Structure, memory and splitting of turbulent spots in transitional pipe flow without axially periodic boundary condition

We begin our investigation by studying scalar flash, turbulent spot and transition statistics in a 500 radii-long pipe configuration at Reynolds number 6500, based on the bulk velocity and the pipe diameter. During the late stage of transition, second-order statistics such as the rate of dissipation of turbulent kinetic energy exhibit substantial overshoot, which is accounted for by the observed stronger mid-to-high frequency content in the spectra of the rate of dissipation. Transitional turbulent spots are found to have a dual-type structural composition. The near-wall region consists of primarily reverse hairpin vortices with their head element directing towards the upstream direction and towards the wall. This composition is related to the high-speed streaks arising from the prescribed inlet perturbation. The core region of the spots on the other hand is populated by normal hairpin vortices. Passive scalar injected at the center of the inlet plane develops during transition into what we call the Type-1 flash, which is bounded by non-turbulent region(s) from at least one end, and it is directly associated with the transitional-turbulent spot. Immediately downstream of the high-scalar-value Type-1 flash is a zone with sharply lower scalar value. This results in a segmented scalar field pattern propagating well into the downstream fully turbulent pipe flow, forming what we call the Type-2 scalar flash residing in a turbulent environment. At several hundred radii downstream of transition where the flow is fully-developed and turbulent, the Type-2 scalar flashes serve as carriers of persistent memory of the far upstream transition. In the second stage of the investigation, we use a 1000 radii long pipe flow to study the splitting of turbulent spots, a feature first discovered by E.R. Lindgren (Arkiv Fysik, 16, 101-112, 1959a). Reynolds number is 2300. The simulation design asymptotes the idealized scenario in which a blob of turbulence introduced from the inlet develops through fully-developed laminar flow in a very-long smooth pipe. The instantaneous axial velocity along the centerline remains almost exactly as the expected laminar value both upstream and downstream of the migrating turbulent spot packet, which permits simple and accurate capturing of the front and tail positions of the perturbed region. Although the first generation of splitting event occurs in a relatively straightforward manner, the ensuing turbulent spot packet enters an unexpected quasi-cyclic process containing previously unknown sub-processes of parent-child reconnection and re-splitting rather than the anticipated successive generational splitting. Conditional sampling with the aid of the iso-surfaces of swirling strength shows that the frontal zone of a spot travels measurably and constantly faster than its middle section, suggesting that the splitting of pipe turbulent spot is most likely due to a sustained zonal speed difference (streamwise stretching) between the spot’s frontal zone and the core. Passive scalar results demonstrate that the zone occupied by the migrating spot packet is only a small subset of the zone impacted by the packet. We are of the opinion that turbulent spot splitting is an interesting feature that is only important for internal transitional flows within a very narrow range of Reynolds number.