The onset of absolute instability of rotating Hagen-Poiseuille flow: A spatial stability analysis

A spatial, viscous stability analysis of Poiseuille pipe flow with superimposed solid body rotation is considered. For each value of the swirl parameter (inverse Rossby number) L>0, there exists a critical Reynolds number Re-c(L) above which the flow first becomes convectively unstable to nonaxisymmetric disturbances with azimuthal wave number n=-1. This neutral stability curve confirms previous temporal stability analyses. From this spatial stability analysis, we propose here a relatively simple procedure to look for the onset of absolute instability that satisfies the so-called Briggs-Bers criterion. We find that, for perturbations with n=-1, the flow first becomes absolutely unstable above another critical Reynolds number Re-t(L)>Re-c(L), provided that L>0.38, with Re-t-->Re-c as L-->infinity. Other values of the azimuthal wave number n are also considered. For Re>Re-t(L), the disturbances grow both upstream and downstream of the source, and the spatial stability analysis becomes inappropriate. However, for Re