DIRECTED PERCOLATION PHENOMENA IN SUBCRITICAL TRANSITION OF HIGH-ASPECT-RATIO DUCT FLOW

Directed percolation (DP) and subcritical turbulent transitions in channel flow, which have been a debatable issue in recent years, are investigated by direct numerical simulations for high-aspect-ratio channel flows with spanwise sidewalls, i.e., very thin, wide duct flows. The presence of sidewalls in the duct flow prevented sustained stable localized turbulence band at low Reynolds numbers (700 ≲ Re ≲ 1000), which allowed global turbulence maintenance in the infinitely wide channel flow, and the critical values were approximately Re_c = 1000. Localized turbulence was spatio-temporally intermittency, and its split and decay were generally similar to those in the channel flow, although there were some behaviors specific to the duct flow. Long-term Lagrangian observation of the split and decay of localized turbulence near the criticality showed the branching of turbulence in the space-time-diagrams. The spatial dimension of the branching depended on the duct geometry, with a spatial one-dimensional spread when the distance between sidewalls was not wide enough (like in a square duct), but two-dimensional when it was wide, qualitatively confirming (1 + 1)-dimensional and (2 + 1)-D DP characteristics, respectively. The power-law scaling exponents for the Reynolds number dependence of the transition profiles were found to be consistent with the specific critical exponents of the two types of DPs, respectively.