[1] Interstitial flows in stream gravel beds are driven by stream slope and controlled by hydraulic conductivity (underflows) or induced by pressure differentials on the streambed surface (hyporheic flows). They enhance solute exchange between surface water and a streambed. To study the solute transport in a stream gravel bed, a 2-D transient advectiondispersion mass transfer model was formulated. The velocity field includes an underflow and a spatially periodic hyporheic flow, e.g., due to standing surface waves or bed forms. Two dimensionless scaling parameters emerged: R measures the relative strength of hyporheic flow to underflow in the streambed and l is the ratio of dispersivity of the gravel bed to the pressure wavelength along the streambed. In the analysis of mass transfer of nonconservative substances into a streambed, an explicit 2-D analysis of interstitial flow is often undesirable. Therefore the numerical solutions for the 2-D concentration fields under periodic boundary conditions were reduced to 1-D vertical concentration profiles (by streamwise averaging of the solute concentrations). The profiles were matched to the solution of an unsteady vertical 1-D dispersion equation that introduces a depth variable ''enhanced dispersion coefficient D E (y)'' that lumps all forms of interstitial advective and dispersive transport in the streambed. Functions D E (y) were determined for many combinations of independent parameters by inverse modeling, and the dependence of D E (y) on the dimensionless parameters R and l was determined from these results. Analytical relationships for D E (y, R, l) have been proposed and validated against available experimental data. Knowledge of D E (y) allows the estimation of solute/mass transfer rates in streambeds under wavy boundary conditions, without explicit analysis of the interstitial flow. This is a distinct advantage for applications in stream water quality and/or pore water quality studies.Citation: Qian, Q., V. R. Voller, and H. G. Stefan (2008), A vertical dispersion model for solute exchange induced by underflow and periodic hyporheic flow in a stream gravel bed, Water Resour. Res., 44, W07422,

Studies to dale indirectly indicate that only a small percentage of the sediment discharged by the Huanghe (Yellow River) is presently transported from the Gulf of Bohai to the Huanghai (Yellow Sea). Direct measurements in early summer 1985 show low concentrations of suspended sediment east of 119°45'E but high concentrations in Bohai Bay. Stokes drift associated with an amphidrome of the M,_ tide may contribute to a northwestward transport of Huanghc sediment.

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SUMMARYTransient, advective transport of a contaminant into a clean domain will exhibit a moving sharp front that separates contaminated and clean regions. Due to 'numerical diffusion'-the combined effects of 'crosswind diffusion' and 'artificial dispersion'-a numerical solution based on a first-order (upwind) treatment will smear out the sharp front. The use of higher-order schemes, e.g. QUICK (quadratic upwinding) reduces the smearing but can introduce non-physical oscillations in the solution. A common approach to reduce numerical diffusion without oscillations is to use a scheme that blends low-order and high-order approximations of the advective transport. Typically, the blending is based on a parameter that measures the local monotonicity in the predicted scalar field. In this paper, an alternative approach is proposed for use in scalar transport problems where physical bounds C Low C C High on the scalar are known a priori. For this class of problems, the proposed scheme switches from a QUICK approximation to an upwind approximation whenever the predicted upwind nodal value falls outside of the physical range [C Low , C High ]. On two-dimensional steady-state and one-dimensional transient test problems predictions obtained with the proposed scheme are essentially indistinguishable from those obtained with monotonic flux-limiter schemes. An analysis of the modified equation explains the observed performance of first-and second-order time-stepping schemes in predicting the advective transport of a step. In application to the transient two-dimensional problem of contaminate transport into a streambed, predictions obtained with the proposed flux-limiter scheme agree with those obtained with a scheme from the literature.