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Group theory analysis of early-time scale-dependent dynamics of the Rayleigh-Taylor instability with time varying acceleration

Hill, Desmond L. and Bhowmick, Aklant K. and Ilyin, Dan V. and Abarzhi, Snezhana I. (2019) Group theory analysis of early-time scale-dependent dynamics of the Rayleigh-Taylor instability with time varying acceleration. Physical Review Fluids, 4 (6). Art. No. 063905. ISSN 2469-990X. doi:10.1103/physrevfluids.4.063905.

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We consider the long-standing problem of Rayleigh-Taylor instability with variable acceleration, and focus on the early-time scale-dependent dynamics of an interface separating incompressible ideal fluids of different densities subject to an acceleration being a power-law function of time for a spatially extended three-dimensional flow periodic in the plane normal to the acceleration with symmetry group p6mm. By employing group theory and scaling analysis, we discover two distinct subregimes of the early-time dynamics depending on the exponent of the acceleration power-law. The time scale and the early-time dynamics are set by the acceleration for exponents greater than (-2), and by the initial growth-rate (due to, e.g., initial conditions) for exponents smaller than (-2). At the exponent value (-2) a transition occurs from one subregime to the other with varying acceleration strength. For a broad range of the acceleration parameters, the instability growth rate is explicitly found, the dependence of the dynamics on the initial conditions is investigated, and theory benchmarks are elaborated.

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Additional Information:© 2019 American Physical Society. Received 15 October 2018; published 21 June 2019. S.I.A. thanks the University of Western Australia (AUS) for financial support under the project Grant No. 10101047 and the National Science Foundation (USA) for financial support under the Award No. 1404449. The authors’ contributions to this work are as follows: D.L.H. conducted analytical studies. A.K.B. made plots for Figs. 5, 6, and 7. D.V.I. made plots for Figs. 3, 4, and 9. S.I.A. conducted analytical studies and led the project, including its scientific and organizational aspects.
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University of Western Australia10101047
Issue or Number:6
Record Number:CaltechAUTHORS:20190621-110416336
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:96624
Deposited By: Tony Diaz
Deposited On:22 Jun 2019 18:15
Last Modified:16 Nov 2021 17:22

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