Asymptotic Solutions for One-Dimensional Dispersion in Rivers

One-dimensional dispersion in a river from an instantaneous point source is examined by using asymptotic solutions from three different models. The first solution is obtained for the Hays dead-zone equations. In comparison with the Taylor solution, the only major change seems to be that dead zones retard downstream movement of concentration peaks without changing either peak decay rates or tail geometries on concentration-time distributions. A second solution allows the dispersion coefficient to increase with $t$ at large times after contaminant release. It calculates peak concentrations that decay inversely with $t^{(1+n)∕2}$ for $n⩾0$ , reduces to the Taylor solution for $n=0$ , has a major effect on the tails of concentration-time curves as $n$ increases, and gives a close description of field measurements made on the Monocacy River. The third solution allows the dispersion coefficient to increase with the first power of $x$ at large distances downstream. In conclusion, the second model is believed to be relatively simple, flexible, and accurate and is recommended for use in describing one-dimensional contaminant dispersion in rivers.