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# Nikesh, PhD, Warsaw University of Technology, Warsaw, Poland, "Modal and Non-Modal stability analysis of Couette-Poiseuille flow"

The stability problem of Couette-Poiseuille flow in a channel with longitudinal grooves is numerically investigated. In the considered problem, flow is driven by the movement of the wall and a pressure gradient applied in the opposite direction to wall motion. A range of base flows has been obtained by varying the pressure gradient while keeping the same wall velocity. Hydrodynamic stability of flows is investigated by tracking the growth of small perturbations, that are either attenuated or amplified when evolved by the linearized flow evolution operator (Linearised Navier-Stokes (LNS) operator) in the modal or transient (non-modal) mechanism. Using the modal approach, It was found that the flow becomes linearly unstable if the applied pressure gradient is greater than a quarter of plane Poiseuille flow. For the case of, small pressure gradient, flow found to be linearly stable using a modal approach but non-modal analysis shows significant transient growth. Optimal disturbance corresponding to the highest transient growth is used as perturbations that cause the subcritical transition of base flow. It is found that the growth of unstable perturbations, either due to the modal or transient mechanism will eventually lead to flow transitioning from its base state to, potentially more complex form.** **