Axisymmetric travelling waves in annular couette-poiseuille flow

A computational study of the stability of the axial pressure-gradient-driven viscous flow between concentric sliding cylinders is presented. Nonlinear axisymmetric travelling wave solutions, which bifurcate from the linear neutral curve, are found for a range of radius ratio, sliding velocity and disturbance amplitude. Solutions which come into existence at finite amplitude and are not connected to the linear state in wavenumber-Reynolds number space are also found. The critical Reynolds numbers associated with these solutions are found to be substantially lower than those predicted by linear theory. For some combinations of parameters, two nonlinear solutions with different wavelengths are found to coexist and appear to merge into one as the amplitude is increased.