International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 1, Pages 63-72

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

Copyright © 2001 Arthur D. Gorman and Huijun Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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