Statistical turbulence modelling: capacities and limitations

Statistical turbulence modelling has experienced some very different and even contradictory fortunes: it can lead to highly satisfactory results in complex industrial geometries, like in flows around aeroplanes, but can meet with almost insurmountable problems when applied to apparently simple geometries. This paradoxical situation arises mainly because the hypotheses on which the different models of turbulence are based vary in their suitability (sometimes completely unsuitable) for the specific physics that is relevant for each studied flow. The aim of this paper is to display some of the great difficulties that remain to be resolved in order that statistical turbulence modelling can become a truly reliable tool, both in attempts to understand phenomena (the objective of the research scientist) and for the optimal development of industrial systems (the engineer's objective). From the starting point of straightforward observations made on running computational simulations of turbulent jets, we attempt to show in stages where the sources of weakness in present turbulence models lie, especially in the case where energy spectra are no longer in equilibrium. These analyses have resulted in our driving a new approach, while still drawing on the established knowledge attained by classical statistical modelling. The new method is based on a new way of breaking down physical values into two parts: coherent and incoherent. We will also deal in this paper with the choice of the level of modelling: turbulent viscosity models and models using Reynolds stress transport equations. The Boussinesq behaviour law has also been questioned, in many situations. This leads to the elaboration of non linear models and to certain kinds of constants which are in reality structure functions. In conclusion, new prospects are put forward concerning continued follow-up research in this area. (C) Academie des sciences/Elsevier, Paris.