Splitting of a turbulent puff in pipe flow

Abstract

The transition to turbulence of the flow in a pipe of constant radius is numerically studied over a range of Reynolds numbers where turbulence begins to expand by puff splitting. We first focus on the case Re = 2300 where splitting occurs as discrete events. Around this value only long-lived pseudo-equilibrium puffs can be observed in practice, as typical splitting times become very long. When Re is further increased, the flow enters a more continuous puff splitting regime where turbulence spreads faster. Puff splitting presents itself as a two-step stochastic process. A splitting puff first emits a chaotic pseudopod made of azimuthally localized streaky structures at the downstream (leading) laminar-turbulent interface. This structure can later expand azimuthally as it detaches from the parent puff. Detachment results from a collapse of turbulence over the whole cross-section of the pipe. Once the process is achieved a new puff is born ahead. Large-deviation consequences of elementary stochastic processes at the scale of the streak are invoked to explain the statistical nature of splitting and the Poisson-like distributions of splitting times reported by Avila,

Localised turbulence in a circular pipe flow with gradual expansion

“…In the case of Re = 5000, the flow downstream the intense region of turbulence exhibits small patches of intense vorticity (see figure 7(d)). The streamwise velocity trace (see figure 7(f )) suggests weak turbulence, that does not return to laminar flow and eventually could lead to puff splitting (Avila et al 2011;Shimizu et al 2014). This property of expansion flow with laminar inlet profile forming localised turbulence and decaying in the outlet section is in good relation with experiments (Peixinho & Besnard 2013).…”

Transitional structures in annular Poiseuille flow depending on radius ratio

“…Further decrease to Re τ = 52 displays relaminarisation or replication events (over longer time scales) but no merging events, see figure 6(a-f ). This dynamics featuring only individual puffs is identical to the regime just above the critical point in cPf (Avila et al 2011;Shimizu et al 2014). Further decrease of Re τ to 48 shows only puffs with finite lifetimes, but no replication events, suggesting (in the thermodynamic limit) that Re τ lies here below the critical point.…”

Theoretical perspective on the route to turbulence in a pipe

“…There are three specific open issues for which such a model could assist experimental and numerical studies of pipe flow: the mechanism of puff splitting (e.g. Shimizu et al 2014), the scalings associated with directed percolation, and control of transition through mean-flow modification (e.g. Hof et al 2010;Barkley et al 2015).…”

“…This corresponds to larger Reynolds number, but still within the puff regime. In this case one observes a process known as puff splitting, whereby a daughter puff is nucleated downstream from an existing mother puff (Wygnanski et al 1975;Avila et al 2011;Shimizu et al 2014). The process results in an increase in turbulence fraction (percentage of the flow that is turbulent) rather than a decrease as in the case of decay.…”