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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
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. Finally, 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.
Schilling, Oleg. "Self-similar Reynolds-averaged mechanical–scalar turbulence models for Rayleigh–Taylor mixing induced by power-law accelerations in the small Atwood number limit." Physics of Fluids, vol. 36, no. 7, Jul. 2024. https://doi.org/10.1063/5.0216754
Schilling, Oleg (2024). Self-similar Reynolds-averaged mechanical–scalar turbulence models for Rayleigh–Taylor mixing induced by power-law accelerations in the small Atwood number limit. Physics of Fluids, 36(7). https://doi.org/10.1063/5.0216754
Schilling, Oleg, "Self-similar Reynolds-averaged mechanical–scalar turbulence models for Rayleigh–Taylor mixing induced by power-law accelerations in the small Atwood number limit," Physics of Fluids 36, no. 7 (2024), https://doi.org/10.1063/5.0216754
@article{osti_2407211,
author = {Schilling, Oleg},
title = {Self-similar Reynolds-averaged mechanical–scalar turbulence models for Rayleigh–Taylor mixing induced by power-law accelerations in the small Atwood number limit},
annote = {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. Finally, 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.},
doi = {10.1063/5.0216754},
url = {https://www.osti.gov/biblio/2407211},
journal = {Physics of Fluids},
issn = {ISSN 1070-6631},
number = {7},
volume = {36},
place = {United States},
publisher = {American Institute of Physics (AIP)},
year = {2024},
month = {07}}
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 368, Issue 1916https://doi.org/10.1098/rsta.2010.0020
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 371, Issue 2003https://doi.org/10.1098/rsta.2013.0267