Nikesh Yadav (Warsaw University of Technology)

We present the first numerical result on the Couette-Poiseuille (CP) flow configuration in the presence of longitudinal grooves. The flow is actuated by movement of the flat wall and pressure imposed in the opposite direction decreasing overall advective velocity of the system. Stationary wall features longitudinal grooves that modify the flow, change hydrodynamic drag on the driving wall and cause onset of hydrodynamic instability with consequent supercritical bifurcation, already at moderate ranges of the Reynolds number. Current analysis begins with concise characterization of stationary, laminar CP flow and effects of applying selected corrugation pattern, followed by determination of conditions leading to onset of linear destabilization. In the second part we illustrate selected nonlinear solutions obtained for low, supercritical values of the Reynolds numbers and due to unstable travelling waves of possibly low phase velocities. The primary objective of this work is determination of flow conditions that lead to onset of unstable modes and a consequent bifurcation of the solution to nonlinear saturation state, characterized by possibly low advective speed allowing capture using small scale experimental configurations. The importance of the results presented here comes down to providing guidelines for prospective experimental, corrugated CP flow arrangement that would be capable of experimental verification of the reported hydrodynamic instability mechanism. We show that distances required for the onset of measurable, nonlinear effects can be decreased substantially, allowing for experimental capture before bulk of the flow flushes them out of the test domain.