Importance of Vertical Variations of Velocity for Shear Dispersion in Rivers: Fid-Bau Portal

Importance of Vertical Variations of Velocity for Shear Dispersion in Rivers

Schwab, Lauren E. / Rehmann, Chris R.

An expression for the dispersion coefficient in a rectangular channel is derived to evaluate the importance of transverse and vertical variations in velocity for dispersion. The contribution of vertical variations to dispersion depends not on the ratio of the width $B$ and depth $H$ of the channel—as is usually assumed—but on the ratio of mixing times, $τ = (H^{2} / D_{z}) / (B^{2} / D_{y})$ , where $D_{y}$ and $D_{z}$ are the transverse and vertical mixing coefficients, respectively. The analysis allows the role of vertical variations to be assessed quantitatively as a function of the time scale ratio and the shape of the velocity profile. The time scale ratio is estimated using data sets compiled by others and several empirical formulas for $D_{y}$ . In almost all cases, vertical variations contribute a small amount to the overall dispersion. The results support the usual practice of considering only transverse variations in computing the dispersion coefficient, and the analysis provides an approach for including vertical variations in calculations of dispersion in cases in which $τ$ is not small.