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On the propagation of oceanic waves driven by a strong macroscopic flow

On the propagation of oceanic waves driven by a strong macroscopic flow
Isabelle Gallagher 1Thierry Paul 2Laure Saint-Raymond 3

In this work we study oceanic waves in a shallow water flow subject to strong wind forcing and rotation, and linearized around a inhomogeneous (non zonal) stationary profile. This extends the study~cite{CGPS}, where the profile was assumed to be zonal only and where explicit calculations were made possible due to the 1D setting. Here the diagonalization of the system, which allows to identify Rossby and Poincaré waves, is proved by an abstract semi-classical approach. The dispersion of Poincaré waves is also obtained by a more abstract and more robust method using Mourre estimates. Only some partial results however are obtained concerning the Rossby propagation, as the two dimensional setting complicates very much the study of the dynamical system.
1 :  Institut de Mathématiques de Jussieu (IMJ)
CNRS : UMR7586 – Université Pierre et Marie Curie - Paris VI – Université Paris-Diderot - Paris VII
2 :  Centre de Mathématiques Laurent Schwartz (CMLS-EcolePolytechnique)
CNRS : UMR7640 – Polytechnique - X
3 :  Département de Mathématiques et Applications (DMA)
CNRS : UMR8553 – Ecole Normale Supérieure de Paris - ENS Paris
Mathématiques/Equations aux dérivées partielles
Semiclassical analysis – microlocal analysis – Mourre estimates – Geophysical flows
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