DESCRIPTION OF TURBULENCE USING THE RENORMALIZATION-GROUP METHOD

At the beginning a brief review of ideas and of the renormalization-group (RG) method in the field-theoretic and Wilson's forms, a concept of fixed points, a method for obtaining the correlation function asymptotic behavior and the epsilon-expansion technique are presented. A statement is formulated that the RG method allows to get a description of turbulent cascade processes. Further it is shown how to obtain Kolmogorov's exponents for statistical moments with the help of the RG method. The Yakhot-Orszag theory is considered enabling to calculate a set of turbulent universal constants without using any empirical parameters. Some methodical difficulties of the Yakhot-Orszag theory could be eliminated within the frameworks of the field-theoretical form of the RG method. In this form the problem of locality of the intermodal interaction is formulated in a different manner. After elimination of the infrared divergences in ultraviolet limit RG method enables to calculate the corrections to Kolmogorov's exponents which are manifested as an anomalous dimension. In conclusion the results are obtained for subgrid viscosity required for large eddy simulation with the help of the RG method.