三涡旋模式理论中小涡旋的二元和三元速度关联函数和网格湍流的衰变

The Double and Triple Velocity Correlations of Small Vortexes in Three-Vortex Model Theory and the Decay of Grid Produced Turbulence

在三种涡旋分开考虑的湍流模式里,我们用到了小涡旋的二元和三元速度关联函数。本文对小涡旋的二元和三元速度关联函数进行了讨论,并且对它们展开式的头几项中常用到的系数给出了表达式,最后,用它们讨论了网格湍流的衰减问题.计算结果与G.K.Batchelor和A.A.Townsend的实验相符合得很好.

In the three-vortex model theory of turbulence[1'2], the double and the triple velocity correlation functions of small vortexes were employed. In this paper, the double and the triple velocity correlation functions of small vortexes are further disscussed, and the expressions of some coefficients in the expansions in terms of relative displacement of two points are given. Finally, by using these coefficients,the decay of grid-produced trubulence is calculated. The result of calculations gives good agreement with the experimental data of G. K. Batchelor and A. A. Townsend[3].