Critical behavior in the relaminarization of localized turbulence in pipe flow

The statistics of the relaminarization of localized turbulence in a pipe are examined by direct numerical simulation. As in recent experimental data [J. Peixinho and T. Mullin, Phys. Rev. Lett. 96, 094501 (2006)10.1103/PhysRevLett.96.094501], the half-life for the decaying turbulence is consistent with the scaling (Rec-Re) -1, indicating a boundary crisis of the localized turbulent state familiar in low-dimensional dynamical systems. The crisis Reynolds number is estimated as Rec=1870, a value within 7% of the experimental value 1750. We argue that the frequently asked question, of which initial disturbances at a given Re trigger sustained turbulence in a pipe, is really two separate questions: the "local phase space" question (local to the laminar state) of what threshold disturbance at a given Re is needed to initially trigger turbulence, followed by the "global phase space" question of whether Re exceeds Rec at which point the turbulent state becomes an attractor.