A study of the fluctuations of the atmospheric planetary flow patterns represented by spherical harmonics
A study of the fluctuations of the atmospheric planetary flow patterns represented by spherical harmonics
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球谐函数代表的大气行星流型的涨落研究
DOI：
10.1111/j.2153-3490.1965.tb01414.x
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发表时间：
1965
期刊：
影响因子：
2
通讯作者：
Bannert Machenhauer
中科院分区：
文献类型：
--
作者：
E. Eliasen;Bannert Machenhauer
本文叙述了用一系列球谐分量展开北方半球压力面高度的方法。利用地转平衡条件，得到了相应的流函数球谐表达式。从这个表示平均值的动能谱分布在500毫巴的水平，1957年1月。在1956年12月1日至1957年2月28日的90天期间，在500 mb和1000 mb水平上考虑了具有最大水平尺度的成分的行为。在一般情况下，这些组件表现出较小或较大的波动，它是试图通过消除流场的常数和长周期部分，以调查较短的周期波动的字符。对于波数为1、2和3的分量，以及最大尺度的纬向变化，24小时趋势场显示出或多或少有规律的向西传播，传播速度的平均值对应于约5天的周期。对于具有相同波数但具有第二大纬向尺度的分量，我们发现15天平均流量位移的每日偏差也主要朝向西方，并且传播速度的平均值随着水平尺度的减小而减小。以这种方式获得的不同分量的传播速度的平均值几乎与由Rossby效应确定的速度一致，特别是如果这种效应被弱发散效应稍微减小的话。本文根据正压涡度方程的谱形式，计算了1957年1月逐日500毫巴流函数的展开系数、振幅和相角的时间导数，包括纬向流的某些分量和波数为1、2、5、6的某些分量。从这些时间导数48小时的趋势进行了评估，并与相应的观察比较。在一般情况下，它被发现的协议是更好的组件具有中等规模比非常大的规模的组件。在某种程度上，这可以用忽略准定态效应来解释，作为一种非常简单的尝试，这些效应用一个常数项来表示。最后考虑了各组分量间正压相互作用对各分量动能变化的贡献。DOI：10.1111/j.2153-3490.1965.tb01414.x
A procedure used for expanding the height of a pressure surface over the Northern Hemisphere in a series of spherical-harmonic components is described. The corresponding spherical-harmonic representation of the stream function is obtained by utilizing the geostrophic balance condition. From this representation mean values for the spectral distribution of the kinetic energy at the 500 mb level for January 1957 is presented. The behaviour of the components with the largest horizontal scales is considered at the 500 mb and the 1000 mb levels during the 90 days period from 1 December 1956 to 28 February 1957. In general each of these components exhibits smaller or larger fluctuations, and it is attempted to investigate the character of the shorter periodic fluctuations by eliminating the constant and the long periodic parts of the stream field. For the components with wavenumber 1, 2, and 3, and with the most large-scale meridional variation, the 24 hours tendency fields show a more or less regular westward propagation with mean values for the velocity of propagation, corresponding to periods about 5 days. For the components with the same wavenumbers but with the second largest meridional scales we find for the daily deviations from the 15 days mean flow displacements also mainly towards the west and also with mean values for the velocity of propagation, decreasing with decreasing horizontal scale. The mean values of the velocity of propagation obtained in this way for the different components are nearly in accordance with the velocities determined by the Rossby effect, especially if this effect is reduced somewhat by a weak divergence effect. On the basis of the spectral form of the barotropic vorticity equation the time derivatives for the expansion coefficients as well as for the amplitude and phase angle of the stream function at the 500 mb level have been computed for each day in January 1957, for some components of the zonal flow and some of the components with wave-number 1, 2, 5, and 6. From these time derivatives 48 hours tendencies have been evaluated and compared with the corresponding observed ones. In general it is found that the agreement is better for components with moderately large scales than for components with very large scales. To some extent this may be explained by the neglect of quasi-stationary effects, and as a very simple attempt, these are represented by a constant term. Finally the contributions from the barotropic interactions between different groups of components to the change of kinetic energy of individual components are considered. DOI: 10.1111/j.2153-3490.1965.tb01414.x