Digital Object Identifier (DOI) 10.1007/s00162-004-0109-5 Theoret. Comput. Fluid Dynamics (2004) 17: 407–431 Theoretical and Computational Fluid Dynamics Original article Contribution to single-point closure Reynolds-stress modelling of inhomogeneous flow G.A. Gerolymos, E. Sauret, I. Vallet LEMFI, Universit´ e Pierre et Marie Curie, case 800, 4 place jussieu, 75005 Paris, France Received August 11, 2003 / Accepted March 17, 2004 Published online July 1, 2004 –  Springer-Verlag 2004 Communicated by Y. Zhou Abstract. This paper is concerned with recent advances in the development of near wall- normal-free Reynolds-stress models, whose single point closure formulation, based on the inhomogeneity direction concept, is completely independent of the distance from the wall, and of the normal to the wall direction. In the present approach the direction of the inhomogeneity unit vector is decoupled from the coefficient functions of the inhomogeneous terms. A study of the relative influence of the particular closures used for the rapid redistribution terms and for the turbulent diffusion is undertaken, through comparison with measurements, and with a baseline Reynolds-stress model (RSM) using geometric wall normals. It is shown that wall- normal-free rsms can be reformulated as a projection on a tensorial basis that includes the inhomogeneity direction unit vector, suggesting that the theory of the redistribution tensor clo- sure should be revised by taking into account inhomogeneity effects in the tensorial integrity basis used for its representation. Key words: Turbulence, Reynolds-stress model, wall topology independent, 3-D flow PACS: 47.32.Fg; 47.85.Gj; 47.27.Eq 1 Introduction 1.1 Wall-normal-free Reynolds-stress models Classical single point second moment closures [26, 36,70, 75], use geometric wall parameters in their for- mulation, such as the distance from the wall d n and the normal to the wall direction (unit normal) e n = n i e i . These parameters appear either in the echo terms of the modelled redistribution tensor φ w ij = φ w ij 1 + φ w ij 2 ( where φ w ij 1 and φ w ij 2 are the echo terms corresponding to the slow and rapid parts of the redistribution tensor, respectively ) , or in various models accounting for the anisotropy of the rate of dissipation tensor ε ij . The use of geometric wall topology related parameters (such as the normal to the wall and the distance from the wall) in a turbulence closure makes its implementation for the computation of geometrically com- plex configurations (such as those encountered in aerospace applications, [1, 56, 78]) quite awkward. A very Correspondence to: I. Vallet (e-mail: vallet@ccr.jussieu.fr)