中国物理B ›› 2009, Vol. 18 ›› Issue (10): 4360-4365.doi: 10.1088/1674-1056/18/10/044

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Single point velocity distributions in homogeneous isotropic turbulence

燕秀林, 冉政   

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
  • 收稿日期:2008-09-20 修回日期:2009-02-25 出版日期:2009-10-20 发布日期:2009-10-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 90816013 and 10572083).

Single point velocity distributions in homogeneous isotropic turbulence

Yan Xiu-Lin(燕秀林), Ran Zheng(冉政)   

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
  • Received:2008-09-20 Revised:2009-02-25 Online:2009-10-20 Published:2009-10-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 90816013 and 10572083).

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摘要： The starting point for this paper lies in the results obtained by Tatsumi (2004) for isotropic turbulence with the self-preserving hypothesis. A careful consideration of the mathematical structure of the one-point velocity distribution function equation obtained by Tatsumi (2004) leads to an exact analysis of all possible cases and to all admissible solutions of the problem. This paper revisits this interesting problem from a new point of view, and obtains a new complete set of solutions. Based on these exact solutions, some physically significant consequences of recent advances in the theory of homogenous statistical solution of the Navier--Stokes equations are presented. The comparison with former theory was also made. The origin of non--Gaussian character could be deduced from the above exact solutions.

关键词: isotropic turbulence, probability distribution function

Abstract: The starting point for this paper lies in the results obtained by Tatsumi (2004) for isotropic turbulence with the self-preserving hypothesis. A careful consideration of the mathematical structure of the one-point velocity distribution function equation obtained by Tatsumi (2004) leads to an exact analysis of all possible cases and to all admissible solutions of the problem. This paper revisits this interesting problem from a new point of view, and obtains a new complete set of solutions. Based on these exact solutions, some physically significant consequences of recent advances in the theory of homogenous statistical solution of the Navier--Stokes equations are presented. The comparison with former theory was also made. The origin of non--Gaussian character could be deduced from the above exact solutions.

Key words: isotropic turbulence, probability distribution function

中图分类号:  (Isotropic turbulence; homogeneous turbulence)

  • 47.27.Gs
47.10.ad (Navier-Stokes equations)