In order to numerically investigate confined rotating flows, we have developed two numerical methods based on a spectral approximation of the solution of the incompressible Navier-Stokes equations. The first approach consists in solving 3D Navier-Stokes equations in the case of simple rotating cavities corresponding to two discs enclosing either a cylindrical or an annular. The velocity-pressure coupling is treated with a modified projection scheme. The second approach consists in solving axisymmetric Navier-Stokes equations written in the vorticity-streamfunction formulation in the case of semi-complex geometric configurations and singular solutions. A spectral domain decomposition method has been developped based on the influence matrix technique. In this paper, we present some results about complex physical phenomena. Three-dimensional boundary layers instabilities are obtained and vortex breakdown phenomena are shown along the axis of a rotating cylinder. The axisymmetric multidomain method is shown efficient to simulate convective and absolute instabilities at the neighbourhood of a side cavity in a meridain plane of a rotating 'channel-cavity' system submitted to an axial throughflow.