Abstract: One of the major issues of present times, i.e. water quality degradation and a need for precise answers to transport of pollutants by overland flow, is addressed with special reference to the evaporator pits located adjacent to streams in the oil-producing regions of Eastern Kentucky. The practical shortcomings of the state-of-the-art kinematic wave are discussed and a new mathematical modeling-approach for overland flows using the more comprehensive diffusion wave is attempted as the

more »

... first step in solving this problem. A Fourier series representation of the solution to the diffusion wave is adopted and found to perform well. The physically justified boundary conditions for steep slopes is considered and both numerical and analytical schemes are developed. The zero-depth-gradient lower condition is used and found to be adequate. The steady state analysis for mild slopes is found to be informative and both analytical and numerical solutions are found. The effect of imposing transients on the steady state solution are considered. Finally the cases for which these techniques can be used are presented. Funding information: The work upon which this report is based was supported in part by funds provided by the United States Department of the Interior, Washington, D.C., as authorized by the Water Research and Development Act of 1984, Public Law 98-146. The research work that led to this thesis was funded by U.S. Dept. of the Interior through U.S.G.S. and KWRII. This support is gratefully acknowledged.