Global mode analysis of a pipe flow through a 1:2 axisymmetric sudden expansion

We report the results of the global mode analysis to characterize the onset of unsteadiness in a circular pipe flow through an axisymmetric sudden expansion of inlet-to-outlet diameter ratio of d/D=0.5. We find that the axisymmetric state becomes linearly unstable at a significantly higher critical Reynolds number than the one reported in previous experimental works. This unstable global mode corresponds to an oscillatory bifurcation with wavenumber |m|=1 located at the end of the recirculation region.