Search

Colloque avec actes et comité de lecture. Internationale.; International audience; On s'intéresse à la stabilité des écoulements de deux fluides miscibles en canal plan sous l'hypothèse d'incompressibilité et pour de grandes variations de la masse volumique. On considère deux types d'écoulements de base : un écoulement de Poiseuille ainsi que deux couches limites de blaisus pour le cas de deux et trois couches superposées en négligeant les effets de gravités. Il a été observé que l'instabilité est accrue lorsque la zone de mélange se rapproche des parois, de même qu'en diminuant l'épaisseur de celle-ci. Finalement, cette instabilité n'est pas une instabilité de Kelvin Helmholtz classique.

Homogeneous approximations have particularly been used to derive the second moment closure models, because they enable to study and derive the models of the pressure - strain-rate process and of the stress dissipation, separated from other interactions: modelling these two processes is still one of the most challenging issues in single-point closure modelling (e.g. (Lumley, 1970), Speziale et al. (1991)). In this report we present a comparative analysis of the performance of various second moment closure models published in the literature, in a range of homogeneous flows.

The statistical two-point description of turbulence has been regarded as a convenient mathematical framework for better understanding and modelling of the one-point quantities. K'arm'an and Howarth (1938) used this technique to study the evolution of the turbulent length scales in decaying isotropic turbulence. It was also used later by Crow (1968) to express the rapid distortion of isotropic turbulence and by Naot et al. (1973) to derive a transport equation for the Reynolds stress tensor. The two-point description of turbulence provides indeed a convenient framework to study the length scales equations. Rotta (1951) applied the integral operator of the two-point correlation equations to derive the equation for the product of the Reynolds stresses and a scalar integral length-scale. The two-point description served also to derive transport equations for the length-scale tensor (Lin and Wolfshtein (1980), Donaldson and Sandri (1981) or Oberlack and Peters (1993)), and to provide a better insight in the closure of the classical one-point dissipation equation (Jovanovi'c et al. (1995), Oberlack (1994)). However, most of these studies were confined to homogeneous turbulent flows. The two-point spatial approach has also been used to develop multiple-scales models (Schiestel, 1987), though this can also be achieved by starting from a description of the two-point equations in the spectral space through a Fourier transformation. The latter approach is adopted in this study.