MULTI-SCALE EFFECTS AND STATISTICAL THEORY OF THE TURBULENCE

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.