Rethinking Pipe Flow Stability: Insights from a Meshless Global Analysis

TL;DR

This paper introduces a meshless global stability analysis method for pipe flow, revealing new localized modes and providing insights into turbulence onset, challenging traditional linear stability approaches.

Contribution

It presents a novel meshless global analysis framework for pipe flow stability, uncovering new modes and insights into turbulence that differ from local stability analysis results.

Findings

Identified new localized modes in pipe flow

Demonstrated the global approach captures instabilities without multiple simulations

Provided insights into transient energy growth mechanisms

Abstract

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.