SIMULATIONS OF FREE SURFACE FLOWS
WITH CROSS STREAM VARIATIONS OF THE WALL ROUGHNESS
S. Zaouali1, A. Soualmia1, L. Masbernat2*
1 Ecole Nationale d’Ingénieurs de Tunis BP 37 Le Belvédère, 1002 Tunis, Tunisie,
2 Institut de Mécanique des Fluides de Toulouse, Allée du Professeur Camille Soula 31400, Toulouse, France
* corresponding author. e-mail: email@example.com
Received: 06 August 2007; revised version accepted: 02 January 2008
We present numerical simulations of the fully developed flow in a straight rectangular open channel with a sharp transverse variation of the bottom roughness. The algebraic stress model adopted in this work is issued from a Reynolds stress transport model including surface proximity functions to simulate the effects of the wall and the free surface on the turbulence anisotropy. The comparison with the experimental results shows that the model predicts correctly the transverse evolution of the vertical profiles of the Reynolds stress tensor components. This work deals also with the closure problems of the 2D-Saint Venant equations obtained by the depth averaging of the field equations: the 3D-simulations are used to calculate the terms present in 2D-equations, such as the local bottom friction, the transverse dispersion due to the turbulence and to the advection by the secondary flows. These calculations allow us to suggest and discuss new closure assumptions relative to those terms.
Keywords: turbulence; anisotropy; roughness; Secondary flows ; second-order closure; 2D-Saint Venant equations; dispersion.