Richtmyer–Meshkov instability: theory of linear and nonlinear evolution

Nishihara, Katsunobu; Wouchuk, J. G.; Matsuoka, Chihiro; Ishizaki, R.; Zhakhovsky, V. V.

doi:10.1098/rsta.2009.0252

Cited by 129 publications

(138 citation statements)

References 101 publications

(250 reference statements)

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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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Section: Introductionmentioning

confidence: 99%

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

et al. 2015

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“…The paradigms of turbulent mixing considered in this collection are the passive scalar mixing (Sreenivasan & Schumacher 2010) and mixing induced by hydrodynamic instabilities, including Rayleigh-Taylor (RT) and RichtmyerMeshkov (RM) (Abarzhi 2010;Aglitskiy et al 2010;Andrews & Dalziel 2010;Gauthier & Creurer 2010;Kadau et al 2010;Nishihara et al 2010). The passive scalar problem is standard, but the focus in this issue is the Lagrangian approach.…”

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confidence: 99%

“…In the next paper, Nishihara et al (2010) present a theoretical framework for the studying linear and nonlinear RM instability. Because the contact surface is rippled, the transmitted and reflected wave fronts are also corrugated, and some circulation is generated at the boundary.…”

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Turbulent mixing and beyond

Abarzhi

Sreenivasan

2010

Phil. Trans. R. Soc. A.

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Turbulence is a supermixer. Turbulent mixing has immense consequences for physical phenomena spanning astrophysical to atomistic scales under both high-and lowenergy-density conditions. It influences thermonuclear fusion in inertial and magnetic confinement systems; governs dynamics of supernovae, accretion disks and explosions; dominates stellar convection, planetary interiors and mantle-lithosphere tectonics; affects premixed and non-premixed combustion; controls standard turbulent flows (wall-bounded and free-subsonic, supersonic as well as hypersonic); as well as atmospheric and oceanic phenomena (which themselves have important effects on climate). In most of these circumstances, the mixing phenomena are driven by non-equilibrium dynamics. While each article in this collection dwells on a specific problem, the purpose here is to seek a few unified themes amongst diverse phenomena.Keywords: turbulent mixing; passive scalars; Rayleigh-Taylor instability; Richtmyer-Meshkov instability; high-energy-density physics; holographic technologies Compared with the vast variety of physical circumstances in which turbulent mixing occurs, our knowledge of it is still limited. The problem is relatively straightforward for a simple velocity field (e.g. a constant or periodic in two dimensions), but very few rigorous results exist if the fluid mixing is threedimensional and fully turbulent. The case we do understand better, though incompletely, is the mixing of a passive scalar in isotropic and homogeneous turbulence at high Reynolds numbers, for which sound phenomenological understanding exists (e.g. Obukhov 1949;Yaglom 1949;Corrsin 1951;Batchelor 1959;Kraichnan 1968).Most realistic mixing problems in nature and technology are more complex than passive scalar mixing and involve strong gradients of pressure and density, heat release, transfer of species and changes in chemical composition. Remington et al. 2006). These phenomena are essentially anisotropic, involve non-local interactions among the many scales constituting the physical phenomena, as well as phase changes of matter, and are often driven by shocks or acceleration. In continuum approximation, their scaling laws, spectral shapes and invariant properties differ substantially from those of classical Kolmogorov (1941) turbulence. Singular aspects and similarity of their dynamics are interplayed with the fundamental properties of the Euler and Navier-Stokes equations (Ladyzhenskaya 1975;Scheffer 1976). In the kinetic limit, the non-equilibrium dynamics depart qualitatively from the standard scenario of the Gibbs ensemble and the Boltzmann weight (Hoover 1991;Evans & Morriss 2008). There is thus a strong need for advancing new theoretical methods well beyond the idealized (e.g. isotropic, homogeneous and statistically steady) domain.The state-of-the-art numerical simulations have the potential for developing predictive modelling of the multi-scale non-equilibrium mixing dynamics. With computational power doubling every 18 months or so, larger simulations involving g...

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“…large-scale numerical modelling of a supernova explosion and nuclear burning [18,25]), in laboratory experiments (especially those in highpower laser systems [6,8]), in technology development (including possibilities for improvements in precision, dynamic range, reproducibility, motion-control accuracy, and data acquisition rate [12]), in theoretical analysis (in particular, new approaches for handling complex multi-scale, non-local and statistically unsteady transport [7,9,10,23,24]) renders unparallel opportunities to explore properties of turbulent mixing and probe the matter at the extremes. This success as well as the striking similarity in behaviour of non-equilibrium turbulent processes in vastly different physical regimes make this moment right for integrating our knowledge of the subject and for further enriching its development.…”

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confidence: 99%

“…At atomistic and meso-scales, their non-equilibrium dynamics differ from a standard scenario given by the Gibbs ensemble [17,18]. Their theoretical description is intellectually challenging, as it has to account for the multi-scale, nonlinear, non-local and statistically unsteady character of the dynamics [5,7,[19][20][21][22][23][24]. Their numerical modelling effectively pushes the boundaries of computations to the exascale level and demands significant improvement of numerical methods in order to capture shocks, track interfaces and accurately account for the dissipation processes, non-equilibrium and singularities [18,25].…”

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confidence: 99%

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

Abarzhi

Gauthier

Sreenivasan

2013

Phil. Trans. R. Soc. A.

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Turbulent mixing is a source of paradigm problems in physics, engineering and mathematics. Beyond this important interdisciplinary role, it has immense consequences for a broad range of applications in astrophysics, geophysics, climate and large-scale energy systems. In two volumes, we summarize and provide a perspective on the topic through some 20 articles focusing on turbulent mixing and beyond. The volumes are grouped, somewhat loosely, into those associated with fundamental aspects of turbulence and those specific to Rayleigh–Taylor turbulent mixing.

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Richtmyer–Meshkov instability: theory of linear and nonlinear evolution

Cited by 129 publications

References 101 publications

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

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

Turbulent mixing and beyond

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

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