A solute in a stream will be transported into its porous sediment bed. If the stream slope is small, and the bed and stream water surface flat, the transport of solute is modeled with a one-dimensional diffusion equation (in the direction of depth). In this model the penetration rate of solute into an initially clean, saturated sediment bed is controlled by the value of the molecular diffusion. In reality, however, the bed and water surface of a stream are not flat (bed forms and wave motion) and the form of these surfaces will induce pressure variations over the water-sediment interface resulting in a fluid flow field in the sediment bed. Through addition of an advective transport, this flow field enhances the rate of penetration of the solute into the stream bed; a process that can be further influenced by the stream slope driven hyporheic flow.

The objective of the current project is to model the influence of flows below the water-sediment interface on the transport of solutes into stream beds. The approach is to capture the 2-dimensional transport of solute by diffusion and advection via a pseudo (laterally averaged) one-dimensional (depth) diffusion model characterized by an enhanced dispersion coefficient. In this way it is expected that modified and relatively simple one-dimensional diffusion models should be able to predict the movement of contaminates through a stream bed; an approach that will have very practical and worthwhile merit in steam restoration projects.   

Major accomplishments:

1. A solution for the flow field in a sediment stream bed under the condition of a standing wave has been constructed.

2. The solution in (1) has been coupled with numerical solution of a two-dimensional advection-diffusion equation describing the solute transport in a cross-section of the stream bed. Appropriate lateral averaging of the results led to depth averaged profiles used to calculate values for a depth dependent enhanced dispersion coefficient. This work involved an extensive testing of numerical approaches that would eliminate (reduce) numerical dispersion and dissipation in the solutions (Reported in part in [1] and [2]).

3. The values of the calculated depth dependent dispersion coefficient show a dependence on the amplitude of the standing wave, often exhibit an interesting non- monotonic dependence on depth, can be several of magnitude order larger than the value of the molecular diffusion coefficient. Practical equations for determining the appropriate enhanced value to use in a given situation have been developed (Reported in part in [1], [2] and [3]).

Papers
Qian, Q., V.R. Voller, and H.G. Stefan (in review), Enhancement of solute transfer below a sediment/water, Water Resources Research.

Qian, Q., H. G. Stefan, and V. R. Voller (in press), Modeling of solute transport into sub-aqueous sediments, Applied Mathematical Modelling, 31, 1461-1478.

Qian, Q., V.R. Voller, and H. G. Stefan (2005), Enhancement of solute transfer into sediment by water surface wave motion, EOS Trans., AGU, 86:52, Fall Meeting Supplement, Abstract H31B-1293.