期刊名称：Tellus A: Dynamic Meteorology and Oceanography
电子版ISSN：1600-0870
出版年度：2019
卷号：71
期号：1
页码：1-8
DOI：10.1080/16000870.2019.1618133
摘要：The eigenfrequencies of freely propagating divergent barotropic planetary and gravity waves in a spherical
polar cap are discussed. The key amplitude equation is derived with the full spherical geometry maintained
and leads to a second-order differential equation with coefficients functions of the co-latitude. Previous study
of this problem has derived approximations to the requisite frequencies by evaluating these coefficients at
some chosen fixed value of the co-latitude thereby reducing the problem to that of a constant coefficient
differential equation solved easily using routine methods. Here, we demonstrate that such a simplification can
be avoided since the full equation can be solved by standard asymptotic methods based on the latitudinal
limit of the polar basin as the natural small parameter. Three-term asymptotic series are developed which are
in remarkably good accord with numerical solutions of the full equation.
