First and second order modelling of turbulent scalar transport in homogeneous turbulence


H. Ayed1,2* , J. Chahed1, V. Roig2

1Ecole Nationale d’Ingénieurs de Tunis BPN°37, 1002 Le Belvédère, Tunis, Tunisia,

2Institut de Mécanique des fluides de Toulouse, UMR CNRS 5502, Av. C. Soula, 31400, Toulouse, France

* Corresponding author. E-mail:

Received: 17 July 2006; revised version accepted: 02 January 2007



     The present work aims at developing a full second order model for turbulent transport of a passive scalar. A turbulent Prandtl number formulation is obtained by reducing the second order modelling. A first order turbulence model is than proposed with an algebraic formulation of the turbulent scalar flux. The model is tested in homogeneous shear flow with an imposed mean scalar gradient. The Direct Numerical Simulation (DNS) data by [1] were used in the validation of the first and second order modelling of the turbulent passive scalar transport. The comparison of the numerical results with DNS data shows good agreements.


Keywords: Passive scalar; Turbulent flux; Homogeneous shear flow; Turbulence modeling.


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