Effect of waveform on turbulence transition in pulsatile pipe flow

Pulsatile flow in a straight pipe is a model system for unsteady internal flows in industrial engineering and physiology. In some parameter regimes, the laminar flow is susceptible to helical perturbations, whose transient energy growth scales exponentially with the Reynolds number (Re). In this paper, we link the transient growth of these perturbations to the instantaneous linear instability of the laminar flow. We exploit this link to study the effect of the waveform on turbulence transition by performing linear stability and transient growth analyses of flows driven with different waveforms. We find a higher-energy growth in flows driven with longer low-velocity phases as well as with steeper deceleration and acceleration phases. Finally, we perform direct numerical simulations and show that cases with larger transient growth transition faster to turbulence and exhibit larger turbulence intensities. However, these same cases are also more prone to relaminarisation once turbulence has been established. This highlights that, in pulsatile flows, the linear mechanisms responsible for turbulence transition are distinctly different from the nonlinear mechanisms sustaining turbulence.