Victor Yakhot

Renormalization group analysis of turbulence I. Basic theory

AbstractWe 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 transferPt=0.7179; Batchelor constantBa=1.161; and skewness factor¯S3=0.4878. A differentialK-

The renormalization group, the e-expansion and derivation of turbulence models

\bar \varepsilon

Analytical theories of turbulence and the ε expansion

model is derived, which, in the high-Reynolds-number regions of the flow, gives the algebraic relationv=0.0837 K2/

Flame front propagation in nonsteady hydrodynamic fields

\bar \varepsilon

Asymptotic exponents from low-Reynolds-number flows

, 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,