Free Surface Flow over Permeable Wavy Bed

A theoretical analysis based on potential flow theory over a permeable wavy bed and a linear Darcy equation shows that the perturbations of the flow field have a phase shift relative to the wavy bed form. This phase shift results in a net form resistance on the permeable wavy surface of the bed form. The experimental results indicate that there is a phase shift between the permeable wavy bed form and the water surface profile. The theoretical results show that the phase shift and friction factors increase with the Reynolds number of the porous media flow; however, the experimental results show that the phase shift decreases with the Reynolds number of the porous media flow. This is caused by the phenomenon of flow separation on the wavy bed. The water surface profiles over the permeable wavy bed are compared with those over the impermeable wavy bed in the case of the same Froude numbers. The velocity distributions over the permeable and the impermeable wavy bed are also investigated experimentally and theoretically. The boundary wavy profiles of the permeable and the impermeable bed form vary sinusoidally.