宽级配卵石推移质输移随机过程的分维研究

Fractal Study on the Stochastic Process of Bed Load Transport with a Wide Range Size Distribution

深入探讨、分析长江三峡工程上游河道宽级配卵石推移质输移特点及其随机过程 ,更清楚地认识三峡工程回水变动区河道泥沙运动规律是一个很重要的研究课题。本文应用 70年代发展起来的现代数学手段分形(分维 )几何学、R/S分析 ,对长江上游年来沙量过程进行分形特性分析 ,用R/S分析计算其分形维数 ,表明长江上游悬沙和推移质年沙量的分形维DH 分别为 1 .32 1和 1 .378;赫斯特数H分别为 0 .6 79和 0 .6 2 2 ,均大于 0 .5 ,根据分形几何学、R/S分析原理 ,说明三峡工程上游来沙量发展过程发现为正相关 ,是具有持久记忆性、周期性的随机过程———分式布朗运动过程 ,长江上游沙量发展趋势有可能表现为 :“良性循环或恶性循环”两种 ,长江上游来沙量必须依靠持久的水土保持治理和水库群拦截 ,否则会出现恶性循环的可能。文中用分形几何学、R/S分析方法对宽级配卵石推移质输移实测随机过程进行计算 ,结果表明对测量时间间隔 8～ 9分钟的采样 ,所获得的输沙率随机过程的分维数DH=1 .47(H =0 .5 3) ,接近马氏过程 (DH=1 .5 )。测量时间间隔 3分钟的采样 ,所获得的输沙率随机过程的分维数DH=1 .33(H =0 .6 7) ,为非马氏过程 ,表明过程具有持久记忆性和周期性。

A considerable important research topic is to investigate and analyze the characteristics and stochastic process of non-uniform sediment transport with a wide range of size distribution. In this paper, fractal and R/S analysis methods, developed in 1970's, are presented to analyze fractal features of the annual sediment discharge process in the upper Yangtze River. Fractal dimensions D H of annual suspended load and bed load discharge are 1.321 and 1.378 respectively. Based on the principles of fractal and R/S analysis method, a positive correlation is shown for sediment transport discharge process in the upper Yangtze River. This means that the characteristics of the stochastic process are the features with long time memory and periods, which is also called as differential Brown's stochastic process. The tendency of sediment discharge in the upper Yangtze River will therefore be of two possible types: one goes from a good case to a better case, and other one from a bad case to a worse case. The Water\|and\|soil conservation works should be done for a long time, otherwise more sediment disasters may occur.