Is uniform pipe turbulence permanent or an extremely long transient?
In plain words
Single turbulent puffs in a pipe always decay eventually, with lifetimes that grow faster than exponentially with flow speed. Whether fully turbulent flow at high speed is truly permanent, or also only a very long-lived transient, is unknown.
Precise statement
Puff lifetimes in pipe flow grow superexponentially with Re without diverging (Hof et al. 2006, 2008). For featureless turbulence at $\mathrm{Re} >> \mathrm{Re}_c$ in a periodic pipe of fixed length $L/D$, does the mean relaminarization time diverge at a finite Re (a chaotic attractor appears), or stay finite for all Re (a chaotic saddle)? Answer: yes or no for fixed $L/D$, with the Re and $L$ dependence of the escape rate.
What would settle it
Large ensembles of DNS in short and moderate periodic pipes measuring escape-rate statistics versus Re and L, or a proof in a reduced model with controlled error.