An interpretation of the Yakhot–Orszag turbulence theory

Yakhot and Orszag have recently developed a theory of turbulence [J. Sci. Comput. 1, 3 (1986)] based on dynamic renormalization‐group (RNG) techniques. They predict parameters of the Kolmogorov inertial range and then successfully use eddy‐viscosity formulas from the inertial‐range theory in computations of shear flows. In the present paper a critical analysis of the Yakhot–Orszag theory is offered based on comparison with a simple perturbative model. The latter appears to parallel much of the physical and operational content of the lowest order of the Yakhot–Orszag theory, without using RNG methods. The essence is as follows: (1) the dynamics of modes in the inertial and dissipation ranges are assumed to be dominated by interactions more‐or‐less local in wavenumber that are modeled by a white‐noise force acting against an effective viscosity; and (2) the effective viscosity is estimated by extrapolation from the small contributions of interactions very nonlocal in wavenumber (distant interactions). In common with the Yakhot–Orszag theory, the only explicit contacts with the Navier–Stokes equation are overall energy conservation by nonlinear terms and the interaction coefficients of highly nonlocal wave vector triads.