Stochastic Theory for Irregular Stream Modeling. II: Solute Transport

Abstract

A stochastic theory is developed for longitudinal dispersion in natural streams. Irregular variations in river width and bed elevation are conveniently represented as one-dimensional random fields. Longitudinal solute migration is described by a one-dimensional stochastic solute transport equation. When boundary variations are small and statistically homogeneous, the stochastic transport equation is solved in closed-form using a stochastic spectral technique. The results show that large scale longitudinal transport can be represented as a gradient dispersion process described by an effective longitudinal dispersion coefficient. The effective coefficient reflects longitudinal mixing due to flow variation both within the river cross section and along the flow and can be considerably greater than that of corresponding uniform channels. The discrepancy between uniform channels and natural rivers increases as the variances of river width and bed elevation increase, especially when the mean flow Froude number is high.