大涡旋的分类和模式理论的封闭<sup>*</sup>

林多敏; 蔡树棠

大涡旋的分类和模式理论的封闭^*

林多敏¹,
蔡树棠²

1.
上海市应用数学和力学研究所上海工业大学;
2.
中国科学技术大学

基金项目: * 国家自然科学基金资助项目

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出版历程
- 收稿日期: 1988-08-08
- 刊出日期: 1989-10-15

The Separation of Large Vortexes and the Closed Equations of Turbulence Model

Lin Duo-min¹,
Tsai Shu-tang²

1.
Shanghai Inst.of Appl.Math, and Mech Shanghai Univ.of Tech., Shanghai;
2.
Dept.of Modern Mech., Univ.of Set.and Tech.of China, Hefei, Shanghai Inst.of Appl.Math, and Mech., Shanghai

摘要

摘要: 本文依据前文^[1]大小涡旋分开考虑的湍流模式,对局部产生的湍流大涡旋引进了新的几率分布,由此引入了一种新的平均过程和平均值.通过这种平均,我们就可以把局部产生的湍流大涡旋和外来的湍流大涡旋进行严格的区分.然后,再引进适当的辅助条件和根据外来干扰的实际情况确定了外来大涡旋的耗散尺度l_N,使得湍流脉动二阶矩的方程组封闭,同时对前文^[1]中的一些扩散系数进行了适当的修改.最后,得到了一个封闭的、能够数值求解的方程组.

Abstract: This paper presents a new kind of everage for the loeally-generated large vortexes so that the physieal quantities of the locally-generated large vortexes and the external large vortexes canberigorously separated from the equal ions for the large vortexes proposed in a previous paper^[1] To the equations for the two kinds of large vortexes,some auxiliary relations are introduced,and the value,of the length-scale l_N of energy dissipation of the external large vortexes may he determined according to the actual circumstances of the disturbance of external sources.Thus the resulting equations of the second moments of turbulent velocity fluctuations for the two kinds of large vortexes can be made closed.Meanwhile,the corresponding coefficients of diffusion in the previous paper^[1] are improved,Finally,a closed set of numerically-solvable equations of turbulence model are obtained.

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参考文献(10)

[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),849-868.
[2]	蔡树棠,《湍流理论》,中国科技大学和浙江大学讲义(1985).
[3]	Chou,P.Y.(周培源),On the velocity corrclations and the solutions of the equations of turbulent fluctuation,Quart.of Appl.Math.,3,1(1945),38-54.
[4]	Chou,P.Y.(周培源),On the velocity correlations and the equation of turbulent vorticity fluctuation,The Science Reports of National Tsinghua Univ.,5,I,Scries A(1948),52-70.
[5]	Rotta,J.C.,Statische Theorie Nichomogener Turbulenz,Zeitsch.für Physik,129(1951),547-572.
[6]	Launder,B.E.,G.J.Recce and W.Rodi,Progress in the development of a Reynolds-stress turbulence closure,J.F.M.,68(1975),537.
[7]	Launder,B.E.and D.B.Spalding,Mathematical Models of Turbulence,Academic Press,London and New York(1972).
[8]	Launder,B.E.,W.C.Reynolds,W.Rodi,J.Mathieu and D.Jeandel,Turbulence Models and Their Applications,Editions Enrolles(1984).
[9]	蔡树某、周光洞、魏中磊、谢象春,湍流研究最近半世纪的一些进展,力学进展,10,(1980),16-36.
[10]	蔡树棠,《湍流的模式理论》,水动力学研究与进展研讨会讲义,无锡(1986,8).