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Perspective: group theory analysis and special self-similarity classes in Rayleigh–Taylor and Richtmyer–Meshkov interfacial mixing with variable accelerations

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Abstract

Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities and RT/RM interfacial mixing govern a broad range of processes in nature and technology, at astrophysical and at molecular scales. They are a source of paradigm shifts in science, mathematics, and engineering. In realistic environments, RT/RM dynamics are often caused by variable accelerations. This work employs the group theory to systematically approach RT/RM dynamics with accelerations varying as power law in time and in space, through the direct link of the governing equations to the momentum model. We identify characteristics of RT dynamics and RM dynamics and RT-to-RM transitions, and investigate symmetries, invariant forms, scaling relations, correlations, fluctuation, and spectra of scale-invariant RT mixing and RM mixing. For accelerations varying in time and in space, we discover special self-similarity classes of RT/RM mixing, and explore attributes of their point and interval sub-classes. Depending upon the accelerations, the scale-invariant RT dynamics can be ballistic, quasi-Kolmogorov, steady flex, and quasi-diffusive; it can also belong to the associated super- and sub-intervals; the scale-invariant RM dynamics is sub-diffusive. For any acceleration, RT/RM mixing retains memory of the deterministic (initial and flow) conditions. These characteristics significantly impact the understanding of RT/RM relevant processes in nature, open perspectives unexplored before for better control of RT/RM instabilities in technology, and advance modeling capabilities of RT/RM dynamics in fluids, plasmas, and materials.

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The methods, the results, and the data presented in this work are freely available to the readers in the paper and on the request from the corresponding author.

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Acknowledgements

The support of the University of Western Australia, AUS (project grant 10101047), the Australian Research Council (award LE220100132), and the National Science Foundation, USA (award 1404449) is gratefully acknowledged.

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    Snezhana I. Abarzhi

  2. California Institute of Technology, Pasadena, USA

    Snezhana I. Abarzhi

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Abarzhi, S.I. Perspective: group theory analysis and special self-similarity classes in Rayleigh–Taylor and Richtmyer–Meshkov interfacial mixing with variable accelerations. Rev. Mod. Plasma Phys. 8, 15 (2024). https://doi.org/10.1007/s41614-023-00142-3

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