  The Navier-Stokes-Coriolis system is a simple model for rotating fluids,
which allows to study the influence of the Coriolis force on the dynamics of
three-dimensional flows. In this paper, we consider the NSC system in an
infinite three-dimensional layer delimited by two horizontal planes, with
periodic boundary conditions in the vertical direction. If the angular velocity
parameter is sufficiently large, depending on the initial data, we prove the
existence of global, infinite-energy solutions with nonzero circulation number.
We also show that these solutions converge toward two-dimensional Lamb-Oseen
vortices as time goes to infinity.
