  In this paper, we shall implement KAM theory in order to construct a large
class of time quasi-periodic solutions for an active scalar model arising in
fluid dynamics. More precisely, the construction of invariant tori is performed
for quasi-geostrophic shallow-water equations when the {\it Rossby deformation
length} belongs to a massive Cantor set. As a consequence, we construct
pulsating vortex patches whose boundary is localized in a thin annulus for any
time.
