Rayleigh-Taylor instability under sinusoidal acceleration profiles across a broad parameter range

We study the dynamic properties of the Rayleigh-Taylor instability (RTI) that occurs at the interface between fluids of varying density, subjected to an external acceleration. Classical RTI occurs when the fluid is subjected to a constant gravity field. RTI subjected to time-dependent acceleration fields are less studied, although they are theorized to better represent hydrodynamic instabilities observed in high-energy-density processes. Previous studies have considered variable acceleration profiles in a piece-wise acceleration reversal. In this study, we consider smoother acceleration profiles that vary sinusoidally with time, as such reversals are conjectured to better represent the acceleration sign reversals that occur in most relevant engineering and astrophysical applications. We consider four acceleration profiles: constant acceleration, ADA, and two sinusoidal profiles, one matching the period of the ADA profiles, and the other matching the amplitude. We use the double-integral of acceleration as a relevant length scale to compare the sinusoidal cases; all results are compared to the constant gravity RTI case. This allows us to comment on the self-similar evolution of the RTI under variable acceleration profiles in terms of low-order parameters such as mixing layer width growth, mass flux, Reynold's stresses, anisotropy tensor, and molecular mixing.