  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.
