An analytical nonlinear theory of Richtmyer-Meshkov instability

Zhang, Qiang; Sohn, Sung-Ik

doi:10.1016/0375-9601(96)00021-7

Cited by 89 publications

(74 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The mixing width is the largest scale of mixing in the flow, and it is dominated by the vorticity deposited at the initial interface [12][13][14][15]. Mixing zone width measurements for Ma ≤ 2 show that growth rates are independent of shock and reshock strength when the widths are plotted as a function of distance travelled [16,17].…”

Section: Mach Number Effectsmentioning

confidence: 99%

Experiments of the Richtmyer–Meshkov instability

Prestridge

Orlicz

Balasubramanian

et al. 2013

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

The Richtmyer–Meshkov instability is caused by a shock interacting with a density-stratified interface. The mixing of the fluids is driven by vorticity created by the interaction of the density and pressure gradients. Because the flow is shock driven, the ensuing mixing occurs rapidly, making experimental measurements difficult. Over the past 10 years, there have been significant improvements in the experimental techniques used in shock-driven mixing flows. Many of these improvements have been driven by modelling and simulation efforts, and others have been driven by technology. High-resolution measurements of turbulence quantities are needed to advance our understanding of shock-driven flows, and this paper reviews the current state of experimental diagnostics, as well as paths forward in studying shock-driven mixing and turbulence.

show abstract

Section: Mach Number Effectsmentioning

confidence: 99%

Experiments of the Richtmyer–Meshkov instability

Prestridge

Orlicz

Balasubramanian

et al. 2013

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

show abstract

“…We refer readers to the original sources of these more complex models. [13][14][15][16][17] B. Start-up time Lombardini 12 has developed a modified impulsive model that takes into account the affect of a reflected and transmitted shock on the instability start-up phase.…”

Section: E Boundary Conditionsmentioning

confidence: 99%

“…17,[43][44][45][46][47][48][49] Among these are incompressible potential flow models focused on predicting the behavior of the flows large-scale coherent structure based on an incompressible treatment of the flow localized to the bubble or spike tip. 17,43,[45][46][47] Fourier series expansion for the velocity potential is utilized in such models yielding a set of coupled ordinary differential equations. Solution to the system generally predicts an asymptotic bubble velocity inversely proportional to time 43…”

Section: -mentioning

confidence: 99%

“…A great deal of research has been performed on Richtmyer-Meshkov instability since its introduction. [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] A common component of most previously performed experimental and computational work has been the use of gases at conditions close to room temperature and pressure. In light of this, the current investigation is focused on exploring the role of the equation of state in RichtmyerMeshkov instability specifically in relation to commonly studied perfect gas cases.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A study of planar Richtmyer-Meshkov instability in fluids with Mie-Grüneisen equations of state

Ward¹,

Pullin

2011

Physics of Fluids

View full text Add to dashboard Cite

We present a numerical comparison study of planar Richtmyer-Meshkov instability with the intention of exposing the role of the equation of state. Results for Richtmyer-Meshkov instability in fluids with Mie-Grüneisen equations of state derived from a linear shock-particle speed Hugoniot relationship (Jeanloz, J. Geophys. Res. 94, 5873, 1989; McQueen et al., High Velocity Impact Phenomena (1970) (2010)). Results for single and triple mode planar Richtmyer-Meshkov instability when a reflected shock wave occurs are first examined for mid-ocean ridge basalt (MORB) and molybdenum modeled by Mie-Grüneisen equations of state. The single mode case is examined for incident shock Mach numbers of 1.5 and 2.5. The planar triple mode case is studied using a single incident Mach number of 2.5 with initial corrugation wavenumbers related byComparison is then drawn to Richtmyer-Meshkov instability in perfect gases with matched nondimensional pressure jump across the incident shock, post-shock Atwood ratio, post-shock amplitude-to-wavelength ratio, and time nondimensionalized by Richtmyer's linear growth time constant prediction. Differences in start-up time and growth rate oscillations are observed across equations of state. Growth rate oscillation frequency is seen to correlate directly to the oscillation frequency for the transmitted and reflected shocks. For the single mode cases, further comparison is given for vorticity distribution and corrugation centerline shortly after shock interaction. Additionally, we examine single mode Richtmyer-Meshkov instability when a reflected expansion wave is present for incident Mach numbers of 1.5 and 2.5. Comparison to perfect gas solutions in such cases yields a higher degree of similarity in start-up time and growth rate oscillations. The formation of incipient weak waves in the heavy fluid driven by waves emanating from the perturbed transmitted shock is observed when an expansion wave is reflected.

show abstract

“…When the perturbation continues its growth, and the ratio a/λ reaches the value of ∼ 0.1, harmonics of high-order develop [27,28], and the linear solution presented in Eq. (1) is no longer valid.…”

Section: Introductionmentioning

confidence: 99%

Concept Development for Astrophysically Relevant Turbulence on NIF

Drake¹

2012

View full text Add to dashboard Cite

(a) Abstract: We carried out the research proposed in the proposal and developed a specific concept for the generation of fully developed Rayleigh-Taylor turbulence on NIF. Under this contract we carried out the design study that we proposed. We demonstrated that NIF is capable of producing self-similar turbulence resulting from the Rayleigh-Taylor instability. Our detailed study shows that NIF can in fact produce a more-developed turbulent state than we estimated in the proposal. Thus, NIF can go far beyond any previous experiment in the generation of a hydrodynamic state that can be described as fully developed turbulence.To accomplish our study, we first assessed what sort of experimental system NIF was capable of driving, for modest values of the laser parameters. We developed a desgin for a specific target that could produce Rayliegh-Taylor turbulentce. We then performed hydrodynamic simulations of of this system. We analyzed the results of these simulations to determine the likely evolution of the turbulence in a NIF experiment.The results of our work are discussed in the following, which is a draft paper for publication. We are now undertaking multidimensional simulations, which will also be included in the paper before it is submitted. 1A preliminary design of a two-dimensional Rayleigh-Taylor experiment on NIF AbstractAn preliminary design of an experiment meant to investigate the evolution of multimode Rayleigh-Taylor instability (RT) is presented. This experiment is intended to provide a direct measurement of the two-dimensional bubble front evolution in the hydrodynamic regime. RT growth for the proposed design has been analyzed using one-dimensional direct numerical simulations in HYADES, and a self-similar behavior model. The proposed design assures a significant bubble merging process (∼ 3-4 bubble merger generations), bringing the bubble front to the self-similar stage. The design takes advantage of the National Ignition Facility (NIF) capabilities to provide a large enough laser spot area (∼0.5-1 cm 2 ), along with a low enough drive, so preheat effects remain reasonably small.

show abstract

An analytical nonlinear theory of Richtmyer-Meshkov instability

Cited by 89 publications

References 11 publications

Experiments of the Richtmyer–Meshkov instability

Experiments of the Richtmyer–Meshkov instability

A study of planar Richtmyer-Meshkov instability in fluids with Mie-Grüneisen equations of state

Concept Development for Astrophysically Relevant Turbulence on NIF

Contact Info

Product

Resources

About