The late-time development of the Richtmyer–Meshkov instability

Prasad, J. K.; Rasheed, Adam; Kumar, Sanjay; Sturtevant, B.

doi:10.1063/1.870456

Cited by 45 publications

(41 citation statements)

References 19 publications

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“…Our numerical simulations ͑Zabusky et al 8 ͒ to early-intermediate times obtained p ϭ0.683 which agreed very well with Prasad et al33 experimental data fitting range, 0.67р pр0.74. These exponents are obviously smaller than the pϭ1 law of Sadot et al13 JK01 juxtaposed their amplitude measurements with two nonlinear theories, Zhang and Sohn 9 and Sadot et al13 JK01 found better agreement with the smaller exponent pϭ1 of…”

supporting

confidence: 91%

“…I, the scaling exponent p is still controversial. Two recent experiments for a single-mode air-SF 6 interface by Prasad et al 33 the latter than pϭ2 for A*ϭ0.635 given by Zhang and Sohn. 9 However, our data which are in excellent agreement with experimental data, as presented in Fig.…”

Section: A Late-intermediate Time ȧ and Vavdmentioning

confidence: 94%

“…Secondary positive and negative vorticity generation is clearly seen at t/t M ϭ1.96 and t/t M ϭ4. 33. The oscillations of the later time curves in Fig.…”

Section: B Time Varying Spatially Periodic Single Point Vortex Modelmentioning

confidence: 95%

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Vortex-accelerated secondary baroclinic vorticity deposition and late-intermediate time dynamics of a two-dimensional Richtmyer–Meshkov interface

2003

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We study the vortex-accelerated secondary baroclinic vorticity deposition ͑VAVD͒ at late-intermediate times, and dynamics of sinusoidal single-mode Richtmyer-Meshkov interfaces in two dimensions. Euler simulations using a piecewise parabolic method are conducted for three post-shock Atwood numbers (A*), 0.2, 0.635, and 0.9, with Mach number ͑M͒ of 1.3. We initialize the sinusoidal interface with a slightly ''diffuse'' or small-but-finite thickness interfacial transition layer to facilitate comparison with experiment and avoid ill-posed phenomena associated with evolutions of an inviscid vortex sheet. The thickness of the interface is chosen so that there are no secondary structures along the interface prior to the multivalue time t M , which is defined as the time when the extracted medial axis of an interfacial layer first becomes multivalued. For an interval of 11t M beyond t M , the simulations reveal nearly monotonic strong growth of both positive and negative baroclinic circulation in a vortex bilayer pattern inside the complex roll-up region. The circulations grow and secondary baroclinic circulation dominates at intermediate times, especially for higher A*. This vorticity deposition is due to misalignment of density gradient across the interface and vortex-centripetal acceleration ͑secondary baroclinic͒, and enhanced by the intensification of interfacial density gradient arising from the vortex-induced strain. Our simulation results for A*ϭ0.635 agree with the recent air-sulfur hexafluoride (SF 6 ) experiment of Jacobs and Krivets ͓Proceedings of the 23rd International Symposium on Shock Waves, Fort Worth, Texas, ͑2001͔͒, including several large-scale features of the evolving mushroom structure: The usual interface spike-bubble amplitude growth rate ȧ and the dimensions of the spike roll-up cavity. VAVD plays an important role in the intermediate time dynamics of the interfaces. Our amplitude growth rate ȧ disagrees with the O(t Ϫ1 ) result of Sadot et al. ͓Phys. Rev. Lett. 80, 1654 ͑1998͔͒.Instead, it approaches a constant which increases with A*(р0.9). An adjusting periodic single point vortex model which uses the calculated net circulation magnitude and its location, gives excellent results for the amplitude growth rates to late-intermediate times at low Atwood numbers (A* ϭ0.2,0.635). The evolution of enstrophy, vorticity skewness, and flatness are quantified for the entire run duration, and one-dimensional averaged kinetic-energy spectra are presented at several times.

