Modeling Unsteady Open-Channel Flows Having Longitudinally Varied Fluid Density

by Chintu Lai, (M.ASCE),
Tsan-Wen Wang,

Abstract: Unsteady flows in waterways with fluid density varying longitudinally can be described by various sets of partial differential equations, according to conditions of density variation. Each set consists of the equations of continuity and of motion for constituent-laden flow, and the equation of continuity for constituent discharge. From these sets, various numerical models can be developed via application of the multimode method of characteristics. If the flow is of well mixed type with little dispersion, the three-equation system yields two coupled water waves and a decoupled transport wave. The flow can be analyzed separately by the conventional unsteady-flow approach followed by the constituent advection. If the flow is partially mixed or moderately stratified, the longitudinal dispersion is no longer negligible, and the system transforms to a coupled three-characteristics flow system. Two models of this category, one having a constant, and the other a linearly variable longitpilinal dispersion coefficient, are studied herein. Finally, if constituents are allowed to deposit and resuspended, another component representing the bed-deformation wave, is induced. For uniformity of model treatment, this last system has been simplified to three components as the other three.

Subject Headings: Fluid flow | Unsteady flow | Density currents | Coupling | Water waves | Water flow | Continuity equations | Numerical models

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