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An interpretation of the Yakhot-Orszag turbulence theory. (English) Zbl 0642.76069
Summary: V. Yakhot and S. A. Orszag have recently developed a theory of turbulence [J. Sci. Comput. 1, 3-51 (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 folows: (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.

MSC:
76F10 Shear flows and turbulence
76M99 Basic methods in fluid mechanics
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