What is certain and what is not so certain in our knowledge of Rayleigh–Taylor mixing?

Anisimov, S. I.; Drake, R. P.; Gauthier, Serge; Meshkov, E. E.; Abarzhi, Snezhana I.

doi:10.1098/rsta.2013.0266

Cited by 56 publications

(209 citation statements)

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“…At macroscopic (i.e., continuous) scales, these conditions lead to the formation of discontinuities (referred to as fronts or interfaces) between the flow nonuniformities (phases). [11][12][13] Here, we consider from a far field the evolution of a hydrodynamic discontinuity separating fluids of different densities. The fluids are incompressible and ideal.…”

Section: Introductionmentioning

confidence: 99%

“…In the presence of acceleration, the front separating fluids of different densities may be subject to the Rayleigh-Taylor instability (RTI). 1,4,[11][12][13] A rigorous group theory approach has been developed to solve the boundary value problem and to describe Rayleigh-Taylor (RT) flows which account for their non-local, anisotropic, and heterogeneous dynamics. 4,11,31 This approach captures the fundamental properties of the RTI and RT mixing (such as the multi-scale RT dynamics, and the order in RT mixing) and explains experimental observations.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of dynamics, stability, and flow fields' structure of an accelerated hydrodynamic discontinuity with interfacial mass flux by a general matrix method

et al. 2018

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We develop a general matrix method to analyze from a far field the dynamics of an accelerated interface between incompressible ideal fluids of different densities with interfacial mass flux and with negligible density variations and stratification. We rigorously solve the linearized boundary value problem for the dynamics conserving mass, momentum, and energy in the bulk and at the interface. We find a new hydrodynamic instability that develops only when the acceleration magnitude exceeds a threshold. This critical threshold value depends on the magnitudes of the steady velocities of the fluids, the ratio of their densities, and the wavelength of the initial perturbation. The flow has potential velocity fields in the fluid bulk and is shear-free at the interface. The interface stability is set by the interplay of inertia and gravity. For weak acceleration, inertial effects dominate, and the flow fields experience stable oscillations. For strong acceleration, gravity effects dominate, and the dynamics is unstable. For strong accelerations, this new hydrodynamic instability grows faster than accelerated Landau-Darrieus and Rayleigh-Taylor instabilities. For given values of the fluids' densities and their steady bulk velocities, and for a given magnitude of acceleration, we find the critical and maximum values of the initial perturbation wavelength at which this new instability can be stabilized and at which its growth is the fastest. The quantitative, qualitative, and formal properties of the accelerated conservative dynamics depart from those of accelerated Landau-Darrieus and Rayleigh-Taylor dynamics. New diagnostic benchmarks are identified for experiments and simulations of unstable interfaces. Published by AIP Publishing.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of dynamics, stability, and flow fields' structure of an accelerated hydrodynamic discontinuity with interfacial mass flux by a general matrix method

et al. 2018

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“…It should also be mentioned that in the past 10-15 years significant progress has been achieved with respect to the theoretical understanding of RMI. Comparison with rigorous theories, see (Abarzhi 2008(Abarzhi , 2010Anisimov et al 2013;Nishihara et al 2010;Sreenivasan and Abarzhi 2013) and references therein, would be beneficial for numerical simulations and this would be part of future work.…”

Section: Introductionmentioning

confidence: 99%

Computing multi-mode shock-induced compressible turbulent mixing at late times

et al. 2015

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Both experiments and numerical simulations pertinent to the study of self-similarity in shock-induced turbulent mixing often do not cover sufficiently long enough times for the mixing layer to become developed in a fully turbulent manner. When the Mach number of the flow is sufficiently low, numerical simulations based on the compressible flow equations tend to become less accurate due to inherent numerical cancellation errors. This paper concerns a numerical study of the late time behaviour of single-shocked Richtmyer-Meshkov Instability (RMI) and associated compressible turbulent mixing using a new technique that addresses the above limitation. The present approach exploits the fact that RMI is a compressible flow during the early stages of the simulation and incompressible at late times. Therefore, depending on the compressibility of the flow field the most suitable model, compressible or incompressible, can be employed. This motivates the development of a hybrid compressible-incompressible solver that removes the low-Mach number limitations of the compressible solvers, thus allowing numerical simulations of late time mixing. Simulations have been performed for a multi-mode perturbation at the interface between two fluids of densities corresponding to an Atwood number of 0.5, and results are presented for the development of the instability, mixing parameters and turbulent kinetic energy spectra. The results are discussed in comparison with previous compressible simulations, theory and experiments.

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“…The concluding article in this Theme Issue is by Anisimov et al [12]. In the past few decades, significant advances have been made by theoretical analysis in the understanding of RT dynamics.…”

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confidence: 99%

“…This part II of the Theme Issue consists of the following papers: the paper by Sreenivasan & Abarzhi on acceleration and turbulence in Rayleigh-Taylor (RT) mixing [1]; by Meshkov on experimental studies of unstable interfaces [2]; by Youngs on numerical modelling simulations of self-similar regimes in mixing flows [3]; by Grinstein et al [4] on a pragmatic approach for reproducing complex multiphase flows in simulations; by Glimm et al [5] on the so-called alpha problem; by Nevmerzhitskiy on the implementation and diagnostics of RT/Richtmyer-Meshkov (RM) mixing in experiments [6]; by Livescu on high resolution approaches for numerical modelling of RT instabilities [7]; by Statsenko et al [8] on subgrid scale models applied to RT/RM mixing; by Prestridge et al analysing the RM mixing experiments conducted over the past decade [9]; by Levitas on mixing applications in reactive flows [10]; by Pudritz & Kevlahan on supersonic processes and shock waves in interstellar media [11]; and by Anisimov et al [12] summarizing the status of our understanding of RT mixing. We observe the development of the Rayleigh-Taylor instability (RTI) when fluids of different densities are accelerated against the density gradient [13,14].…”

mentioning

confidence: 99%

Turbulent mixing and beyond: non-equilibrium processes from atomistic to astrophysical scales II

Abarzhi

Gauthier

Sreenivasan

2013

Phil. Trans. R. Soc. A.

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This Introduction summarizes and provides a perspective on the papers representing one of the key themes of the ‘Turbulent mixing and beyond’ programme—the hydrodynamic instabilities of the Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) type and their applications in nature and technology. The collection is intended to present the reader a balanced overview of the theoretical, experimental and numerical studies of the subject and to assess what is firm in our knowledge of the RT and RM turbulent mixing.

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What is certain and what is not so certain in our knowledge of Rayleigh–Taylor mixing?

Abstract: Past decades significantly advanced our understanding of Rayleigh–Taylor (RT) mixing. We briefly review recent theoretical results and numerical modelling approaches and compare them with state-of-the-art experiments focusing the reader's attention on qualitative properties of RT mixing.

Cited by 56 publications

References 98 publications

Analysis of dynamics, stability, and flow fields' structure of an accelerated hydrodynamic discontinuity with interfacial mass flux by a general matrix method

Analysis of dynamics, stability, and flow fields' structure of an accelerated hydrodynamic discontinuity with interfacial mass flux by a general matrix method

Computing multi-mode shock-induced compressible turbulent mixing at late times

Turbulent mixing and beyond: non-equilibrium processes from atomistic to astrophysical scales II

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