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Analysis and Extension of the Renormalization Group Treatment of Fluid Turbulence

出版	University of Toronto, 2000
URL	http://books.google.com.hk/books?id=L9c9zwEACAAJ&hl=&source=gbs_api

註釋The Navier-Stokes equations driven by a random stirring force have been treated with the Renormalization Group (RNG) methods by Yakhot and Orszag and other authors to obtain theoretical predictions of various constants of turbulence without empirically adjusted parameters. The analysis contains many approximations, some of which may be justified when the ratio of the resolution cutoff wavenumber ([Lambda]c) to the wavenumber under consideration (k) is very large. However, when this ratio approaches one (local interactions) many of the approximations required by RNG are no longer valid. Various methods attempting to extend RNG to include the local interactions have failed to produce results that could be validated. These attempts have been outlined and discussed in the first part of this study. In part two of this work, further attempt is made to extend the RNG method to produce turbulence models valid near the cutoff, specifically an eddy viscosity as a function of the wavenumber ratio (k/[Lambda]c) with a cusp up behavior for k/[Lambda]c [right arrow] 1. General properties of the partial averaging operation have been presented and modified to allow different methods of averaging subgrid Fourier triads. Three methods of deriving an eddy viscosity function have been proposed. The results do not match the most likely form of eddy viscosity obtained in other studies. The validity of the temporal approximations made in the RNG are analyzed.