A method for analysis of stability of flows in ribbed annuli

A spectrally-accurate algorithm for the linear stability analysis of pressure-gradient-driven flows in corrugated annuli is presented. The algorithm is suitable to analyze three-dimensional disturbances in the form of spiral traveling waves as well as in the form of streamwise vortices. A separate algorithm for the analysis of axisymmetric disturbances is presented. The discretization method relies on Fourier expansions in the streamwise and circumferential directions and on Chebyshev expansions in the radial direction. The Immersed Boundary Conditions (IBC) method is used to enforce the physical boundary conditions at the corrugated walls. Numerous tests confirm the spectral accuracy of the results. The performance of the algorithm is consistent with the theoretical predictions.