基于动理学理论的推移质输沙公式  

A bed-load formula based on kinetic theory

作　　者：张磊[1] 钟德钰[1] 王光谦[1] 吴保生[1] 

机构地区：[1]清华大学水利水电工程系水沙科学与水利水电工程国家重点实验室,北京100084

出　　处：《水科学进展》2013年第5期692-698,共7页Advances in Water Science

基　　金：国家自然科学基金资助项目(51039004);"十二五"国家科技支撑计划资助项目(2012BAB05B01)~~

摘　　要：根据Boltzmann方程得到了床面附近运动颗粒的速度分布函数，将其在速度空间上积分，同时考虑床面颗粒起动概率的影响得到了床面颗粒的冲刷率函数。在此基础上，将该函数代人Einstein提出的推移质输沙基本模式中得到了基于动理学理论的推移质输沙公式。研究结果表明：①公式计算结果与实验数据吻合，相对误差为10％～50％，可用于高强度和低强度输沙，能够较好地反映出床面附近运动的推移质颗粒的统计属性；②得到的推移质输沙率理论表达式与经典推移质输沙公式十分接近，同时大大改善了Einstein公式在高强度输沙情况下的计算结果，这也说明了本文理论推导的正确性。Bed-load plays an important role in sediment transport in fluvial rivers. This paper presents a bed-load for- mula on the basis of kinetic theory. The pick-up rate of bed-load sediment in the formula is obtained by integrating the velocity distribution function derived by solving the Bohzmann equation of kinetic theory. During the integration, the effect of incipient probability is considered. The bed-load formula is derived by substituting the expression of the pick- up rate into the basic equation of bed-load transport developed by Einstein. Comparisons of the simulations with avail- able experimental data for both weak and intensive sediment transport are presented. The relative errors range from 10% to 50% , which illustrates that the new formula can reasonably represent the statistical characteristics of the bed- load particles moving on the bed surface. Furthermore, the new formula has remarkably improved the result of Ein- stein equation for intensive sediment transport, and is very similar to the classical bed-load formulas, which proves the validity of the theoretical derivation of the formula.

关 键 词：推移质 输沙率 紊动 动理学 

分 类 号：TV142[水利工程—水力学及河流动力学]