从单个跃移沙粒在气流中的运动方程出发导出了风沙两相流中沙粒相速度分布函数的Boltzmann方程.对风沙流研究中几种不同的分布函数及其相应的统计平均值等基本概念给出了严密的数学定义, 指出了不同分布函数之间的区别和联系.在略去铅垂方向空气阻力的情况下,给出了沙粒相速度分布函数沿铅垂方向的边缘分布,作为风沙流中跃移理论的主要基础之一.利用结果对前人在风沙流研究中发现的某些重要规律和现象进行了解释.%In this paper, Boltzmann equation for velocity distribution function ofthe particle phase in wind-blown sand two phase flow is derived fromthe motion equation of single particle saltating in the air flow. Exactmathematical definitions are given for several different distributionfunction, which are usually confused in literature, such as velocitydistribution function in 3-D space, velocity distribution function ofparticle launching across plane, saltation height distribution function.The difference and relationship among them are pointed out. Severalmacroscopic average quantities corresponding to each distributionfunction are introduced. The particle flux in unit wide is expressed interms of these introduced statistical mean quantities. Some importantphenomena found previously in airborne movement are properly explainedby the theory developed in this paper.rn In the case of ignoring vertical drag in boundary layer, it is approvedthat the following 5 propositions are equivalent to each other: (1) Thevelocity distribution function of particle launching across horizontalplane is Rayleigh distribution. (2) The boundary distribution along ydirection of velocity distribution function in 3-D space is normaldistribution. (3) Saltation height distribution function acrosshorizontal plane is normal distribution. (4) the particle mass densityattenuates as an exponential function of height y. (5) The secondorder moment of velocity distribution along y direction is constant.rn The stroboscopic photography method in the wind tunnel test is used tomeasure the particle speeds, and particle flux is test bysand-collection. The present experiments and previous literatureshow that the above 5 propositions are good approximations to approachexperiments.
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