Role of stochasticity in the transition to turbulence in pipe flow

In transitional pipe turbulence, a sequence of phases is observed experimentally in the range of Reynolds numbers between 1900 and 5000, passing through the laminar-turbulent transition at Re ~ 2040. These phases are characterized by transient decay of puffs (Re 4500). We propose a statistical mechanics model of transitional pipe flow turbulence based on energy balance in the interaction between turbulence, zonal flow, and the baseline shear flow. The resulting model recapitulates the entire phase diagram of the transition, including decaying and splitting puff, the puff-slug transition, and weak and strong slugs. We demonstrate the critical role of stochasticity in all phases. Specifically, we show how stochasticity induces a decaying profile in the low-Reynolds regime and how it reveals the deep connection between the subcritical bifurcation picture and the directed percolation picture of the transition. The model is not restricted to pipe flow geometry and is extendable to other transitional shear flows like quasi-one-dimensional Taylor-Couette flow.