Observable to distinguish successful from unsuccessful puff splits near the split edge

Identify a physically meaningful observable on pipe-flow velocity fields at Re = 2200 that quantifies the process distinguishing states that successfully split from those that do not near the split-edge state, for example by capturing the nucleation of a laminar gap at an appropriate axial location within the turbulent core.

Background

At Re = 2200, puff splitting follows a two-step slug-gap-split pathway, and the split edge state serves as a tipping point. Not all expanded puffs proceed to split: approximately half of cases retract or split off a patch that subsequently decays.

The authors explicitly note that it remains unclear what precisely differentiates successful splits from failures and that they have not yet identified an appropriate observable to quantify this process, suggesting the need for a predictive measure related to gap nucleation.