| Summary: | This thesis considers the axisymmetric stability of a flow, subject to an axial pressure gradient, between concentric sliding cylinders, or annular Couette-Poiseuille flow (ACPF). The flow geometry and governing equations are set out and we analyse the linear and nonlinear stability of ACPF for a range of inner cylinder velocity, radius ratio and disturbance amplitude. We establish that the flow is inviscidly stable and introduce an axisymmetric travelling wave disturbance to the flow. We find that ACPF is linearly unstable and comparisons are made with published work such as those of Walton (2004) and Webber (2008). Using a continuation method, the linearly unstable solutions provide a starting point to compute finite-amplitude, nonlinear axisymmetric travelling wave solutions. These nonlinear solutions also exist in the wavenumber-Reynolds number, or neutral curve, space where linear stability predicts no solutions. The nonlinear travelling wave solutions result in lower critical Reynolds number and higher critical inner cylinder velocity compared to that of linear stability predictions. The nonlinear wave disturbance influence is strongest near the inner and outer cylinder walls and the mean flow distortion has the general effect of slowing the basic flow velocity. We also present the existence of multiple neutral curves in nonlinear space and these multiple neutral curves appear to unite as the disturbance amplitude increases. In an effort to link our results to Hagen-Poiseuille flow (HPF), we analyse the special case of ACPF where the maximum velocity of the flow is always achieved on the inner cylinder and find that this flow is linearly stable.
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