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<sup>*</sup>

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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^*

基金项目: * 国家自然科学基金资助项目

1.
Shanghai Inst. of Appl. Math. Mech, Shanghai University of Technology, Shanghai;
2.
Univ. of Sci. Tech. of China, Hefei, Shanghai Inst. ofAppl, Math. Mech, Shanghai University ofTechnology, Shanghai

摘要: 在三种涡旋分开考虑的湍流模式^[1,2]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^[3]相符合得很好.

Abstract: In the three-vortex model theory of turbulence^[1,2] and 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 discussed, 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].

[1]	蔡树棠、麻柏坤,大小涡旋分开考虑的模式理论,应用数学和力学,8,10(1987),849-858.
[2]	林多敏、蔡树棠,大涡旋的分类和模式理论的封闭,应用数学和力学,10,10(1989),853-864.
[3]	Batchelor,G.K.and A.A.Townsend,Decay of turbulence in the final period,Proc.Roy.Soc.London,A 194(1948),527-543.
[4]	Chou,P.V..(周培源),On the velocity correlations and the solutions of the equations of turbulent fluctuation,Quarterly of Applied Mathematics,3,1(1945),38-54.
[5]	瑰中磊、诸乾康、钮珍南、俞达诚,网格湍流微结构的实验研究,力学学报,20,3(1988)200-206.