Longitudinal dispersion coefficient estimation in two dimensional open channel flow
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Longitudinal dispersivities are evaluated for two-dimensional open channel flow using a new velocity profile developed by Gomez (2006) as an alternative to the traditional "law of the wall" logarithmic profile commonly used. The modified profile improves on the logarithmic profile by incorporating a zero velocity gradient at the surface as well as a non-zero bottom slope, which is necessary for steady uniform flow. Non-dimensional forms of dispersivities are calculated based on Taylor's (1954) dispersivity equation using numerical integration with a polynomial approximation to enable integration of the indefinite integrals in that expression. While the velocities predicted by the traditional and modified profiles are relatively similar, significantly larger eddy viscosities are predicted with the new profile, and these are associated with slightly smaller longitudinal dispersivities. Flume experiments are performed to provide detailed velocity profile measurements, Reynolds stresses, and turbulent kinetic energy distributions. These data are used to compare the two profiles and to evaluate bottom shear stress and shear velocity for a range of conditions, and to provide a database for further research applications. The present results are meant to provide a stronger theoretical basis on which additional factors can be built for making final determinations of longitudinal dispersivity in the field. Further experiments are needed to directly measure longitudinal dispersivity and to confirm the present calculations.