  We study the steady state motion of incompressible and viscous fluid flow in
a rotating reference frame where vortices may take place. An approximated
analytic solution of the Stokes flow problem is proposed for situations where
the vorticity is highly concentrated along a given direction. The approximation
disconnects the component of velocity along the axis of rotation from the
momentum equation. This enables to find the vorticity from the solution of the
Poisson's equation. We use the Green's function approach to provide solutions
of the three-dimensional flow on cylindrical domains with radial inlet/outlet
velocity profiles by using an exact expansion of the Green's function. This
approximated analytical solution for the vorticity is in good agreement with
numerical solutions computed with the Finite Difference Method (FDM). Keywords:
Analytic approximations, Stokes flow, Green's function, FDM.
