A. Frishman and T.Grafke
The transition to turbulence in pipes is characterized by a coexistence of laminar and turbulent states. At the lower end of the transition, localized turbulent pulses, called puffs, can be excited. Puffs can decay when rare fluctuations drive them close to an edge state lying at the phase-space boundary with laminar flow. At higher Reynolds numbers, homogeneous turbulence can be sustained, and dominates over laminar flow. Here we expand this landscape of states, placing it within a unified bifurcation picture, and reveal the role it plays in transitions. We demonstrate our claims within the Barkley model, and motivate them generally. We first suggest the existence of an anti-puff and a gap-edge---states which mirror the puff and related edge state. Previously observed laminar gaps forming within homogeneous turbulence are then naturally identified as anti-puffs nucleating and decaying through the gap edge. We further propose a novel mechanism for puff splits, possible in a coexistence region between puffs, homogeneous turbulence and the gap edge: (i) a puff expands into a slug, which has a homogeneous turbulent core, and (ii) a laminar gap is formed within the core, mediated through the gap edge. We present the corresponding split-edge state, discuss the effect of the Reynolds number on the two transition mechanisms, and confirm our picture for stochastic splits within the Barkley model.