Longitudinal dispersion in fluvial environments: new empirical formulations and applications to pollutant transport modeling

Abstract In this paper, we analyze the transport dynamics of instantaneous and continuous release of pollutants in rivers. We begin with proposing new formulations for longitudinal dispersion coefficient in narrow and wide channels. Considering the observed trends in field-derived datasets, the channel aspect ratio to demarcate narrow and wide channels is set as 10. The analysis shows that the longitudinal dispersion coefficient depends nonlinearly on the channel aspect ratio and shear velocity ratio. Finally, the robustness of the proposed formulations is established through a comparative analysis with existing formulations available in the literature. To simulate the pollutant transport dynamics, the one-dimensional advection−dispersion equation is numerically solved using the proposed formulations of dispersion coefficient. The numerical simulations are performed for instantaneous and continuous pollutant release scenarios in both narrow and wide channels. The pollutant concentration profiles in a narrow channel with instantaneous release manifest a distinct peak concentration. Conversely, for continuous release scenario, the pollutant concentration remains at its maximum magnitude for a finite temporal interval and spatial extent. For instantaneous release case, the enhanced dispersion in wide channels causes the intensified attenuation of the concentration peak. In addition, the continuous release of pollutants in wide channels characterize a decay of peak concentration in downstream direction. The predicted pollutant concentration profiles are in agreement with the classical analytical solution and field observations of Atkinson and Devis (2000).