基于分形理论的流速及含沙量垂线分布规律研究

明渠水流的流速分布和含沙量垂线分布规律目前大多是利用现代流体力学的基本理论结合一些假设得到的近似解，因而寻求更具理论基础更能与实际相符的公式一直是学术界研究热点问题之一。本文利用分形理论中自相似分形的标度律，研究了流速垂线分布和含沙量垂线分布的局部与整体之间的自相似现象，从而得到了二维明渠垂线流速分布和含沙量分布的规律。结果表明，基于分形标度律可以得到指数流速分布公式、对数流速分布公式及其它形式的流速分布公式；同样，基于分形标度律也可以得到含沙量垂线分布的Laursen公式、Rouse公式及其它形式的含沙量分布公式。

Study on the vertical velocity and sediment concentration distribution laws based on the fractal theory

At present, the velocity and sediment concentration distributions in open-channel flow are approximately solved by using of modern fluid mechanics theories combined with some assumptions, hence searching for distributions equations with more theoretical basis and higher reliability is a research focus at all the time. In this paper, the velocity and sediment concentration distributions in 2D open-channel flow are studied from the scaling law of self similarity in fractal theory because the whole distribution of velocity or sediment concentration is similar to partial distribution. The results show that the equations of power form, log form and other forms for velocity distribution can be derived from fractal scaling law, and the equations of Laursen, Rouse and others for sediment concentration can be derived from fractal scaling law too.