A Stable Non-Laminar Invariant Solution in Pipe Turbulence

The features of the chaotic saddle in a short pipe at Re = 2200 and the ergodic trajectories that visit it are detailed. The domain contains a handful of unstable solutions of the incompressible Navier-Stokes equations (NSE), as well as a marginally stable solution, the first non-laminar stable solution in pipe to be reported. As in longer pipes, the lifetimes of the turbulent trajectories in a short pipe are found to be exponentially distributed, an indicator of memorylessness, and a regular feature of chaotic saddles that give rise to chaos. In addition, a positive correlation between the lifetimes of the ergodic trajectories and the number of sufficiently close passages to the invariant solutions is observed: in general, the longest-lived ergodic trajectories spend more time near invariant solutions.