A deterministic analysis of effects of external body forces on transition to turbulence

The present study investigates the impact of externally-applied traveling-wave body forces on the transition to turbulence of plane Poiseuille flow through direct numerical simulation. The friction Reynolds number ranges from 85 to 400. As expected, higher Reynolds numbers escalate the likelihood of transition, and the likelihood is further intensified as the frequency of the external body force decreases. To comprehensively analyze the effects of the body force on transition, we apply it to the nonlinear traveling-wave solutions of the Navier-Stokes equations, also known as exact coherent structures. Two solution families are considered, namely a core mode and a critical-layer mode, depending on flow structure. Similar observations are made in which the body force triggers an early transition. However, the critical-layer mode exhibits a faster transition compared to the core mode. Additionally, an increase in Reynolds number augments the bursting magnitude during transition, commonly referred to as the transition instability. We further express the transition and bursting magnitude in terms of a drag reduction map, which allows us to characterize the optimal parameters for achieving the desired transition. Lastly, flow dynamics and structures of the traveling-wave solutions during transition are investigated to provide a deeper insight into the underlying mechanisms at play.