Instability and transition in an elementary porous medium

Instability and transition in an elementary porous medium are investigated via global linear stability analysis and numerical simulation. The porous medium is presented by a representative elementary volume which consists of a staggered array of square cylinders. The stability analysis indicates the first critical Reynolds number at Re-cr approximate to 84. Two unstable modes are captured from the linear stability analysis: a two-dimensional oscillatory mode and a three-dimensional stationary mode. A series of analyses based on direct and adjoint methods is conducted on both the unstable modes. The energy analysis shows that lift-up and converging-flow effects are both responsible for the unstable modes. In the numerical simulation, the averaged fluctuation profiles exhibit spatial distributions similar to those of the perturbation kinetic energy from the three-dimensional mode, which confirms the prediction from the stability analysis. In addition, we observe stationary counterrotating streamwise vortices beginning at the subcritical Reynolds number, which is a consequence of lift-up instability.