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

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 Poincar\'e waves, is proved by an abstract semi-classical approach. The dispersion of Poincar\'e 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.