Semiclassical and spectral analysis of oceanic waves

Christophe Cheverry (1) , Isabelle Gallagher (2) , Thierry Paul (3) , Laure Saint-Raymond (4, 5)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 IMJ - Institut de Mathématiques de Jussieu
3 CMLS - Centre de Mathématiques Laurent Schwartz
4 DMA - Département de Mathématiques et Applications - ENS Paris
5 LJLL - Laboratoire Jacques-Louis Lions

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 times closed trajectories due to the propagation of Rossby waves, while Poincaré waves are shown to disperse. The methods used in this paper involve semi-classical 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.

Mots clés: Semiclassical analysis; microlocal analysis; integrable systems; Bohrn-Sommerfeld quantization; Geophysical flows

Domaines: Equations aux dérivées partielles [math.AP]

Christophe Cheverry, Isabelle Gallagher, Thierry Paul, Laure Saint-Raymond. Semiclassical and spectral analysis of oceanic waves. Duke Mathematical Journal, 2012, 161 (5), pp.845-892. ⟨hal-00481593v3⟩