Nonlinear growth of the shock-accelerated instability of a thin fluid layer

Jacobs, J. W.; Jenkins, D. G.; Klein, David; Benjamin, R. F.

doi:10.1017/s002211209500187x

Cited by 77 publications

(108 citation statements)

References 19 publications

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“…As in the case of experiments, the quantitative data obtained from these simulations were mainly limited to the consideration of perturbation amplitude growth. Numerical studies of the reshocked single-mode impulsive Richtmyer-Meshkov instability experiment of Jacobs, Jones, and Niederhaus 20,21 were performed by Kotelnikov and Zabusky 22 and Kotelnikov, Ray, and Zabusky 23 using the vortex-in-cell method and the contour advection semi-Lagrangian method ͑n.b., the Jacobs et al 24 and Rightley et al 25 Mach 1.2 experiment with reshock was also simulated using a Godunov method 23 ͒. Kremeyer et al 26 used a fifth-order WENO method to simulate the Richtmyer-Meshkov instability in a shock tube containing gases with different initial transverse density profiles to investigate shock splitting and, in particular, the role of shock bowing and vorticity dynamics.…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

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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“…Most of the experiments [17][18][19][20][21] reported in this area have concentrated on the instability of initially single-scale ͑sinusoidal͒ or multimode perturbations in straight or conical geometries. The more complex configuration of a double interface, i.e., a gas curtain interacting with a shock wave, has been studied by Jacobs et al, 22 Rightley et al, 23,24 and Prestridge et al 25,26 A comprehensive review of the RM instability is presented in the review articles by Brouillette, 27 Zabusky, 28 and Vorobieff and Kumar. 29 A simple test problem to understand some aspects of the RM instability is the interaction of a shock wave with cylindrical interfaces ͑resulting from gaseous columns͒ between two gases having significantly different densities.…”

Section: Introductionmentioning

confidence: 99%

Stretching of material lines in shock-accelerated gaseous flows

et al. 2005

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A Mach 1.2 planar shock wave impulsively accelerates one of five different configurations of heavy-gas ͑SF 6 ͒ cylinders surrounded by lighter gas ͑air͒, producing one or more pairs of interacting vortex columns. The interaction of the columns is investigated with planar laser-induced fluorescence in the plane normal to the axes of the cylinders. For the first time, we experimentally measure the early time stretching rate ͑in the first 220 s after shock interaction before the development of secondary instabilities͒ of material lines in shock-accelerated gaseous flows resulting from the Richtmyer-Meshkov instability at Reynolds number ϳ25 000 and Schmidt number ϳ1. The early time specific stretching rate exponent associated with the stretching of material lines is measured in these five configurations and compared with the numerical computations of Yang et al. ͓AIAA J. 31, 854 ͑1993͔͒ in some similar configurations and time range. The stretching rate is found to depend on the configuration and orientation of the gaseous cylinders, as these affect the refraction of the shock and thus vorticity deposition. Integral scale measurements fail to discriminate between the various configurations over the same time range, however, suggesting that integral measures are insufficient to characterize early time mixing in these flows.

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“…Works in the second group, gas-curtain studies, deal with two nearby density interfaces resulting in a curtain of heavy gas (usually sulfur hexafluoride mixed with gaseous or aerosol tracer) embedded in a lighter gas (air). Investigations of the flow in a shock-accelerated gas curtain have been carried out by Jacobs et al [6,7], Budzinski et al [8], Rightley et al [9,10] and Vorobieff et al [11].…”

Section: Introductionmentioning

confidence: 99%

Shock-driven gas curtain: fractal dimension evolution in transition to turbulence

Vorobieff

Rightley

Benjamin

1999

Physica D: Nonlinear Phenomena

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We present estimates of the Hausdorff fractal dimension of a planar section of the interfaces on the sides of a thin curtain of heavy gas (SF 6 ) embedded in air and accelerated with a planar shock wave at Mach 1.2. As the Richtmyer-Meshkov instability develops, eventually leading to a transition to turbulence in the curtain, the fractal dimension of the interfaces increases from an initial value not exceeding 1.10 to a maximum value 1.36 ± 0.07. This value is close to that experimentally measured for fully developed turbulence. The growth of the fractal dimension is closely related to mixing in the flow. It represents an important and previously unmeasured property in the transition to turbulence due to Richtmyer-Meshkov instability.

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Nonlinear growth of the shock-accelerated instability of a thin fluid layer

Cited by 77 publications

References 19 publications

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

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

Stretching of material lines in shock-accelerated gaseous flows

Shock-driven gas curtain: fractal dimension evolution in transition to turbulence

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