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.
Willis
Ashley P
AP
Department of Mathematics, University of Bristol, University Walk, Bristol, UK. a.willis@bris.ac.uk
Kerswell
Rich R
RR