International Journal of Mathematics and Mathematical Sciences 
Volume 25 (2001), Issue 1, Pages 63-72
doi:10.1155/S0161171201005002

Caustic consideration of long planetary wave packet analysis in the continuously stratified ocean

Arthur D. Gorman1 and Huijun Yang2

 1Department of Mathematics, Lafayette College, Easton 18042, PA, USA
2College of Marine Science, University of South Florida, St. Petersburg 33701, FL, USA
Received 19 April 2000

Abstract

The wave packet method, one form of the WKB technique, recently has been employed to investigate the evolution of long planetary wave packets in relation to the complex climate variability in the world oceans. However, such a method becomes invalid near the caustics. Here, the Lagrange manifold formalism is used to extend this analysis to include the caustic regions. We conclude that even though the wave packet method fails near the caustics, the equations derived from this method away from caustics are identical to ones from the Lagrange manifold formalism near caustics