Modeling of solute transport into sub-aqueous sediments

A model for investigating the solute transport into a sub-aqueous sediment bed, under an imposed standing water surface wave, is developed. Under the assumption of Darcy flow in the bed, a model based on a two-dimensional, unsteady advection-diffusion equation is derived; the relative roles of the advective and diffusive transport are characterized by a Peclet number, Pe. Two solutions for the equation are developed. The first is a basic control volume method using the power-law scheme. The second is a smear-free, modified upwind solution for the special case of Pe → ∞. Results, at a given time step, are reported in terms of a laterally averaged solute verse depth profile. The main result of the paper is to demonstrate that the one-dimensional solute concentration verse depth profile is essentially independent of any numerical dissipation present in the solute field predictions. This demonstration is achieved by (i) using an extensive grid refinement study, and (ii) by comparing Pe → ∞ predictions obtained with the basic and smear-free solutions.