Simplified dispersion analysis based on dye tests at a small stream

Abstract

The modelling of solid transport in open channels requires good knowledge about parameters related to basic processes such as hydrodynamic dispersion, advection and decay rates. Such parameters are usually determined by dye tests. Numerous tracer studies have been performed on laboratory flumes and natural rivers. However, on-site sampling is often difficult, expensive and needs special apparatus. The main aim of the study was to justify simplified method based on the monitoring of the dye cloud shape in order to determine both longitudinal and transversal dispersion coefficients. In this study, four dye tests were carried out on a small local stream (the Lipkovsky) using Rhodamine WT fluorescein dye as a tracer. The tests were carried out in such a manner that both longitudinal and horizontal transversal dispersion data were obtained. For this purpose, the visually determined extent of the dye cloud was interpreted via the analytical solution of the advection-dispersion equation. The results obtained by this simplified approach indicated that the longitudinal dispersion coefficient Dx = 0.051–0.057 m2/s and the coefficient of horizontal transversal dispersion Dy = 0.00024–0.00027 m2/s. The method was justified by corresponding root mean square error (RMSE) counting RMSE = 0.65–1.02 m for the dye cloud centre, RMSE = 1.87–2.46 m for the head and tail of the cloud and RMSE = 0.025–0.11 m for the cloud width, the Nash-Sutcliffe efficiency coefficients ranged from 0.9 to 0.998. The comparison of these values with empirical formulae and other tracer studies indicated significant overestimation of the mentioned values of Dx, which can be attributed to the uniform velocity distribution along the width of Lipkovsky Stream. Much better agreement was achieved for Dy.

The modelling of solid transport in open channels requires good knowledge about parameters related to basic processes such as hydrodynamic dispersion, advection and decay rates. Such parameters are usually determined by dye tests. Numerous tracer studies have been performed on laboratory flumes and natural rivers. However, on-site sampling is often difficult, expensive and needs special apparatus. The main aim of the study was to justify simplified method based on the monitoring of the dye cloud shape in order to determine both longitudinal and transversal dispersion coefficients. In this study, four dye tests were carried out on a small local stream (the Lipkovsky) using Rhodamine WT fluorescein dye as a tracer. The tests were carried out in such a manner that both longitudinal and horizontal transversal dispersion data were obtained. For this purpose, the visually determined extent of the dye cloud was interpreted via the analytical solution of the advection-dispersion equation. The results obtained by this simplified approach indicated that the longitudinal dispersion coefficient Dx = 0.051–0.057 m2/s and the coefficient of horizontal transversal dispersion Dy = 0.00024–0.00027 m2/s. The method was justified by corresponding root mean square error (RMSE) counting RMSE = 0.65–1.02 m for the dye cloud centre, RMSE = 1.87–2.46 m for the head and tail of the cloud and RMSE = 0.025–0.11 m for the cloud width, the Nash-Sutcliffe efficiency coefficients ranged from 0.9 to 0.998. The comparison of these values with empirical formulae and other tracer studies indicated significant overestimation of the mentioned values of Dx, which can be attributed to the uniform velocity distribution along the width of Lipkovsky Stream. Much better agreement was achieved for Dy.