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

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.

[1]  David R. Nelson,et al.  Large-distance and long-time properties of a randomly stirred fluid , 1977 .

[2]  R. Kraichnan.  Inertial-range transfer in two- and three-dimensional turbulence , 1971, Journal of Fluid Mechanics.

[3]  Riley,et al.  Analysis of subgrid-scale eddy viscosity with use of results from direct numerical simulations. , 1987, Physical review letters.

[4]  M. Lesieur,et al.  Parameterization of Small Scales of Three-Dimensional Isotropic Turbulence Utilizing Spectral Closures , 1981 .

[5]  M. Tabor,et al.  Time correlations and random sweeping in isotropic turbulence , 1990 .

[6]  Uriel Frisch,et al.  Remarks on the renormalization group in statistical fluid dynamics , 1983 .

[7]  R. Kraichnan.  Eddy Viscosity in Two and Three Dimensions , 1976 .

[8]  Uriel Frisch,et al.  d-dimensional turbulence , 1978 .

[9]  Steven A. Orszag,et al.  Analytical theories of turbulence and the ε expansion , 1987 .

[10]  Paul C. Martin,et al.  Energy spectra of certain randomly-stirred fluids , 1979 .

[11]  S. Orszag,et al.  Space‐time correlations in turbulence: Kinematical versus dynamical effects , 1989 .

[12]  S. Orszag,et al.  Renormalization group analysis of turbulence. I. Basic theory , 1986 .

[13]  A. Townsend.  On the fine-scale structure of turbulence , 1951, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[14]  V. C. Patel,et al.  Turbulence models for near-wall and low Reynolds number flows - A review , 1985 .

[15]  C. W. Atta,et al.  Reynolds number dependence of skewness and flatness factors of turbulent velocity derivatives , 1980 .

[16]  Robert H. Kraichnan,et al.  An interpretation of the Yakhot–Orszag turbulence theory , 1987 .

[17]  J. Lumley,et al.  A First Course in Turbulence , 1972 .

[18]  W. Reynolds.  Computation of Turbulent Flows , 1975 .

[19]  G. Batchelor,et al.  The theory of homogeneous turbulence , 1954 .