Space-time resolvent model for near-wall flow reversal in time-evolving turbulent Couette–Poiseuille flow

Capturing unsteady near-wall dynamics in wall-bounded shear flows remains a fundamental challenge in fluid mechanics. In this study, we develop a space-time resolvent framework to analyze and model near-wall flow reversal in a time-evolving turbulent Couette–Poiseuille flow configuration, a simplified framework for investigating wall-bounded turbulence under adverse pressure gradient and separation. We compute the space-time resolvent modes by linearizing the Navier–Stokes equations around the time-varying mean profile obtained from direct numerical simulations. For a selection of streamwise and spanwise wavenumbers, we reconstruct the unsteady flow field using the leading response modes. Despite the low-rank nature of the reconstruction, the model captures several essential features of the reverse flow. These results demonstrate the potential of low-order space-time models to represent key mechanisms in unsteady wall-bounded flows.