Examination of the onset and decay of turbulence in pipe flow

The crisis (or critical) Reynolds number (Rec) is established at 1870, describing the threshold beyond which the lifetimes of turbulent puffs prior to the relaminarization extend from O(104)toO(106) time units (D/Um), where D and Um denote the pipe diameter and mean velocity, respectively. To analyze the role of inplane motion for sustaining turbulence, fully resolved direct numerical simulations have been performed to generate a localized, equilibrium turbulent puff at Re=1920. Employing our approach based on proper orthogonal decomposition, the research confirms that azimuthal motion significantly contributes to the transition to turbulence. Notably, at supercritical Reynolds numbers (Re>Rec) ranging from Re=1920 to Re=2100, reducing azimuthal motion energy by 80% substantially shortens the lifetime of turbulent puffs. It has been shown that the relaminarization of turbulent puffs at subcritical Reynolds numbers, Re=1720-1840, clearly implies an exponential time decay of turbulence energy. The expression for the decay rate was obtained as a best-fit curve of direct numerical simulations.