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DIRECT STUDY OF THE CONSTITUTIVE EQUATION FOR TURBULENT NEAR-WALL FLOWS USING DNS DATA

Francois Schmitt
Laboratoire d'Ocanologie et de Gosciences CNRS UMR LOG 8187, Universite des sciences et technologies de Lille - Lille 1 28, av. Foch, 62930 Wimereux, France

Charles Hirsch
Department of Fluid Mechanics Vrije Universiteit Brussel Pleinlaan 2, B-1050 Brussels, Belgium

Abstract

Eddy-viscosity turbulence models rest on a constitutive equation providing the Reynolds stress tensor from the mean velocity gradient tensor, together with transport equations for turbulent quantities such as k or ε. The classical constitutive equation is a linear stress-strain relation, leading to linear k-ε type models, which have clear limitations to predict complex flows. Nonlinear generalizations have been proposed, but have not often been directly tested. Here we consider a quadratic nonlinear constitutive equation; in this framework we focus on the determination of its coefficients. For this we use DNS data of simple shear flows and directly show that nonlinear constitutive equations are necessary, and study their coefficients using invariants.