面向大气热力潮汐结构分析的Hough函数计算

作为一种刻画行星尺度大气波动基本结构的函数，Hough函数为开展有关大气潮汐全球结构的分析提供了具有物理基础的手段，它们也被作为一种数值工具应用于大气模式中以提高数值积分的效率.本文介绍了我们以拉普拉斯潮汐方程为基础，在发展求取Hough函数方面取得的进展，包括对有关计算方案和详细步骤的说明.针对39种分别具有三种主要频率，即周日、半日和1/3日，与此同时纬向波数落在6，6]区间的潮汐成份，通过计算得到了与每一种成份对应的本征值、本征函数（Hough函数）集合.作为计算结果的示例，本文给出了针对迁移性周日潮和迁移性半日潮开展计算取得结果.这些结果说明这些函数具有正确的空间结构，与此同时还说明相关的本征值计算结果都达到了相当准确的水平.所有这些结果显示当前计算结果已经可以满足普通的应用.

On the calculation of Hough functions for resolving atmospheric thermal tidal structure

As the functions that characterize the fundamental structures of global scale atmospheric waves, Hough funtions provide a physically based means in analyzing the dynamics atmospheric tides, and are also used as an numerical tool with enhanced efficiency in the integration of atmospheric models. This paper introduces our development in the calculation of Hough functions based upon Laplace's tidal equation. The framework of the calculation and the details of the procedures are described. The Eigen values and the Hough functions associating to each of the 39 tidal components, i.e., that include the components falling in three primary frequencies, viz., diurnal, semidiurnal and terdiurnal, and in zonal wavenumber range -6, 6], are all calculated. As examples, the results of the Hough functions associating to the migrating diurnal and semidiurnal tides are presented here to show the correctness in the structure of these functions. And the results of the corresponding Eigen values show that substantial accuracies in these values are maintained, which suggests that the cuurent results are sufficiently applicable for conventional applications.