Recovery towards self-similarity in Rayleigh-Taylor instability under stepwise and sinusoidal acceleration reversals

The dynamic properties of an interfacial flow between heavy and light incompressible fluids that are initially Rayleigh-Taylor unstable and are subjected to an external acceleration field oriented in opposition to the density gradient are studied. Rayleigh-Taylor instability occurs in nature with a constant acceleration driven by gravity. However, there are some engineering applications, such as high-energy-density processes observed in inertial and magnetic confined fusion capsules where the acceleration field is not constant. In those applications, Rayleigh-Taylor instability is known to evolve under time-varying acceleration profiles, a phenomenon also observed in supernova formation. Here, we perform implicit large-eddy simulations of density stratification under time-dependent acceleration profiles. Most earlier studies of Rayleigh-Taylor instability under variable acceleration have used a sequence of step functions to simulate acceleration reversals (accel-decel-accel). For the current study, we use a sinusoidal profile, which allows a smoother transition between acceleration and deceleration, and represents smooth transitions that occur in engineering and astrophysical applications. For various imposed acceleration profiles, we compare spatially averaged statistics of the evolving flow against a straightforward and widely utilized scaling, the double integral of acceleration. It will be shown here that this scaling allows distinction between the mean behaviors due to the stepwise and the smooth acceleration profiles and, importantly, that the flow tends to move towards self-similar evolution quicker when the acceleration profile is smoother.