In this work we prove that the shallow water flow, subject to strong wind forcing and linearized around an adequate stationary profile, develops for large time closed trajectories due to the propagation of Rossby waves, while Poincaré waves are shown to disperse. The methods used in this paper involve semiclassical analysis and dynamical systems for the study of Rossby waves, while some refined spectral analysis is required for the study of Poincaré waves, due to the large time scale involved which is of diffractive type.
Christophe Cheverry. Isabelle Gallagher. Thierry Paul. Laure Saint-Raymond. "Semiclassical and spectral analysis of oceanic waves." Duke Math. J. 161 (5) 845 - 892, 1 April 2012. https://doi.org/10.1215/00127094-1548407