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Chinese Physics, 2007, Vol. 16(5): 1186-1196    DOI: 10.1088/1009-1963/16/5/003
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Mathematical concepts and their physical foundation in the nonstandard analysis theory of turbulence

Wu Feng(吴峰)
Department of Mechanics and Mechanical Engineering, University of Science and\\ Technology of China, Hefei 230026, China
Abstract  Main mathematical concepts and their physical foundation in the nonstandard analysis theory of turbulence are presented and discussed. The underlying fact is that there does not exist the absolute zero fluid-volume. Therefore, the physical object corresponding to the absolute point is just the uniform fluid-particle. The fluid-particle, in general, corresponds to the monad. The uniform fluid-particle corresponds to the uniform monad, while the nonuniform fluid-particle to the nonuniform monad. There are two kinds of the differentiations, one is based on the absolute point, and the other based on the monad. The former is adopted in the Navier--Stokes equations, and the latter in the fundamental equations presented in this paper for the nonstandard analysis theory of turbulence. The continuity of fluid is elucidated by virtue of the concepts of the fluid-particle and fluid-particle at a lower level. Furthermore, the characters of the continuity in two cases, i.e. in the standard and nonstandard analyses, are presented in this paper. And the difference in discretization between the Navier--Stokes equations and the fundamental equations given herein is also pointed out.
Keywords:  turbulence      monad      fluid-particle at a lower level      nonstandard analysis theory of turbulence  
Received:  24 January 2006      Revised:  14 October 2006      Accepted manuscript online: 
PACS: (Navier-Stokes equations)  
  47.27.-i (Turbulent flows)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No 10572135).

Cite this article: 

Wu Feng(吴峰) Mathematical concepts and their physical foundation in the nonstandard analysis theory of turbulence 2007 Chinese Physics 16 1186

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