VORTEX PARADIGM FOR ACCELERATED INHOMOGENEOUS FLOWS: Visiometrics for the Rayleigh-Taylor and Richtmyer-Meshkov Environments

Zabusky, Norman J.

doi:10.1146/annurev.fluid.31.1.495

Cited by 205 publications

(131 citation statements)

References 118 publications

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“…where ρ is the density, ω is the vorticity, and p is the pressure, the mechanism primarily involved in the process is the deposition of baroclinic vorticity at the interface (Zabusky 1999;Aure and Jacobs 2008;Mikaelian 2003), which increases the circulation in this area with time. When the shock wave passes from one fluid to the other, clockwise vorticity is deposited and an unstable sheet of vortices, which drives the deformation of the interface, is created.…”

Section: The Richtmyer-meshkov Instabilitymentioning

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: The Richtmyer-meshkov Instabilitymentioning

confidence: 99%

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

et al. 2015

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“…As the shock fronts are not uniform, their corrugations will induce a highly perturbed flow behind them, which will be the seed for the Rayleigh-Taylor instability (RTI) that occurs later during the acceleration phase of the target (Ishizaki & Nishihara 1997;Piriz et al 1997;Nishihara et al 1998;Goncharov 1999;Velikovich et al 2000). The RMI has also been thoroughly studied in experiments designed in shock tubes (Jones & Jacobs 1997;Zabusky 1999;Brouillette 2002) and has also become a fascinating research topic in the field of high-energy density experiments in matter. Furthermore, this type of perturbation flow may be used to our advantage by creating those perturbed flows artificially in the laboratory to excite the related instabilities and using them as a tool to extract information from matter at extreme conditions of pressure, density and temperature.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, the non-uniformly distributed vorticity results in complex dynamics of the interface in the nonlinear phase. Zabusky et al visualized its complex dynamics with the use of hydrodynamic simulations, and coined the terms 'vortex paradigm' and 'vortex projectile' (Hawley & Zabusky 1989;Zabusky & Zeng 1998;Zabusky 1999;Zabusky & Zhang 2002). In tank experiments (Jacobs & Sheeley 1996), they also visualized complex dynamics of the interface, such as the spiral structure of a spike.…”

Section: Introductionmentioning

confidence: 99%

Richtmyer–Meshkov instability: theory of linear and nonlinear evolution

Nishihara

Wouchuk

Matsuoka

et al. 2010

Phil. Trans. R. Soc. A.

130

128

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A theoretical framework to study linear and nonlinear Richtmyer-Meshkov instability (RMI) is presented. This instability typically develops when an incident shock crosses a corrugated material interface separating two fluids with different thermodynamic properties. Because the contact surface is rippled, the transmitted and reflected wavefronts are also corrugated, and some circulation is generated at the material boundary. The velocity circulation is progressively modified by the sound wave field radiated by the wavefronts, and ripple growth at the contact surface reaches a constant asymptotic normal velocity when the shocks/rarefactions are distant enough. The instability growth is driven by two effects: an initial deposition of velocity circulation at the material interface by the corrugated shock fronts and its subsequent variation in time due to the sonic field of pressure perturbations radiated by the deformed shocks. First, an exact analytical model to determine the asymptotic linear growth rate is presented and its dependence on the governing parameters is briefly discussed. Instabilities referred to as RM-like, driven by localized non-uniform vorticity, also exist; they are either initially deposited or supplied by external sources. Ablative RMI and its stabilization mechanisms are discussed as an example. When the ripple amplitude increases and becomes comparable to the perturbation wavelength, the instability enters the nonlinear phase and the perturbation velocity starts to decrease. An analytical model to describe this second stage of instability evolution is presented within the limit of incompressible and irrotational fluids, based on the dynamics of the contact surface circulation. RMI in solids and liquids is also presented via molecular dynamics simulations for planar and cylindrical geometries, where we show the generation of vorticity even in viscid materials.

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“…The largeand small-scale motions present in the flow field distort the interface and enhance the diffusive mixing of the two fluids. Reviews by Brouillette (2002) and Zabusky (1999) offer more comprehensive descriptions of the problem.…”

Section: Introductionmentioning

confidence: 99%

An experimental investigation of mixing mechanisms in shock-accelerated flow

et al. 2008

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An experimental investigation of mixing mechanisms in a shock-induced instability flow is described. We obtain quantitative two-dimensional maps of the heavy-gas (SF 6 ) concentration using planar laser-induced fluorescence for the case of a shockaccelerated cylinder of heavy gas in air. The instantaneous scalar dissipation rate, or mixing rate, χ, is estimated experimentally for the first time in this type of flow, and used to identify the regions of most intense post-shock mixing and examine the underlying mechanisms. We observe instability growth in certain regions of the flow beginning at intermediate times. The mixing rate results show that while these unstable regions play a significant role in the mixing process, a large amount of mixing also occurs by mechanisms directly associated with the primary instability, including gradient intensification via the large-scale strain field in a particular non-turbulent region of the flow.

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VORTEX PARADIGM FOR ACCELERATED INHOMOGENEOUS FLOWS: Visiometrics for the Rayleigh-Taylor and Richtmyer-Meshkov Environments

Cited by 205 publications

References 118 publications

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

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

Richtmyer–Meshkov instability: theory of linear and nonlinear evolution

An experimental investigation of mixing mechanisms in shock-accelerated flow

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