2010/11/19 by Isabelle Gallagher, Gallagher, Isabelle, Paul, Thierry +2
Earth and Planetary Sciences · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Ocean Waves and Remote Sensing #Oceanographic and Atmospheric Processes
paper · doi:10.48550/arxiv.1011.4435
openalex publication_date 2010/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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 \citeCGPS, 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.