Saddle-node bifurcation during relaminarization of turbulent puffs in pipe flow

In the Reynolds number range from 1720 to 1920, the turbulent puff regime in the pipe abruptly escapes the chaotic state before exponentially decaying to laminar flow. The decay rate is weakly dependent on the Reynolds number; the relaminarization time is approximately O(100) measured in advective (D/Um) units. Direct numerical simulations revealed persistent saddle, nodal and inflection points. With the onset of relaminarization, saddle points have detached from the near-wall region, and they closely coincide with the azimuthal positions where streamwise velocity profiles exhibit inflection points, which are the source of instability. The saddle-node bifurcation is characterized by the collision and annihilation events that occur during relaminarization, which leads to a decrease in the number of saddles and nodes. The complete relaminarization of the flow is the result of the self-sustaining mechanism's breakdown, as symbolized by the annihilation of saddle points during relaminarization.