The high-Reynolds-number stability of unsteady pipe flow to axisymmetric
disturbances is studied using asymptotic analysis. It is shown that as the disturbance
amplitude is increased, nonlinear effects first become significant within the critical
layer, which moves away from the pipe wall as a result. It is found that the flow
stabilizes once the basic profile has become sufficiently fully developed. By tracing
the nonlinear neutral curve back to earlier times, it is found that in addition to
the wall mode, which arises from a classical upper branch linear stability analysis,
there also exists a nonlinear neutral centre mode, governed primarily by inviscid
dynamics. The centre mode problem is solved numerically and the results show the
existence of a concentrated region of vorticity centred on or close to the pipe axis
and propagating downstream at almost the maximum fluid velocity. The connection
between this structure and the puffs and slugs of vorticity observed in experiments is
discussed.