摘要
坡面薄层水流速度是研究坡面土壤侵蚀的基础，但由于坡面水流很浅，同时含有泥沙，其水流速度测量一直是一个没有很好解决的问题。示踪法测量结果需采用经验系数修订才能得到水流速度；而经验系数受多种因素的影响，在不同的条件下如何使用，有较大的随意性。同时经验系数与水流速度有关，这样就出现了循环引用的问题。因此从理论作进一步的探索开发其测量原理，研制和开发新的、相应简单的适用仪器，具有理论和实际意义。
本项研究在对坡面侵蚀动力学分析的基础上，结合有关的理论，创立了电解质脉冲法测量薄层水流流速的方法和相应的测量系统。具体研究内容和结果如下：
(1)利用溶质在恒定水流中对流-扩散运移理论，通过坡面薄层水流的形态分析了电解质在水流中迁移的动力学特征，建立了电解质脉冲在坡面薄层水流中运移的动力学模型。建模过程中，假定坡面薄层水流为一维的，降雨与入渗的影响忽略不计；水流恒定或变化可以忽略不计；盐液的注入水流时历时很短，可以认为是一个电解质脉冲输入。由此，建立了一维的电解质脉冲在坡面薄层水流中的迁移数学模型，包括控制微分方程及其定解条件。采用Laplace变换方法，求得了溶质迁移的解析解。解析解图示分析表明，解析解从定性地看是合理的，体现了溶质在水流中弥散的基本规律。理论分析发现，利用溶质浓度在观测点达到最大值的时间计算得到的速度无法推算出实际水流速度，以此为基础的染色示踪法或盐液示踪法都缺乏理论依据。同时溶质的弥散系数对示踪法测量水流速度也有较大的影响，弥散系数越大，质心到达观测点的时间与浓度最大值到达该点的时间偏离越远。说明在采用示踪法测量水流速度时，经验修正系数的选取必须考虑水流中泥沙含量或其它水质的差异。
(2)利用电子技术、计算机技术、仪器设计与开发技术，设计了薄层水流速度测试系统。用Visual Basic语言编写了操作／控制系统，实现了数据采集、参数计算和分析自动化。系统实现流速测量的原理如下：通过测量与数据采集系统，测量得到溶质迁移过程中浓度随时间的变化曲线，采用最小二乘法和溶质迁移数学模型的解析解对测量得到的溶质迁移曲线进行拟合，得到模型的相关参数，即水流速度和溶质扩
电解质脉冲法测量坡面薄层恒定水流速度的研究及其初步应用
散系数。该系统操作简单，具有较好的稳定性和防水性能，通过大量室内试验验证了
此电解质脉冲法测量坡面薄层水流速度系统的可靠性。
(3)将坡面薄层水流中的电解质脉冲分布看成为一个质点，利用运动学理论中质
心运动速度公式对电解质迁移数学模型进行比较分析，证明了电解质脉冲数学模型的
解析解中的水流速度与溶质的质心运动速度是一致的，从而证明了溶质迁移模型的解
析解在运动学理论上的准确性。在没有盐液损失的条件下，质心速度可以表示坡面水
流速度。利用质心运动力学、电解迁移模型法和流量法对不同坡度和不同泥沙含量下
的薄层水流流速测量结果进行比较，证明了电解质脉冲法不仅在理论上是正确的，而
且在实际测量中也是可行的。
(4)通过不同泥沙含量下示踪法经验系数分析表明，泥沙含量对示踪法经验系数
的影响不可忽略，示踪法的经验系数随泥沙含量增加而增大，呈线性相关关系，用示
踪法测量坡面水流流速必须考虑水流中的泥沙含量。
(5)冲刷与降雨条件下用电解质脉冲法测量坡面水流速度为土壤侵蚀机理的动力
学分析提供了基础。通过冲刷和降雨条件下水流速度和泥沙含量的测量和分析，发现
了坡面的水流速度与泥沙含量存在同步的关系，水流速度越大，径流的剥离与输沙能
力越强。土壤表面细沟的形成过程也是径流能量消耗的过程，随着细沟的发育，水流
的动能减小，水流速度变小;细沟形成后，细沟为了进一步向浅沟或切沟发育，坡面
径流的一部分动能仍消耗在细沟的进一步发育中。这使得细沟形成后，在不同的坡度
下，相同降雨强度下水流速度相差不大。在较短的时间间隔内测量水流速度能解释细
沟发育过程中的瞬态突发特性，电解质脉冲法达到了示踪法和流量法无法比拟的效
果。
The velocity of sheet flow is the basic in the research of soil erosion on slope, but there is no sound method of measuring it so far for the flow is very shallow and sediment contained in the flow has great influences on the measurement. In the conventional tracer method, the flow velocity is determined by the time for the tracer to cover a certain distance, and an arbitrarily chosen empirical correction coefficient. The empirical coefficient is influenced by many factors. Further the empirical coefficient is a function of velocity; therefore inter-dependence of the two arises. The measurement of sheet flow velocity on hillslope needs more theoretical research, for the development of new instrument.
On the base of erosion research and related theories, an electrolyte pulse method for measuring velocity of sheet flow is advanced. The detailed outcomes are as follows.
(l)The dynamic convective-dispersion transfer theories of electrolyte solute in steady sheet flow on slope were used to analyze the dynamic transport of solute in flowing water. Mathematical models were outlined for the transfer of solutes in sheet flow. The basic assumptions of solute transport were: the flow is one-dimensional with the influences of rainfall and infiltration neglected; the flow is steady or its fluctuation is negligible; and the time interval for solute injection is so short that the input of electrolyte can be treated as a pulse input. The 1-D models, including the governing equation and the initial and boundary conditions were given. Laplace's transformation method was used to obtain the analytical solution ton the convective-dispersion process of solute transport. The analytical
solution was graphically shown to illustrate the conceptual validation of solution, which describes the main characteristics of solute transport in flowing water. Theoretical analysis of the analytical solution indicates that the velocity of flow can not be calculated with the estimated velocity by the time for the solution peak to cover a distance from the injection location to the measuring point, as used in color or salt tracer method. The conventional tracer methods for velocity determination have their theoretical faults. The dispersion coefficient of solute has significant effect on the velocity measured by the tracer method. The bigger the dispersion coefficient, the larger the time interval between the peak and centroid arriving time. Therefore, the sediment content should be considered and different correction coefficient should be used while measuring the velocity of flow using tracer method.
(2)A experimental prototype was developed to measure the velocity of sheet flow, with the integration of electronics technique, compute application knowledge and instrumentation techniques. A Visual Basic based operation and control system were developed for automated data logging, parameters (including velocity) estimation, and file management. The system estimates the velocity with the following procedures. The sensors and data logging system were used to measure the temporal concentration changes of the transporting solute. The least square method was used to fit the analytical solution to the measured solute transport data and the related model parameters, i.e. the velocity and the dispersion coefficient were determined. And the velocity was so \determined. This operation system was found to be easy to use and reliable as well as stable, by numerous laboratory experiments.
(3)Taking distribution of solute in the flowing water of sheet flow as a system of particles, the centroid velocity of the system of particles was calculated with kinematics theory and found to be equal to the velocity calculated by the method outlined above. Therefore, it was proved that the analytical mathematical solution of electrolyte transport is correct in the view of kinematics. Under the assumption of no solute loss, the centroid velocity can be used for the averaged flow velocity. The experiments indicated that there are no differences in flow velocity or rates of f
引文
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