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

Analytic treatment of vortex motion in non-inertial Stokes flows