Research Article
Jun 1973
New Analytical Solutions for Dye Diffusion Equations
Publication: Journal of the Environmental Engineering Division
Volume 99, Issue 3
Abstract
The two- and three-dimensional, unsteady-state, convective-diffusive partial differential equations describing the concentration distribution of a tracer dye released as an instantaneous source (line or point, respectively) and subject to the no-flux boundary conditions at the river bottom and surface (two-dimensional) and banks (three-dimensional) have been derived analytically using integral transform methods. Previous efforts at analytical dye modeling have assumed infinite geometry in all dimensions thus avoiding the complicating second type (no-flux) boundary conditions at the river bottom, surface, and banks. In the present study, the river was considered finite in the vertical and lateral directions, the dye source location was made arbitrary, and to the writer's knowledge the results represent the first two- and three-dimensional analytical solutions of tracer modeling to appear in the literature which include the boundary effects of the river. The solutions will have particular application in the calculation of turbulent diffusion coefficients in two and three dimensions, which for the first time will analytically include any significant effects of the river boundaries.
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Published In
Journal of the Environmental Engineering Division
Volume 99 • Issue 3 • June 1973
Pages: 213 - 227
Copyright
© 1973 American Society of Civil Engineers.
History
Published in print: Jun 1973
Published online: Feb 11, 2021
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Robert W. Cleary, AM.ASCE
Lect. and Res. Assoc., Water Resour. Program, Dept. of Civ. Engrg., Princeton Univ., Princeton, N.J., USA
Donald Dean Adrian, M.ASCE
Assoc. Prof., Dept. of Civ. Engrg., Univ. of Massachusetts, Amherst, Mass., USA
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ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.