Numerical analysis of burgers' turbulent flow field by characteristic eddy decomposition

Abstract

Burgers`` Turbulence Model Characteristics of the Karhunen-Loeve expansion of a strongly inhomogeneous random field possessing small viscous length scale in the near wall region and a large outer scale in the interior region have been investigated in relation to the application of the expansion to turbulent flow fields. Monte Carlo simulations of a randomly forced Burgers`` equation with zero velocity boundary conditions generate the random process numerically. The statistical moments of its field on the full domain and in the wall layer are investigated for various Reynolds numbers. The correlation of instantaneous velocity and the covariance of fluctuation velocity are computed to analyze the coherent structure of the entire flow field. The Karhunen-Loeve eigenfunctions and the eigenvalue spectra are computed for three Reynolds numbers, Re=413.5, 1654, and 6616. The eigenfunctions possess thin viscous boundary layers at the wall, and they are independent of the Reynolds number in the core region where the random process is quasihomogeneous. The eigenfunctions and eigenvalues of the Karhunen-Loeve expansion are known to exhibit similarity outside of the viscous wall layers in the sense of Reynolds number independence. It is known that the Karhunen-Loeve expansion of a wall layer of suitable thickness has low-order eigenvalues and eigenfunctions that are also independent of the Reynolds number when expressed in terms of appropriate wall variable. This leads to a generalized law of the wall in which the basis functions of the Karhunen-Loeve expansion and the eigenvalue spectrum are universal, in the sense of asymptotic independence of Reynolds number. Eigenvalue spectra contain much of energy in the first few modes, but they are as broad as ordinary trigonometric power spectra. The rate at which the expansion converges to within 90\% of the total energy decreases with increasing Reynolds number and the expansion of the mean plus the fluctuation convergences more...