Splitting of turbulent spots in transitional pipe flow.

Splitting of turbulent spots in a Re=2,300 transitional flow developing spatially from weakly perturbed laminar inflow in a 1000 radii long pipe is investigated by DNS, c.f. Wu et al (PNAS, 112, 7920, 2015). Spots are created by blobs of turbulence introduced from the inlet and developing through fully-developed laminar flow. Turbulent spots of scalars were first observed in Osborne Reynolds’ dye experiments, but the splitting phenomenon was not discovered until the work of E.R. Lindgren (Arkiv Fysik, 16, 101-112, 1959a). The center-line axial velocities ahead and behind a spot are very close to the expected laminar value=2 x bulk velocity. Passive scalar from the centerline occupies a smaller region than that impacted by the spot’s velocity field. A first-generation spot splits because a sustained speed difference between the front and middle of the spot pulls it apart. The separated front and back halves reform into 2nd generation spots that one might expect to repeat the process, thereby creating 3rd generation, and so on. In reality, 2nd generation turbulent spots enter an unexpected quasi-cyclic process containing previously unknown sub-processes of parent-child re-connection and re-splitting, rather than successive generational splitting.