Linear Instability of Entry Flow in a Pipe

Abstract

We show that flow in the entry region of a circular pipe is linearly unstable at a Reynolds number of 1000, a factor of 10 smaller than assumed hitherto. The implication that dynamics in this region could greatly hasten the transition to turbulence assumes relevance because in spite of major recent progress, the issue of how pipe flow becomes turbulent is far from settled. Being axisymmetric and close to the centerline, the present instability would be easily distinguishable in an experiment from other generators of turbulence.