均匀各向异性湍流后期衰变的涡性结构与J. C. Bennett禾口S. Corrsin实验

本文在以前几篇文章的基础上,假定后期各向异性湍流场是由我们以前所用的涡旋和涡球迭加所组成。假定涡旋和涡球是彼此独立的。涡旋的轴的方向在空间分布是各个方向机率相等的,而涡球的轴则在空间取某一固定方向。在平均时除了对涡旋和涡球的中心进行平均以外,还要对涡旋的轴的方向进行平均。由于涡球的轴指向某一固定方向,所以并不平均。通过这样平均,我们得到二元速度关联和三元速度关联张量。最后算出了沿某一特定方向的二元速度关联函数和三元速度关联函数的各向异性修正项和。并且作出了f(r)和k(r)的曲线与J. C. Bennett和S. corrsin的实验进行比较。二元速度关联函数f(r)仍旧是指数型的关联函数和实验比较符合,三元速度关联函数k(r)和实验符合得很好。     

THE DOUBLE AND TRIPLE VELOCITY CORRELATIONS OF SMALL VORTEXES IN THREE-VORTEX MODEL THEORY AND THE DECAY OF GRID-PRODUCED TURBULENCE

In the three-vortex model theory of turbulence and double and the triple velocitycorrelation functions of small vortexes were employed.In this paper,the double and thetriple velocity correlation functions of small vortexes are further discussed,and theexpressions of some coefficients in the expansions in terms of relative displacement of twopoints are given.Finally,by using these coefficients,the decay of grid-produced trubulenceis calculated.The result of calculations gives good agreement with the experimental data ofG.K.Batchelor and A.A.Townsend.     

泥沙在动水中的沉淀运动(二)——泥沙在层流中的沉淀运动

在前文中我们已经给出小球在不均匀流场中运动时所受到的阻力。本文中我们假定泥沙和水为两种不同的介质,同时假定泥沙的浓度很小。利用前文所得到的阻力公式,我们建立了在层流状态时泥沙和水各自的运动方程组。然后利用这一组方程来讨论明渠中水流流态为层流时泥沙沉淀的情况。最后我们得到泥沙和水的相对速度在主流方向的分量并不等于零。同时我们求得根据简单假定来计算时所引起的沉积位置的误差。这个误差和水深成正比而和泥沙颗粒的大小无关。一般说来,这个误差并不是一个可以忽略的数值。     

Two Problems of the Semi-Conductor Physics Discussed with the Point of View of the Fluid Dynamics

In this article,we discuss two problems of the semi-conductor physics from the point of view ofthe fluid dynamics.Firstly,we discuss the problem of the p-n junction,and find that the previoustreatment and the previous conclusion of the problem are somewhat erroneous.Secondly,we discussthe coefficient C of the block resistance,and find that the mathematical method of the previoustreatment is erroneous.     

A NEW TURBULENCE MODEL WITH THE SEPARATE CONSIDERATION OF LARGE AND SMALL VORTEXES

Recently the k-ε model has been widely used,but it is a kind of gradient model.Because the life-time of turbulence vortexes is very long,in common flow problems theinfluence of up-stream vortexes must be important,and the vortexes are not in quasi-equilibrium.So the usefulness of the k-εmodel and other gradient models is limited.Inthis paper,according to actual cases of the turbulence,the velocity fluctuations areseparated into large and small vortexes,and the laree vortexes consist of two parts.onecomes from up-stream and around,the other is locally generated.Thus we get a turbulencemodel,which consists of three parts.     

THE VELOCITY OF SAND PARTICLES RELATIVE TO WATER AND THE VARIATI0N 0F FLUCTUATION VELOCITY DUE TO THE CONCENTRATION OF SUSPENDED SAND PARTICLES

In this paper.we discuss three fundamental problemsof the theory of suspended sand particles based on thetheory of fluid dynamics.They are:(1)the relative ve-locity of sand particles to the surrounding fluid in theturbulent flow.(2) the variation of the velocity fluc-tuation of the fluid when the suspended sand particlesexist,(3)the profile of the vertical distribution ofthe concentration of the suspended sand particles in two-dimensional uniform steady channel flow and the modifi-cation of usual diffusion theory.The results of our.theoretical analysis are somewhat different from the cor-responding expressions in the textbooks of hydraulicsand river mechanics.     

涡量脉动相似结构和圆形涡旋流速分布

1.柱坐标中的湍流脉动方程 我们取柱坐标(r,φ,z),用(U__r,U_φ,U_z)代表瞬时速度,我们假定流体为粘性不可压缩的.ρ和μ都是常数,我们把瞬时速度分为平均速度和涨落速度之和,瞬时压强为平均压强和压强涨落ω之和,即     

关于湍流理论中的不封闭性的讨论*

有一种观点认为湍流的不封闭性是由于N-S方程的非线性,这是一似是而非的错误说法。因为工程上要求的量并不仅仅限于湍流的平均速度和平均压力,即使方程式是线性的,也无法把工程上要求的这些量逐个求出来。本文论证了湍流的不封闭性来源于目前的湍流理论中缺少了一个与实际情况符合的有关分布函数,并且进一步说明了湍流模式理论的局限性和用N-S方程直接计算机模拟亦是相当困难的原因。     

On the closure problem of turbulence model theory

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