Journal of Scientific Computing

, Volume 1, Issue 1, pp 3–51 | Cite as

Renormalization group analysis of turbulence. I. Basic theory

  • Victor Yakhot
  • Steven A. Orszag
Article
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Abstract

We develop the dynamic renormalization group (RNG) method for hydrodynamic turbulence. This procedure, which uses dynamic scaling and invariance together with iterated perturbation methods, allows us to evaluate transport coefficients and transport equations for the large-scale (slow) modes. The RNG theory, which does not include any experimentally adjustable parameters, gives the following numerical values for important constants of turbulent flows: Kolmogorov constant for the inertial-range spectrumCK=1.617; turbulent Prandtl number for high-Reynolds-number heat transferP t =0.7179; Batchelor constantBa=1.161; and skewness factor¯S3=0.4878. A differentialK-\(\bar \varepsilon \) model is derived, which, in the high-Reynolds-number regions of the flow, gives the algebraic relationv=0.0837 K2/\(\bar \varepsilon \), decay of isotropic turbulence asK=O(t−1.3307), and the von Karman constantκ=0.372. A differential transport model, based on differential relations betweenK,\(\bar \varepsilon \), andν, is derived that is not divergent whenK→ 0 and\(\bar \varepsilon \) is finite. This latter model is particularly useful near walls.

Key words

Renormalization group turbulence theory inertial range turbulence transport Reynolds number large-eddy simulation computational fluid dynamics 
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Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • Victor Yakhot
    • 1
  • Steven A. Orszag
    • 1
  1. 1.Applied & Computational Mathematics and Mechanical & Aerospace EngineeringPrinceton UniversityPrinceton

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