Mean Velocity and Shear Stress Distribution in Floating Treatment Wetlands: An Analytical Study

Floating treatment wetlands (FTWs) are efficient at wastewater treatment; however, data and physical models describing water flow through them remain limited. A two-domain model is proposed dividing the flow region into an upper part characterizing the flow through suspended vegetation and an inner part describing the vegetation-free zone. The suspended vegetation domain is represented as a porous medium characterized by constant permeability thereby allowing Biot's Law to be used to describe the mean velocity and stress profiles. The flow in the inner part is bounded by asymmetric stresses arising from interactions with the suspended vegetated (porous) base and solid channel bed. An asymmetric eddy viscosity model is employed to derive an integral expression for the shear stress and the mean velocity profiles in this inner layer. The solution features an asymmetric shear stress index that reflects two different roughness conditions over the vegetation-induced auxiliary bed and the physical channel bed. A phenomenological model is then presented to explain this index. An expression for the penetration depth into the porous medium defined by 10% of the maximum shear stress is also derived. The predicted shear stress profile, local mean velocity profile, and bulk velocity agree with the limited experiments published in the literature.

Duke Scholars

Author Gabriel G. Katul Civil and Environmental Engineering