The three-dimensional instability modes that appear on a solid-body rotation flow in a finite-length, straight, circular pipe are analyzed. This study is a direct extension of the Wang and Rusak (1996) analysis of axisymmetric instabilities on swirling flows in a pipe.  It was motivated by our recent DNS results. We study a general mode of perturbation that satisfies the inlet, outlet and wall conditions of a flow in a finite-length pipe.

It was found that  the $m=1$ modes are the first to become unstable as the swirl ratio is increased and dominate the 
perturbation's growth in a certain range of swirl levels.

These results are completely different from the classical normal mode analysis, but are  in good agreement with DNS results. This suggests that the classical vortex stability theory with normal mode approach has fundamental limitations and cannot be applied for the current case. The underlying physical mechanism, as why a finite-length vortex model is a suitable approach, will be discussed in the talk