Drag reduction and subcritical turbulence in controlled pipe flows

Pipe flow controlled by streamwise-travelling waves of azimuthal wall velocity is studied using direct numerical simulations at a bulk Reynolds number italic Re Subscript b Baseline equals 4900 Re b = 4900 $\textit{Re}_b=4900$ . A comprehensive analysis of drag reduction shows that the flow response differs fundamentally from that of channel flow. Under suitable forcing, pipe flow relaminarises, whereas channel flow does not. Depending on the control parameters, the flow exhibits the spatially localised turbulent state characteristic of transitional pipe flow, with turbulent puffs persisting at bulk Reynolds numbers up to three times higher than in the uncontrolled case. The bulk Reynolds number alone does not determine the onset of localisation. Moreover, drag reduction, which alters the natural relation between bulk and friction velocities, is insufficient to identify a universal onset criterion. An intermittency indicator based on the spatial variance of the cross-sectional turbulent kinetic energy relates the emergence of localised turbulence to the low wall friction produced by the control, although the correspondence is not one-to-one. Despite their qualitative resemblance to canonical turbulent puffs, the controlled puffs exhibit distinct properties; for example, their fronts may propagate faster than the bulk flow. Overall, this work provides a comprehensive characterisation of the subcritical turbulent state and its turbulent puffs in controlled pipe flow, and offers a new perspective on control strategies that aim at flow relaminarisation.