Two-length-scale turbulence model for self-similar buoyancy-, shock-, and shear-driven mixing

The three-equation k-L-a turbulence model [B. Morgan and M. Wickett, Three-equation model for the self-similar growth of Rayleigh-Taylor and Richtmyer-Meshkov instabilities, Phys. Rev. E 91, 043002 (2015)PLEEE81539-375510.1103/PhysRevE.91.043002] is extended by the addition of a second length scale equation. It is shown that the separation of turbulence transport and turbulence destruction length scales is necessary for simultaneous prediction of the growth parameter and turbulence intensity of a Kelvin-Helmholtz shear layer when model coefficients are constrained by similarity analysis. Constraints on model coefficients are derived that satisfy an ansatz of self-similarity in the low-Atwood-number limit and allow the determination of model coefficients necessary to recover expected experimental behavior. The model is then applied in one-dimensional simulations of Rayleigh-Taylor, reshocked Richtmyer-Meshkov, Kelvin-Helmholtz, and combined Rayleigh-Taylor-Kelvin-Helmholtz instability mixing layers to demonstrate that the expected growth rates are recovered numerically. Finally, it is shown in the case of combined instability that the model predicts a mixing width that is a linear combination of Rayleigh-Taylor and Kelvin-Helmholtz mixing processes.