Revisiting the late-time growth of single-mode Rayleigh-Taylor instability and the role of vorticity

Growth of the single-fluid single-mode Rayleigh-Taylor instability (RTI) is revisited in 2D and 3D using fully compressible high-resolution simulations. We conduct a systematic analysis of the effects of perturbation Reynolds number (Re-p) and Atwood number (A) on RTI's late-time growth. Contrary to the common belief that single-mode RTI reaches a terminal bubble velocity, we show that the bubble re-accelerates when Re-p is sufficiently large, consistent with Ramaparabhu et al. (2006) and Wei and Livescu (2012). However, unlike in Ramaparabhu et al. (2006), we find that for a sufficiently high Re-p, the bubble's late-time acceleration is persistent and does not vanish. Analysis of vorticity dynamics shows a clear correlation between vortices inside the bubble and re-acceleration. Due to symmetry around the bubble and spike (vertical) axes, the self-propagation velocity of vortices points in the vertical direction. If viscosity is sufficiently small, the vortices persist long enough to enter the bubble tip and accelerate the bubble (Wei and Livescu, 2012). A similar effect has also been observed in ablative RTI (Betti and Sanz, 2006). As the spike growth increases relative to that of the bubble at higher A, vorticity production shifts downward, away from the centerline and towards the spike tip. We modify the Betti-Sanz model for bubble velocity by introducing a vorticity efficiency factor eta = 0.45 to accurately account for re-acceleration caused by vorticity in the bubble tip. It had been previously suggested that vorticity generation and the associated bubble re-acceleration are suppressed at high A. However, we present evidence that if the large Re, limit is taken first, bubble re-acceleration is still possible. Our results also show that re-acceleration is much easier to occur in 3D than 2D, requiring smaller Re-p thresholds. (C) 2019 Elsevier B.V. All rights reserved.