Bridging the local and the global: a physically constrained buoyancy--drag model for unified prediction of Rayleigh--Taylor and Richtmyer--Meshkov mixing widths across density ratios
Accurate prediction of the macroscopic width of Rayleigh--Taylor (RT) and Richtmyer--Meshkov (RM) turbulent mixing layers is central to inertial confinement fusion and supernova dynamics. However, bubble--spike asymmetry, density-ratio dependence and unsteady forcing pose a persistent closure challenge: existing low-order buoyancy--drag models struggle to describe different mixing problems accurately with one model and coefficient set. We combine local front dynamics with global mass conservation in separate buoyancy--drag equations for the bubble and spike fronts. Rather than imposing shared or fixed empirical coefficients, the model retains separate inertia, buoyancy and drag coefficients on the two sides and allows them to vary independently with density ratio. Given the bubble-side state scalings, RT/RM similarity relations, a mean-composition profile and endpoint asymptotics jointly constrain all six effective coefficients without case-by-case fitting. A profile-shape parameter $c$ labels distinct internal composition states and is selected a priori from RT spike scaling measured in linear-electric-motor experiments. The model then cross-predicts the RM spike exponent without recalibration to RM spike data and, by construction, recovers low-Atwood-number bubble--spike symmetry and the high-density-ratio free-fall RT-spike and ballistic RM-spike limits. Tests against constant- and variable-acceleration RT mixing, post-impulse RM evolution and Nova laser deceleration show that one closure describes mixing-width evolution across density ratios and acceleration histories without case-specific retuning, while reducing excessive spike growth at high density ratio. This physically interpretable, asymptotically consistent framework enables cross-problem prediction of wide-density-ratio RT and post-impulse RM mixing.