Buoyancy and drag in Rayleigh-Taylor and Richtmyer-Meshkov linear, nonlinear and mixing dynamics

Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities and RT/RM interfacial mixing are omnipresent in nature and technology and are a source of paradigm shifts in mathematics. This work reports the first derivation of the buoyancy and drag for RT/RM dynamics with variable acceleration. We directly link the governing equations – the conservation laws and the boundary value and initial value problems – to the symmetry-based momentum model, precisely derive the model parameters – the buoyancy and drag – for RT/RM bubbles and spikes in the linear, nonlinear and mixing regimes, and exactly integrate the model equations. The analysis provides extensive benchmarks for future research.