湍流的多尺度效应与统计理论

MULTI-SCALE EFFECTS AND STATISTICAL THEORY OF THE TURBULENCE

  • 摘要: 湍流是一种由不同尺度、不同频率组成的不规则涡结构引起的随机现象。研究表明,在湍流脉动过程中虽然存在湍涡的多尺度效应及其演变,但两种尺度的涡最为重要,一种是与时均流动发生相互作用的大尺度涡,这类涡通过时均剪切作用,从时均流动中源源不断地提取能量以维持湍流的脉动;另一种是小尺度的耗散涡,这类涡与黏性尺度同量级,它们通过黏性而耗散湍流脉动。本文详细分析了湍涡的多尺度效应及其演变、大涡和小涡的量级比较,并在此基础上,阐述了湍流中任意两点脉动速度的相关性和频谱分布特性,以便为初学者提供参考。

     

    Abstract: Turbulence is a random phenomenon induced by irregular vortex structures that composed of different scales and frequencies. Researches have shown that although the multi-scale effects and their evolution of turbulent vortices occurs in the turbulent fluctuation processes, the two scales of vortices are the most important. One type is the large-scale vortices that interact with the time-averaged flow, which continuously extracts energy from the time-averaged flow through the shear interactions to maintain the turbulent fluctuations. Another type is the small-scale dissipative vortices, having the same magnitude as the viscosity scale and dissipating the turbulent fluctuations through viscosity. This article provides a detailed analysis of the multi-scale effects and evolution of turbulent vortices, as well as a comparison of the magnitudes of large and small vortices. Based on this, the correlation and spectral distribution characteristics of the fluctuation velocities at any two points in turbulence are elaborated, in order to provide reference for beginners.

     

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