Temporal Moments for Longitudinal Dispersion

by Yuh Hua Tsai, (A.M.ASCE), Research Asst.; Dept. of Civ. Engrg., Univ. of Illinois at Urbana-Champaign, Urbana, Ill.,
Edward R. Holley, (M.ASCE), Prof.; Dept. of Civ. Engrg., Univ. of Illinois at Urbana-Champaign, Urbana, Ill.,

Serial Information: Journal of the Hydraulics Division, 1978, Vol. 104, Issue 12, Pg. 1617-1634

Document Type: Journal Paper

Discussion: Valentine Eric M. (See full record)
Discussion: Chatwin Philip C. (See full record)
Discussion: Denton Richard A. (See full record)
Discussion: McMillan Alan F. (See full record)
Closure: (See full record)


Aris' moment transformation was used to convert the advective-diffusion equation for two-dimensional (longitudinal and transverse) open channel flow into temporal moment equations. The equation for the zeroth temporal moment of the concentration distribution includes the initial concentration distribution which is a Dirac delta function for instantaneous injections. This equation can be solved analytically for some specific velocity distributions but cannot be solved numerically because of the δ function. Using an implicit finite difference scheme, numerical solutions for both spatial and temporal moments were obtained for plane and centered line source initial conditions and for three velocity distributions. The results were used to examine the relationship between the special and temporal moments during both the initial period and the dispersive period.

Subject Headings: Velocity distribution | Moment distribution | Open channel flow | Two-dimensional flow | Diffusion | Numerical methods | Numerical analysis | Advection

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