for zonal wavenumber m > 0 so that the longitudinal and meridional velocity components and the geopotential can be represented as a series of Hough harmonics. However, Hough harmonics corresponding to m = 0 are incomplete in that the second kind normal modes have all zero frequencies. To fill the need for orthonormal basis functions, Kasahara and Shigehisa have constructed two different sets of the rotational modes of Laplace's tidal equations for m = 0, referred to as the K-modes and the S-modes, respectively. In this study, we compared the characteristic differences between the K- and S-modes in their energy ratio and structures. The zonal-mean components of atmospheric data from the FGGE IIIb reanalysis are projected onto the K- and S-modes separately, in addition to the gravity modes. We showed that the K-mode representation captures the majority of observed zonal energy with a few terms, whereas the S-mode representation requires many terms. The K-mode series converges faster than the S-mode series, especially for small vertical-scale components in the observed zonal fields. The differences between the energy spectra projected upon the K- and S-modes are discussed along with the consideration of the merits of each set as expansion functions for the zonal atmospheric motions. DOI: 10.1034/j.1600-0870.1992.00003.x