%0 Journal Article
%T Accurate approximations for planetary and gravity waves in a polar basin
%A Andrew J. Willmott
%A Andrew P. Bassom
%J Tellus A: Dynamic Meteorology and Oceanography
%D 2019
%R https://doi.org/10.1080/16000870.2019.1618133
%X Abstract 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
%U https://www.tandfonline.com/doi/full/10.1080/16000870.2019.1618133