A two-scale Langevin PDF model for Richtmyer–Meshkov turbulence with a small Atwood number

In this article, we derive a Langevin probability density function (PDF) model in order to predict turbulent mixing zone evolutions when generated by the Richtmyer–Meshkov instability. The aim of the model is to account for the permanence of large eddies which is observed in these flows when the density contrast, as measured by the Atwood number, is small. To this end, a two-scale decomposition of the velocity field is proposed and used to adapt existing Langevin models. In addition, the role played by pressure fluctuations on the transport of kinetic energy is also discussed. A closure for this turbulent process is added to the two-scale Langevin model. Finally, large-eddy simulations of Richtmyer–Meshkov turbulent flows are performed and used to validate the different closures proposed in this work. •Richtmyer–Meshkov turbulence obeys the principle of permanence of large eddies.•A Langevin probability density function model is derived to capture this property.•A two-scale decomposition of the velocity field is used.•The transport of kinetic energy by the pressure field is also accounted for.•Large eddy simulations are performed to validate the model.