A two-time-scale model for turbulent mixing flows induced by Rayleigh-Taylor and Richtmyer-Meshkov instabilities

A two-time-scale closure model for compressible flows previously developed is extended to turbulent Rayleigh - Taylor and Richtmyer - Meshkov driven flows where mixing coexists with mean pressure gradients. Two model coefficients are calibrated with the help of Canuto - Goldman's model. For several Rayleigh - Taylor configurations, it is shown that the characteristic lengths scale as t(2) while the kinetic energies and spectral transfers behave as t(2) and t, respectively. The computed phenomenological coefficients of Youngs' scaling law are compared with experimental data ones. Comparisons with Youngs' three-dimensional numerical simulation ( The Physics of Fluids A 3 ( 1991) 1312) are also performed. Finally three shock tube experiments, where the Richtmyer Meshkov instability initiates the mixing, are simulated. The mixing thickness evolution is well reproduced while the turbulence levels seem to be overestimated with such first order models. The capability of the two-time-sale model to recover available data for different turbulent flows allows us to conclude to a more universal behavior in comparison with single-time-scale models.