Accurate approximations for planetary and gravity waves in a polar basin. Issue 1 (1st January 2019)

• Record Type: Journal Article
• Authors: Bassom, Andrew P.; Willmott, Andrew J.
• Is Part Of: Tellus. Volume 71:Issue 1(2019)
• Publication Date: 2019-01-01
• Subjects: polar basin -- asymptotic expansions -- wave frequencies; Dynamic meteorology -- Periodicals; Oceanography -- Periodicals; 551.5
• DOI: 10.1080/16000870.2019.1618133
• Languages: English
• ISSNs: 0280-6495

Abstract

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.