On the transition to turbulence in subcritical channel flow with external forcing control

The effect of externally imposed spanwise forces on laminar–turbulent transition in plane Poiseuille flow is studied using direct numerical simulation. The subcritical range of Reynolds numbers (Re) is studied, where 1800≤Re≤5000. The laminar base flow is subjected to a finite magnitude of perturbations. For the controlled flow, external forcing is additionally applied, varying its amplitude and frequency. The minimum perturbation magnitude required to trigger transition is computed, showing that smaller magnitudes are required for the controlled flow compared to the uncontrolled flow. The transition dynamics are examined through the temporal evolution of the perturbation energy and wall shear stress, allowing for a quantitative assessment of the transition time and intensity. A controlled flow begins its transition at an earlier time than its uncontrolled counterparts. However, the transition gets delayed as the forcing frequency increases and the forcing amplitude decreases. The transition intensity, measured by the maximum attainable wall shear stress during the transition process, shows a non-trivial dependence on the forcing frequency and amplitude. The intensity is greater than that of the uncontrolled flow at low frequencies, while it becomes lower at high frequencies. A mechanism of these transition dynamics is investigated by its correlation with the level of drag in sustained turbulence that develops long after the transition process. Interestingly, a clear correlation is found, suggesting a predictive framework in which the timing and intensity of the transition can be approximately predicted by the amount of drag reduction or increase in a subsequent turbulent flow.