Dispersion in Varying-Geometry Rivers with Application to Methanol Releases

Most analyses of turbulent mixing in rivers assume constant hydraulic geometry (width, depth, and velocity), despite the fact that in natural rivers these variables typically increase downstream. A comprehensive set of data for the rivers and streams in the United States is used to derive generalized equations for variations in hydraulic geometry. As a preliminary investigation of the importance of these variations, an approximate analytical solution to the one-dimensional advective-dispersion equation is derived for rivers with variable velocity, cross-sectional area, and dispersion coefficient. The solution compares well with previous analyses, and is used to assess the potential environmental impacts of methanol releases into a hypothetical river. The resulting downstream concentrations of methanol are considerably lower than those calculated assuming constant hydraulic geometry.