Rethinking Pipe Flow Stability: Insights from a Meshless Global Analysis

Despite extensive experimental evidence of turbulence in Hagen Poiseuille flow, linear stability analysis has not yet confirmed its instability. One challenge is the singularity introduced by the term 1/r in the center of the pipe, which complicates traditional stability approaches. In this study, we explore a global stability analysis using a meshless framework. Although this approach did not recover the expected unstable modes, it revealed a new set of modes with distinct characteristics from those observed in local stability analysis. We analyze these modes and their impact on transient energy growth, demonstrating the effectiveness of the global approach in capturing localized instabilities without requiring multiple simulations.