Theory and simulations of linear and nonlinear two-dimensional Rayleigh–Taylor dynamics with variable acceleration

Journal Article · Sat Apr 01 00:00:00 EDT 2023 · Physics of Fluids

DOI:https://doi.org/10.1063/5.0137462· OSTI ID:1970051

Chan, Wai Hong Ronald  ^[1]; Jain, Suhas S.  ^[2]; Hwang, Hanul  ^[2]; Naveh, Annie  ^[3]; Abarzhi, Snezhana I.  ^[3]

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1. Department of Mechanical Engineering, Stanford University, Stanford, California 94305, USA, Department of Aerospace Engineering Sciences, University of Colorado, Boulder, Colorado 80303, USA
2. Department of Mechanical Engineering, Stanford University, Stanford, California 94305, USA
3. Department of Mathematics and Statistics, The University of Western Australia, Perth, Western Australia 6009, Australia

Interfacial Rayleigh–Taylor mixing is crucial to describing important natural and engineering processes, such as exploding supernovae, laser micromachining, hot spots in inertial confinement fusion, and optical telecommunications. These require the characterization of the time dependence of the driving acceleration. We compare our theoretical formulation based on group theory foundations with interface-capturing numerical simulations for linear and nonlinear two-dimensional Rayleigh–Taylor instabilities in a finite-sized domain with time-varying acceleration over broad ranges of Atwood numbers and acceleration exponents. Detailed corroboration between theory and simulations is provided for this foundational case. Both demonstrate the strong interfacial nature of Rayleigh–Taylor instabilities, which suggests that practical flow fields can be reconstructed from the derived fluid potential using the proposed theory. A robust agreement is also obtained for the early and late-time evolution of the amplitudes of the bubble and spike, which demonstrate that the Rayleigh–Taylor flow can transition to the mixing regime even for a single-mode initial perturbation. Corroboration with experiments of high energy density plasmas motivated by studies of supernovae is also achieved. In addition, a long-standing puzzle in Rayleigh–Taylor dynamics on the interplay between the acceleration, the shear, and the interface morphology in the theory and simulations is resolved by accounting for finite viscosity of the fluids. The characterization of Rayleigh–Taylor instabilities as a highly interfacial phenomenon provides valuable insight into its multiscale nature, which enhances the design and understanding of numerous processes of practical interest.

• Sponsoring Organization: USDOE
• OSTI ID: 1970051
• Journal Information: Physics of Fluids, Journal Name: Physics of Fluids Vol. 35 Journal Issue: 4; ISSN 1070-6631
• Publisher: American Institute of Physics
• Country of Publication: United States
• Language: English