Analytic treatment of vortex motion in non-inertial Stokes flows

Abstract

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.