  This article is concerned with an oceanographic model describing the
asymptotic behaviour of a rapidly rotating and incompressible fluid with an
inhomogeneous rotation vector; the motion takes place in a thin layer. We first
exhibit a stationary solution of the system which consists of an interior part
and a boundary layer part. The spatial variations of the rotation vector
generate strong singularities within the boundary layer, which have
repercussions on the interior part of the solution. The second part of the
article is devoted to the analysis of two-dimensional and three-dimensional
waves. It is shown that the thin layer effect modifies the propagation of
three-dimensional Poincar\'e waves by creating small scales. Using tools of
semi-classical analysis, we prove that the energy propagates at speeds of order
one, i.e. much slower than in traditional rotating fluid models.
