Yue Zeng-yuan, Zhang Bin. 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”[J]. Applied Mathematics and Mechanics, 1983, 4(2): 179-191.
Citation:
Yue Zeng-yuan, Zhang Bin. 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”[J]. Applied Mathematics and Mechanics, 1983, 4(2): 179-191.
Yue Zeng-yuan, Zhang Bin. 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”[J]. Applied Mathematics and Mechanics, 1983, 4(2): 179-191.
Citation:
Yue Zeng-yuan, Zhang Bin. 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”[J]. Applied Mathematics and Mechanics, 1983, 4(2): 179-191.
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”
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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