Lin Duo-min, Tsai Shu-tang. The Separation of Large Vortexes and the Closed Equations of Turbulence Model[J]. Applied Mathematics and Mechanics, 1989, 10(10): 853-864.
 Citation: Lin Duo-min, Tsai Shu-tang. The Separation of Large Vortexes and the Closed Equations of Turbulence Model[J]. Applied Mathematics and Mechanics, 1989, 10(10): 853-864.

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

• Publish Date: 1989-10-15
• 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 lN 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.
•  [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).

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