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Abstract 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.
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Flow in oscillatory boundary layers over permeable beds
In fluid dynamics applications that involve flow adjacent to a porous medium, there exists some ambiguity in how to model the interface. Despite different developments, there is no agreed upon boundary condition that should be applied at the interface. We present a new analytical solution for laminar boundary layers over permeable beds driven by oscillatory free stream motion where flow in the permeable region follows Darcy's law. We study the fluid boundary layer for two different boundary conditions at the interface between the fluid and a permeable bed that was first introduced in the context of steady flows: a mixed boundary condition proposed by Beavers and Joseph [“Boundary conditions at a naturally permeable bed,” J. Fluid Mech. 30, 197–207 (1967)] and the velocity continuity condition proposed by Le Bars and Worster [“Interfacial conditions between a pure fluid and a porous medium: Implications for binary alloy solidification,” J. Fluid Mech. 550, 149–173 (2006)]. Our analytical solution based on the velocity continuity condition agrees very well with numerical results using the mixed boundary condition, suggesting that the simpler velocity boundary condition is able to accurately capture the flow physics near the interface. Furthermore, we compare our solution against experimental data in an oscillatory boundary layer generated by water waves propagating over a permeable bed and find good agreement. Our results show the existence of a transition zone below the interface, where the boundary layer flow still dominates. The depth of this transition zone scales with the grain diameter of the porous medium and is proportional to an empirical parameter that we fit to the available data.
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- Award ID(s):
- 2048676
- PAR ID:
- 10400595
- Date Published:
- Journal Name:
- Physics of Fluids
- Volume:
- 34
- Issue:
- 9
- ISSN:
- 1070-6631
- Page Range / eLocation ID:
- 092112
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1063/5.0104305
