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REVIEW ARTICLES: Turbulence Theories and Models Incorporating Experimental and Computer Simulation Knowledge of Coherent Structures

Use of Experimental Data for an Efficient Description of Turbulent Flows

[+] Author and Article Information
N. Aubry

The Benjamin Levich Institute and Department of Mechanical Engineering, City College of the City University of New York, NY 10031

Appl. Mech. Rev 43(5S), S240-S245 (May 01, 1990) doi:10.1115/1.3120815 History: Online April 30, 2009

Abstract

The proper orthogonal decomposition (POD), also called Karhunen-Loève expansion, which extracts ‘coherent structures’ from experimental data, is a very efficient tool for analyzing and modeling turbulent flows. It has been shown that it converges faster than any other expansion in terms of kinetic energy (Lumley 1970). First, the POD is applied to the chaotic solution of the Lorenz equations. The dynamics of the Lorenz attractor is reconstructed by only the first three POD modes. In the second part of this paper, we show how the POD can be used in turbulence modeling. The particular case studied is the wall region of a turbulent boundary layer. In this flow, the velocity field is expanded into POD modes in the normal direction and Fourier modes in the streamwise and spanwise directions. Dynamical systems are obtained by Galerkin projections of the Navier Stokes equations onto the different modes. Aubry et al. (1988) applied the technique to derive and study a ten dimensional representation which reproduced qualitatively the bursting event experimentally observed. It is shown that streamwise modes, absent in Aubry et al.’s model, participate to the bursting events. This agrees remarkably well with experimental observations. In both examples, the dynamics of the original system is very well recovered from the contribution of only a few modes.

Copyright © 1990 by American Society of Mechanical Engineers
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