A study of a spectral problem related to the stability of Couette flow between two rotating cylinders

In the paper we consider some methods for solution of a spectral problem related to the stability of Couette flow (a solution to the Navier-Stokes equations) in a domain between two infinite rotating cylinders. An analytical solution of the corresponding spectral problem is given for a number of particular cases. Our numerical results show that the spectra depend on Reynolds numbers and that the spectra are related to the stability of Couette flow. The eigenfunctions computed are illustrated.