Influence of Secondary Currents on Solute Dispersion in Curved Open Channels

Abstract

The dispersion coefficient tensor including off-diagonal components was introduced in the flow with secondary currents, which is called skewed shear flow dispersion (SSFD) coefficient tensor, in this paper. To observe the detailed effect of cross-dispersion terms in SSFD model on solute dispersion, mathematical analysis of eigenvalue problem with respect to the equation with SSFD coefficient tensor was performed. The analysis results show the several differences of SSFD model compared to CSFD (conventional shear flow dispersion) model: the oblique direction of principal dispersion with respect to the streamline, the increase of peak concentration, and the change in the eccentricity of elliptical tracer cloud. SSFD coefficient tensor in a streamwise curvilinear coordinate system of curved channel was transformed to those components of fixed Cartesian coordinate system, and 2D numerical model with finite element method was established in the Eulerian-Cartesian coordinate. Through this process, the transformation equation using the depth-averaged velocity field was derived. Several numerical tests were performed to assure the results obtained in the mathematical analysis and to show the applicability of the derived transformation equation on the flow with continuously changing flow direction.