Longitudinal dispersion coefficient based on theoretical equation for transverse distribution of stream-wise velocity in rivers

Kyong Oh Baek

Wednesday 1 july 2015

12:39 - 12:42h at Asia (level 0)

Themes: (T) Hydro-environment, (ST) Impacts of pollutants on the water environment, Poster pitches

Parallel session: Poster pitches: 9G. Environment - Impact

When one-dimensional mass transport model is applied to predict the concentration variation of pollutants in open channel, a dispersion coefficient which is one of the sensitive parameters should be selected appropriately. It is relatively simple to find out a dispersion coefficient from the measured tracer data if available. However, for streams where mixing and dispersion characteristics are unknown, the dispersion coefficient may be estimated using empirical or theoretical methodologies. For predicting pollutant behavior more precisely, theoretical derivation of the longitudinal dispersion coefficient is needed. In this study, a theoretical formula for estimating the one-dimensional longitudinal dispersion coefficient is developed based on a transverse distribution equation of the depth-averaged stream-wise velocity in open channel. The velocity distribution equation is employed for the Shiono - Knight Method (SKM). SKM has presented an analytical solution to the Navier-Stokes equation to describe the transverse variations, and originally been applied to straight and nearly straight compound channel. In order to use SKM in modeling non-prismatic and meandering channels, the shape of cross-section is regarded as a triangle. And then incorporating the velocity distribution equation to a triple integral formula which was proposed by Fischer (1968), the one-dimensional longitudinal dispersion coefficient can be derived theoretically. The proposed equations for the velocity distribution and the longitudinal dispersion coefficient are verified by using observed data set. Although the proposed equations do not have a simple functional form, they have a sound basis, and have a potential to reveal effects of the shear flow to the dispersion quantitatively.