Depth-Dependent Dispersion Coefficient for Modeling of Vertical Solute Exchange in a Lake Bed under Surface Waves

Variable pressure at the sediment/water interface due to surface water waves can drive advective flows into or out of the lake bed, thereby enhancing solute transfer between lake water and pore water in the lake bed. To quantify this advective transfer, the two-dimensional (2D) advection-dispersion equation in a lake bed has been solved with spatially and temporally variable pressure at the bed surface. This problem scales with two dimensionless parameters: a “dimensionless wave speed” (W) and a “relative dispersivity” (λ). Solutions of the 2D problem were used to determine a depth-dependent “vertically enhanced dispersion coefficient” (DE) that can be used in a 1D pore-water quality model which in turn can be easily coupled with a lake water quality model. Results of this study include a relationship between DE and the depth below the bed surface for W>50 and λ ? 0.1. The computational results are compared and validated against a set of laboratory measurements. An application shows that surface waves may increase the sediment oxygen uptake rate in a lake by two orders of magnitude.