Enhanced One‐Dimensional Modeling of Transport in Rivers

Abstract

Longitudinal dispersion of substances transported in rivers is caused by variations of the advective velocity over the river cross section and by transverse mixing. This two‐dimensional nature of the process is not accounted for by the usually applied one‐dimensional advection‐diffusion equation, which therefore is not valid in the so‐called initial period immediately downstream of a substance input site. An enhanced one‐dimensional model is presented based on a very much simplified transverse velocity profile, with a flow velocity of zero near the riverbanks and a constant value in the center of the river. Dispersion is modeled by the exchange of mass between the two zones, in which no transverse spatial gradients are considered. Dispersion can be estimated in this model by two dimensionless parameters that vary only moderately from one river to another. The behavior of the model in the asymptotic range and in the initial period, the limitations of the model, and its advantages compared to the one‐ and two‐dimensional models are discussed. The main advantage of the model is that it is not more complex than the one‐dimensional model but still yields a good description of substance transport for about 80% of the initial period.