Solute transport in open channel flows and porous streambeds

Abstract

Pore-water flow inside river sediment beds resulting from water flow in the overlying river channel can strongly affect the mass and momentum transfer processes across the channel-bed interface. An analytical model for transport in porous beds, with a two-layer, coupled transport across the interface is presented. Flow and transport in the porous bed and open channel are diffusion and advection driven. The variation in the velocity profile across the flow depth, in both open channel and porous bed, is consistent with experimental studies. A slip velocity at the interface links a parabolic velocity profile in the open channel with an exponentially decaying velocity profile in the porous bed. The contaminant exchange along the interface is accounted through the imposed boundary conditions of concentration and flux continuity. The initial conditions allow the presence of solute in either or both parts of the flow domain, in order to study the transfer of solute across the interface. The Aris' method of moments is used to derive analytical expressions for the zeroth and first moments of concentration and for the velocity and effective dispersion of the solute cloud. The role of dispersion in the bed relative to dispersion in the channel was found to greatly influence the transport characteristics in the river channel-bed interface. The depth of the porous bed relative to the depth of the open channel showed a strong effect on the mean velocity of the solutes particles and the effective dispersion of the solute cloud was found to be sensitive to the flow velocity profile in the open channel in a counter-intuitive way since the transport equations are expressed in terms of axes moving with the mean particle velocity. Finally, the model was validated against experimental data from A.H. Elliott and N.H. Brooks [Water Resour. Res. 33 (1997) 123, 137].