Journal of the Japan Society of Erosion Control Engineering,
Vol.57,No.6,2005
A diffusion equation of suspended load with a source term and its application
Masaharu FUJITA, Takahisa MIZUYAMA
Abstract
There are two important parameters governing suspended load concentration distribution. One is the ratio of a shear velocity to a falling velocity of sand particles. As the distribution proposed by Rouse (1937) shows, it is only a parameter included in the previous diffusion theory. Another is the distribution of source points of suspended particles. Higher source points result in a larger concentration. A sediment supply on the whole water surface produces the uniform concentration distribution. Previous diffusion theory has not contained the parameter concerning source points because it has been developed only for the sand particles already being in suspension. We have found that the Rouse's distribution does not agree with the concentration distribution measured in a steep channel with large roughness. One of the reasons is that the diffusivity is much higher than that in the case of mild slope channels, but another seems to be the lack of a concept of source points. In this paper we have pointed out the necessity and importance of source term in the diffusion equation. Then we have developed a new framework of analysis of suspended load concentration distribution, and presented a diffusion equation with a source term as a more general form for suspended load. This framework can remove the ambiguous points from the previous diffusion theory. A method for calculating the vertical distribution of source points of suspended load was also presented considering the sheltering effect of bed gravels. The calculation results on source points and sediment concentration have indicated that the presented model could express the effect of bed gravels on their distributions as well as their experimental ones.
Key words:suspended load, diffusion equation, source term, suspended load concentration distribution, mountainous river
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