Renormalization group theory for turbulence: Assessment of the Yakhot-Orszag-Smith theory

The purpose of this paper is to estimate the renormalization group theory for turbulence developed by Yakhot and Orszag [J. Sci. Comput. 1 (1986) 3] and reformulated by Yakhot and Smith [J. Sci. Comput. 7 (1992) 35]. We go into derails of their basic theory for the Navier-Stokes equations, the transport equations for the turbulent kinetic energy K, and its dissipation rate epsilon. As a result, it becomes evident that their theory bears no relationship to Wilson's renormalization group theory for critical phenomena. Their (K) over bar-<(epsilon)over bar> model is not directly obtained from the renormalization group theory. They evaluated the Kolmogorov constant by setting the expansion parameter epsilon=0 and epsilon=4 in the same equations. Furthermore, all the constants in their (K) over bar-<(epsilon)over bar> model are invalid because of the same problem.