Onset of transition in tandem-arranged cylindrical porous media at different porosities

The onset and control of unsteadiness in an idealised porous medium are investigated using global stability and sensitivity analysis. The flow is modelled by a periodic representative elementary volume composed of tandem-arranged circular cylinders, and the Hopf bifurcation is characterised over a broad porosity range ( 0.45 less than or slanted equals phi less than or slanted equals 0.95 0.45 ⩽ ϕ ⩽ 0.95 0.45 φ 0.95 ). The neutral stability curve exhibits an approximately linear dependence on phi ϕ φ , indicating that porosity serves as an effective predictor for the transition threshold. In the vicinity of instability onset, several eigenmode families emerge, clarifying the organisation of the competing branches. Energy budget analysis further shows that perturbation production is dominated by the lift-up mechanism. In addition, adjoint-based sensitivity analysis near criticality identifies where a localised steady forcing produces the largest drift of the leading global mode. The result highlights the throat of the main passage as the region of strongest receptivity, offering a clear target and an efficient tool for designing flow-control strategies.