On the Yakhot–Orszag renormalization group method for deriving turbulence statistics and models

Abstract

The purpose of this paper is to provide an independent, comprehensive, critical review of the ‘‘renormalization group’’ theory of turbulence developed by Yakhot and Orszag [J. Sci. Comput. 1, 3 (1986)]. The first part of the paper is a confirmation of their basic theory for the Navier–Stokes equations, followed by a discussion of approximations in the scale removal procedure. The main part of the paper examines the YO derivations of the velocity‐derivative skewness and the transport equation for the energy dissipation rate E. An algebraic error in the derivation of the skewness is corrected. Several problems are identified in the derivation of the E equation which suggest that the derivation should be reformulated. The present paper has become the basis for such a reformulation, to be published separately by Yakhot and Smith.