Correlation effects and turbulent diffusion scalings

A significant deviation of turbulent transport from conventional diffusion necessitates a search for new types of equations and scalings. Long-range correlations are responsible for anomalous transport. An investigation of correlation effects and correlation functions, which are fairly universal tools, plays an important role. This review deals with the methods of direct calculations, diffusive approximation, and the scaling representation of correlation effects. In this paper, we consider different methods for constructing transport equations, ranging from those in the quasi-linear approximation to those with fractional derivatives. The topics to be discussed include renormalized quasi-linear equations, Levy-Khintchine distributions, and continuous time random walk. A variety of instabilities leads to the development of different turbulence types. This variety of forms requires not only special description methods, but also an analysis of the general mechanisms. One such mechanism is percolation transport. Its description is based on the ideas of long-range correlations, borrowed from the theory of phase transitions, and fractality. A detailed analysis of the more important results obtained in this field is presented in this paper. We will focus on scaling arguments that play an important role in obtaining estimates of transport effects