The onset of fully turbulent pipe flow

Transitional turbulence is composed of localized puffs whereas space filling fully turbulent flow only becomes sustained at somewhat larger Reynolds numbers. In the present computational study we introduce a volume forcing that flattens the velocity profile, a method recently used to suppress and even eradicate turbulence in simulations and experiments. Using the forcing amplitude as a control parameter we determine the minimum requirements for fully turbulent flow to be sustained. Interestingly, and despite strongly differing forcing amplitudes, the 'minimal' velocity profiles are found to collapse in inner units and equally collapse with the unforced case at the puff-slug transition point. From these observations we determine the minimum energetic requirements for fully turbulent pipe flow to become sustained and compare these conditions to Couette and channel flow.