湍流的Markov过程理论与Kolmogoroff理论的联系以及对Kolmogoroff定律的推广——Ⅱ对Kolmogoroff“2/3定律”和“-5/3定律”的推广
The Relation between the Markov Process Theory and Kolmogoroff’s Theory of Turbulence and the Extension of Kolmogoroff’s Laws—(Ⅱ) The Extension of Koimogoroff’s“2/3 Law” and “-5/3 Law”
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摘要: 在前一部分分析大雷诺数湍流的Markov过程理论与Kolmogoroff理论联系的基础上,以适当方式建立了两种理论之间的定量联系.从而由拉格朗日观点的弥散运动的结果得出欧拉观点的结构函数、关联函数和能谱函数.所得结果不但适用于惯性子范围,而且适用于比惯性子范围波数更小的全部范围.熟知的Kolmogroff“2/3定律”和“-5/3定律”为本结果当r很小(或k很大)时的渐近解.因而本结果是Kolmogoroff“2/3定律”和“-5/3定律”的推广.Abstract: Based on the physical analysis in part 1 of this paper, we quantitative relation between the Markov process theory of two-particle's in a dispersion turbulence of very large Reynolds number and the Kolmogoroff's theory. In terms of this relation and the results of two-particle s dispersion,we shall obtain the structure functions, the correlation functions and the energy spectrum, which are applicable not only to the inertial subrange,but also to the whole range of the wave number Iess than that in the inertial subrange. The Kolmogoroff's "2/3 law" and "-5/3 Law" are the aspmptotic case of the present result for small r(or large k), Thus, the present result is an extension of Kolmogoroff's laws.
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[1] 岳曾元等,中国科学,2(1974),181-192, [2] 奥布霍夫,A,M.,A.M.,雅格洛姆,《湍流的微结构》,庄逢甘,胡海昌译,(1953). [3] Hinze,J,O.,Turbudence,(1959). -
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