Modeling the pressurestrain correlation of turbulence: An invariant dynamical systems approach
Abstract
The modeling of the pressurestrain correlation of turbulence is examined from a basic theoretical standpoint with a view toward developing improved secondorder closure models. Invariance considerations along with elementary dynamical systems theory are used in the analysis of the standard hierarchy of closure models. In these commonly used models, the pressurestrain correlation is assumed to be a linear function of the mean velocity gradients with coefficients that depend algebraically on the anisotropy tensor. It is proven that for plane homogeneous turbulent flows the equilibrium structure of this hierarchy of models is encapsulated by a relatively simple model which is only quadratically nonlinear in the anisotropy tensor. This new quadratic model  the SSG model  is shown to outperform the Launder, Reece, and Rodi model (as well as more recent models that have a considerably more complex nonlinear structure) in a variety of homogeneous turbulent flows. Some deficiencies still remain for the description of rotating turbulent shear flows that are intrinsic to this general hierarchy of models and, hence, cannot be overcome by the mere introduction of more complex nonlinearities. It is thus argued that the recent trend of adding substantially more complex nonlinear terms containing the anisotropy tensor may be of questionable value in the modeling of the pressurestrain correlation. Possible alternative approaches are discussed briefly.
 Publication:

National Aeronautics and Space Administration Report
 Pub Date:
 January 1990
 Bibcode:
 1990nasa.reptQ....S
 Keywords:

 Correlation;
 Dynamical Systems;
 Homogeneous Turbulence;
 Invariance;
 Pressure Distribution;
 Strain Distribution;
 Turbulence Models;
 Turbulent Flow;
 Anisotropy;
 Closure Law;
 Mathematical Models;
 Nonlinearity;
 Plane Strain;
 Shear Flow;
 Tensors;
 Vortices;
 Fluid Mechanics and Heat Transfer