Duke Mathematical Journal

Semiclassical and spectral analysis of oceanic waves

Christophe Cheverry, Isabelle Gallagher, Thierry Paul, and Laure Saint-Raymond

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Abstract

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.

Article information

Source
Duke Math. J., Volume 161, Number 5 (2012), 845-892.

Dates
First available in Project Euclid: 27 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1332866805

Digital Object Identifier
doi:10.1215/00127094-1548407

Mathematical Reviews number (MathSciNet)
MR2904094

Zentralblatt MATH identifier
1244.35147

Subjects
Primary: 35Q86: PDEs in connection with geophysics
Secondary: 76M45: Asymptotic methods, singular perturbations 35S30: Fourier integral operators 81Q20: Semiclassical techniques, including WKB and Maslov methods

Citation

Cheverry, Christophe; Gallagher, Isabelle; Paul, Thierry; Saint-Raymond, Laure. Semiclassical and spectral analysis of oceanic waves. Duke Math. J. 161 (2012), no. 5, 845--892. doi:10.1215/00127094-1548407. https://projecteuclid.org/euclid.dmj/1332866805


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