Numerical Investigation of the Rayleigh-Taylor Instability Under Various Time-Dependent Acceleration Profile

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 vector field that is orthogonal to the density gradient are studied. Most instances of Rayleigh-Taylor instability occurring in nature are driven by gravity, a constant acceleration. However, there are some engineering applications, such as high-energy-density processes observed in inertial and magnetic confined fusion capsules where the acceleration field has alternative orientations. 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 utilize sinusoidal profiles, which allow for a smoother transition between acceleration and deceleration and are believed to be more representative of 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 displacement length scale, the double-integral of acceleration. It will be shown here that this scaling allows distinction between the mean behaviors due to the step-wise and the smooth acceleration profiles and, importantly, that the flow tends to move towards self-similar evolution quicker when the acceleration profile is smoother.