STOKES MODES IN TAYLOR-COUETTE GEOMETRY

The eigenvalue problem of the Stokes operator is solved for an incompressible fluid contained between two coaxial cylinders of infinite height. Flow field patterns and spectra of the eigenmodes ("Stokes modes") are offered. Furthermore, in finite dimensional subspaces generated by these Stokes modes, the eigenproblem for the Navier-Stokes operator linearized about the laminar Taylor-Couette flow is studied. Although the spectrum's qualitative features are still correct, we quantitatively obtain wrong results. We trace this back to a Gibbs like phenomenon of higher order derivatives of the flow field as probable source, since the Stokes modes do not reflect the discontinuity arising from different velocities at both cylinders.