Nonlinear regime of a multimode Richtmyer–Meshkov instability: A simplified perturbation theory

Vandenboomgaerde, M.; Gauthier, Serge; Mügler, Claude

doi:10.1063/1.1447914

Cited by 48 publications

(44 citation statements)

References 26 publications

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“…In addition, numerous nonlinear analyses have attempted to predict the late-time nonlinear growth. [7][8][9] However, to date there exists no nonlinear solution capable of predicting the behavior from the early linear stages into the far nonlinear regime. As a result, many researchers have resorted to developing heuristic models that capture some of the physics of the late-time asymptotic flow and which have had some success at predicting the late-time behavior.…”

Section: Introductionmentioning

confidence: 99%

Experiments on the three-dimensional incompressible Richtmyer-Meshkov instability

Chapman

Jacobs

2006

Physics of Fluids

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The three-dimensional ͑3D͒ Richtmyer-Meshkov instability of incompressible, miscible liquids with a 3D single-mode initial perturbation is investigated. This study uses the apparatus of the earlier experiments of Niederhaus and Jacobs ͓J. Fluid Mech. 485, 243 ͑2003͔͒ in which the instability is generated by impulsively accelerating a tank containing the two liquids. However, the present investigation uses a tank with square cross section allowing the generation of a square-mode 3D initial perturbation by lateral oscillation along the tank's diagonal. Amplitude measurements of the 3D instability are found to be effectively collapsed by the dimensionless scaling used in the two-dimensional ͑2D͒ study and to be in good agreement with linear stability theory up until a dimensionless time k 0 t Ϸ 1, later than is found for the 2D flow. Late-time 3D amplitude measurements show faster growth than 2D as is predicted by popular bubble models. However, late-time growth rate measurements are found to deviate from model predictions at the latest times showing a constant growth rate instead of the 1 / t dependence given by the models. The constant late-time growth rate is the result of the observed vorticity distribution which takes the form of an array of upward and downward traveling vortex rings. This fundamental difference between existing models and observation indicates that bubble models may not be suitable for predicting the behavior of the low Atwood number instability which is vortex dominated.

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Section: Introductionmentioning

confidence: 99%

Experiments on the three-dimensional incompressible Richtmyer-Meshkov instability

Chapman

Jacobs

2006

Physics of Fluids

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“…The experimental and simulation data are compared to the perturbation series solutions of Zhang and Sohn 48 ͓Eq. ͑14͔͒, Vandenboomgaerde et al 49 ͓Eq. ͑18͔͒ of degree 9 and 11, and Matsuoka et al 50 ͓Eq.…”

Section: Comparison To the Predictions Of Perturbation Modelsmentioning

confidence: 99%

“…Fraley, 45 and Vandenboomgaerde et al; 47 ͑ii͒ the weakly nonlinear perturbation models of Zhang and Sohn, 48 Vandenboomgaerde et al, 49 and Matsuoka et al; 50 and ͑iii͒ the nonlinear empirical model of Sadot et al 51 The bubble and spike velocities were also compared to the predictions of the potential models of Goncharov 53 and Sohn. 54,55 In addition, the bubble amplitude was compared to the prediction of the Mikaelian 58 model.…”

Section: -17mentioning

confidence: 99%

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High-resolution simulations and modeling of reshocked single-mode Richtmyer-Meshkov instability: Comparison to experimental data and to amplitude growth model predictions

2007

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The reshocked single-mode Richtmyer-Meshkov instability is simulated in two spatial dimensions using the fifth-and ninth-order weighted essentially nonoscillatory shock-capturing method with uniform spatial resolution of 256 points per initial perturbation wavelength. The initial conditions and computational domain are modeled after the single-mode, Mach 1.21 air͑acetone͒/SF 6 shock tube experiment of Collins and Jacobs ͓J. Fluid Mech. 464, 113 ͑2002͔͒. The simulation densities are shown to be in very good agreement with the corrected experimental planar laser-induced fluorescence images at selected times before reshock of the evolving interface. Analytical, semianalytical, and phenomenological linear and nonlinear, impulsive, perturbation, and potential flow models for single-mode Richtmyer-Meshkov unstable perturbation growth are summarized. The simulation amplitudes are shown to be in very good agreement with the experimental data and with the predictions of linear amplitude growth models for small times, and with those of nonlinear amplitude growth models at later times up to the time at which the driver-based expansion in the experiment ͑but not present in the simulations or models͒ expands the layer before reshock. The qualitative and quantitative differences between the fifth-and ninth-order simulation results are discussed. Using a local and global quantitative metric, the prediction of the Zhang and Sohn ͓Phys. Fluids 9, 1106 ͑1997͔͒ nonlinear Padé model is shown to be in best overall agreement with the simulation amplitudes before reshock. The sensitivity of the amplitude growth model predictions to the initial growth rate from linear instability theory, the post-shock Atwood number and amplitude, and the velocity jump due to the passage of the shock through the interface is also investigated numerically.

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“…In addition, numerous nonlinear analyses attempted to predict the late time nonlinear growth. [7][8][9] However, to date there exists no nonlinear solution capable of predicting the behavior from the early linear stages far into the nonlinear regime. As a result, a number of heuristic models have been developed that capture some of the physics of the late time asymptotic flow and, as a result, have had some success at predicting the late time behavior.…”

Section: Introductionmentioning

confidence: 99%

Shock tube experiments and numerical simulation of the single-mode, three-dimensional Richtmyer–Meshkov instability

et al. 2009

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A vertical shock tube is used to perform experiments in which an interface is formed using opposed flows of air and SF 6 . A three-dimensional single-mode perturbation is created by the periodic vertical motion of the gases within the shock tube. Richtmyer-Meshkov instability is produced by an impulsive acceleration by a weak shock wave ͑M s = 1.2͒. Planar laser induced fluorescence produces still images, and planar Mie scattering produces movies of the experiment. A three-dimensional numerical simulation of this experiment utilizing the Eulerian adaptive mesh refinement code, RAPTOR, was also conducted. Good agreement is obtained between experiments and the simulations. However, existing late time models, which have a 1 / t dependence, disagree with measurements of the late time instability development. In contrast, both the experiments and simulation suggest a t −0.54 late time dependence for the overall growth rate. Comparisons with individual bubble and spike velocities show the bubbles appear to decay approximately at 1 / t and the spikes to decay at a much slower rate of t −0.38 .

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Nonlinear regime of a multimode Richtmyer–Meshkov instability: A simplified perturbation theory

Cited by 48 publications

References 26 publications

Experiments on the three-dimensional incompressible Richtmyer-Meshkov instability

Experiments on the three-dimensional incompressible Richtmyer-Meshkov instability

High-resolution simulations and modeling of reshocked single-mode Richtmyer-Meshkov instability: Comparison to experimental data and to amplitude growth model predictions

Shock tube experiments and numerical simulation of the single-mode, three-dimensional Richtmyer–Meshkov instability

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