The effect of the pool and riffle on dissolved, non-conservative mass transport in rivers

Abstract

One-dimensional substance transport models assume that the river reach modelled has a uniform cross-sectional shape which manifests as a constant average velocity in the model equations. Rarely do rivers meet this criterion. Their channels are seldom uniform in shape but rather alternate in a quasi-periodic manner between pool and riffle sections. This bedform sequencing imparts a corresponding variation in the average cross-sectional velocity which is not accounted for in constant velocity transport models. The literature points out that the pool and riffle planform may be the reason for the sometimes poor predictions obtained from these models. This paper presents a new variable velocity transport model and confirms that the fluctuation in average cross-sectional velocity caused by the pool and riffle planform does have a marked effect on transport in rivers. The pool and riffle planform promotes an enhanced decay of a substance when a first-order biochemical reaction is simulated with the new transport equation. Investigation of the analytical solution shows that the enhanced decay is the result of the overall lower velocity experienced in a pool and riffle channel as opposed to a uniform channel. This difference in transport velocity between a pool and riffle channel and a uniform channel becomes more pronounced as flow declines a critical finding for total maximum daily load calculations because these regulatory limits are usually determined for low flow levels by models that do not account for this phenomenon.