There have been many investigations of the stability of Hagen–Poiseuille flow in the 125 years since Osborne Reynolds' famous experiments on the transition to turbulence in a pipe, and yet the pipe problem remains the focus of attention of much research. Here, we discuss recent results from experimental and numerical investigations obtained in this new century. Progress has been made on three fundamental issues: the threshold amplitude of disturbances required to trigger a transition
to
turbulence from the laminar state; the threshold Reynolds number flow below which a disturbance decays
from
turbulence to the laminar state, with quantitative agreement between experimental and numerical results; and understanding the relevance of recently discovered families of unstable travelling wave solutions to transitional and turbulent pipe flow.
Intermediate scaling and logarithmic invariance in turbulent pipe flow
