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

Journal Article · 10 November 2019 · Physica. D, Nonlinear Phenomena

DOI: https://doi.org/10.1016/j.physd.2019.132250 · OSTI ID:1574757

Bian, Xin ^[1]; Aluie, Hussein ^[1]; Zhao, Dongxiao ^[1]; Zhang, Huasen ^[1]; Livescu, Daniel  ^[2]

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1. Univ. of Rochester, NY (United States)
2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

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 (Rep) 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 Rep is sufficiently large, consistent with [Ramaparabhu et al. 2006, Wei and Livescu 2012]. However, unlike in [Ramaparabhu et al. 2006], we find that for a sufficiently high Rep, 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 toward the spike tip. We modify the Betti-Sanz model for bubble velocity by introducing a vorticity efficiency factor η = 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 Rep 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 Rep thresholds.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: 89233218CNA000001
• OSTI ID: 1574757
• Report Number(s): LA-UR--19-26670
• Journal Information: Physica. D, Nonlinear Phenomena, Journal Name: Physica. D, Nonlinear Phenomena Journal Issue: C Vol. 403; ISSN 0167-2789
• Publisher: ElsevierCopyright Statement
• Country of Publication: United States
• Language: English