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

Abarzhi, Snezhana I.

doi:10.1007/s41614-023-00142-3

Rev. Mod. Plasma Phys.

2024

DOI: 10.1007/s41614-023-00142-3

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

Snezhana I. Abarzhi

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Cited by 4 publications

References 132 publications

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Receptivity of Rayleigh-Taylor instability to acoustic pulses: Theoretical explanation of pulse propagation

Sengupta,

Joshi,

Sundaram

2024

Physics Letters A

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Receptivity of Rayleigh-Taylor instability to acoustic pulses: Theoretical explanation of pulse propagation

Sengupta,

Joshi,

Sundaram

2024

Physics Letters A

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Interlinking Rayleigh–Taylor/Richtmyer–Meshkov interfacial mixing with variable acceleration and canonical Kolmogorov turbulence

Abarzhi

2024

Physics of Fluids

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Canonical turbulence and Rayleigh–Taylor/Richtmyer–Meshkov mixing with variable acceleration are paradigmatic complexities in science, mathematics, and engineering, with broadly ranging applications in nature, technology, and industry. We employ scaling symmetries and invariant forms to represent these challenging processes and to assess their very different properties. We directly link—for the first time to our knowledge—the attributes of Rayleigh–Taylor/Richtmyer–Meshkov interfacial mixing with variable acceleration to those of canonical turbulence, including scaling laws, spectral shapes, and characteristic scales. We explore the role of control dimensional parameters in quantifying these processes. The theory results compare well with available observations, the chart perspectives for future experiments and simulations, and for better understanding realistic complexity.

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Self-similar Reynolds-averaged mechanical–scalar turbulence models for Rayleigh–Taylor mixing induced by power-law accelerations in the small Atwood number limit

Schilling

2024

Physics of Fluids

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Analytical self-similar solutions to two-, three-, and four-equation Reynolds-averaged mechanical–scalar turbulence models describing turbulent Rayleigh–Taylor mixing driven by a temporal power-law acceleration are derived in the small Atwood number (Boussinesq) limit. The solutions generalize those previously derived for constant acceleration Rayleigh–Taylor mixing for models based on the turbulent kinetic energy K and its dissipation rate ε, together with the scalar variance S and its dissipation rate χ [O. Schilling, “Self-similar Reynolds-averaged mechanical–scalar turbulence models for Rayleigh–Taylor, Richtmyer–Meshkov, and Kelvin–Helmholtz instability-induced mixing in the small Atwood number limit,” Phys. Fluids 33, 085129 (2021)]. The turbulent fields are expressed in terms of the model coefficients and power-law exponent, with their temporal power-law scalings obtained by requiring that the self-similar equations are explicitly time-independent. Mixing layer growth parameters and other physical observables are obtained explicitly as functions of the model coefficients and parameterized by the exponent of the power-law acceleration. Values for physical observables in the constant acceleration case are used to calibrate the two-, three-, and four-equation models, such that the self-similar solutions are consistent with experimental and numerical simulation data corresponding to a canonical (i.e., constant acceleration) Rayleigh–Taylor turbulent flow. The calibrated four-equation model is then used to numerically reconstruct the mean and turbulent fields, and turbulent equation budgets across the mixing layer for several values of the power-law exponent. The reference solutions derived here can be used to understand the model predictions for strongly accelerated or decelerated Rayleigh–Taylor mixing in the large Reynolds number limit.

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

Cited by 4 publications

References 132 publications

Receptivity of Rayleigh-Taylor instability to acoustic pulses: Theoretical explanation of pulse propagation

Receptivity of Rayleigh-Taylor instability to acoustic pulses: Theoretical explanation of pulse propagation

Interlinking Rayleigh–Taylor/Richtmyer–Meshkov interfacial mixing with variable acceleration and canonical Kolmogorov turbulence

Self-similar Reynolds-averaged mechanical–scalar turbulence models for Rayleigh–Taylor mixing induced by power-law accelerations in the small Atwood number limit

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