On the effects of active flow control on exact coherent states in channel flow

Controlling transition in wall-bounded flows remains challenging due to the complex nonlinear dynamics. Exact coherent states (ECSs) are invariant solutions to the Navier-Stokes equations organizing flow evolution in phase space. This study uses ECSs to evaluate external force control in the form of spanwise traveling waves on laminar-to-turbulent transition in a channel flow. Two ECS families near friction Reynolds number of 85 are analyzed, namely P3 with core-centered structures linked to bypass transition, and P4 with near-wall hairpin-like vortices tied to critical-layer dynamics. Spanwise forcing is applied with fixed wavenumber and penetration depth, varying amplitude and frequency. Control promotes early transition in P3 ECS, while P4 ECS shows both delayed and early transition depending on forcing parameters, altering the laminar-turbulent boundary and shifting bifurcation points in phase space. Results reveal how forcing modifies ECS stability and transition pathways, demonstrating the potential of ECS frameworks to guide physics-based control strategies that target nonlinear structures for improved drag reduction.