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confidence: 91%

Section: A Late-intermediate Time ȧ and Vavdmentioning

confidence: 94%

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Vortex-accelerated secondary baroclinic vorticity deposition and late-intermediate time dynamics of a two-dimensional Richtmyer–Meshkov interface

2003

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“…RM instability also finds applications in natural phenomena like supernova collapse, 7 pressure wave interaction with flame fronts, 8 and supersonic and hypersonic combustion. 9,10 Most of the experiments 11,12 so far reported in this area have concentrated on the instability of initially single scale perturbations or multimode perturbations in straight test sections with no area convergence. However, the spherically convergent geometry in the important case of ICF is likely to affect the process significantly.…”

Section: Introductionmentioning

confidence: 99%

Growth of shocked gaseous interfaces in a conical geometry

2003

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The results of experiments on Richtmyer-Meshkov instability growth of multimode initial perturbations on an air-sulfur hexafluoride (SF 6 ) interface in a conical geometry are presented. The experiments are done in a relatively larger shock tube. A nominally planar interface is formed by sandwiching a polymeric membrane between wire-mesh frames. A single incident shock wave ruptures the membrane resulting in multimode perturbations. The instability develops from the action of baroclinically deposited vorticity at the interface. The visual thickness ␦ of the interface is measured from schlieren photographs obtained in each run. Data are presented for ␦ at times when the interface has become turbulent. The data are compared with the experiments of Vetter ͓Shock Waves 4, 247 ͑1995͔͒ which were done in a straight test section geometry, to illustrate the effects of area convergence. It is found from schlieren images that the interface thickness grows about 40% to 50% more rapidly than in Vetter's experiments. Laser induced scattering is used to capture the air-helium interface at late times. Image processing of pictures is also used to determine the interface thickness in cases where it was not clear from the pictures and to obtain the dominant eddy-blob sizes in the mixing zone. Some computational studies are also presented to show the global geometry changes of the interface when it implodes into a conical geometry in both lightheavy and heavy-light cases.

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“…At times beyond the nonlinear stage of instability development, a turbulent mixing zone develops and is well described by power law behavior [14,15]. Most of the experiments [16,17] reported in this area have concentrated on the instability of initially singlescale (sinusoidal) or multimode perturbations in straight or conical geometries. The more complex configurations of a double interface, i.e.…”

mentioning

confidence: 98%

Large-eddy simulations of the Richtmyer-Meshkov instability of rectangular interfaces accelerated by shock waves

Wang

Bai

et al. 2010

Sci. China Phys. Mech. Astron.

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A parallel algorithm and code MVFT (multi-viscous-fluid and turbulence) of large-eddy simulation (LES) is developed from our MVPPM (multi-viscous-fluid piecewise parabolic method), and performed to solve the multi compressible Navier-Stokes (N-S) equations. The effect of the unresolved subgrid-scale (SGS) motions on the large scales is represented by different SGS stress models in LES. A Richtmyer-Meshkov instability experiment of the evolution of a rectangular block of SF 6 , which occupies half of the height of the shock tube test section, following the interaction with a planar shock wave, is numerically and exhaustively simulated by this code. The comparison between experimental and simulated images of the evolving SF 6 block shows that they are consistent. The numerical simulations reproduce the complex developing process of SF 6 block, which grows overturningly. The geometric quantities that characterize the extents of SF 6 block are also compared in detail between numerical simulations and experiment with good agreements between them, a quantitative demonstration of the developing law of SF 6 block. There is an evident discrepancy between the three numerical simulations for the maximum position of the right edge of block at the late stage, because the right interface grows complicated and the dissipation is different for different SGS models. The SGS turbulent dissipation, molecular viscosity dissipation and SGS turbulent kinetic energy have been studied and analyzed. They have a similar distribution to the large eddy structures. The SGS turbulent dissipation is much greater than the molecular viscosity dissipation; the SGS turbulent dissipation of Vreman model is smaller than the Smagorinsky model. In general, the simulated results of Vreman SGS model are better compared with the dynamic viscosity and Smagorinsky SGS model. The vorticity and circulation deposition on the block interface have also been investigated.large-eddy simulation, Navier-Stokes equations, subgrid-scale, Richtmyer-Meshkov instability, turbulent dissipation, turbulent kinetic energy, circulation deposition PACS: 47.10.ad, 47.20.Ma, 47.27.ep The instability of an accelerated interface separating two fluids with different properties is a fundamental hydrodynamic problem. The Richtmyer-Meshkov instability (RMI) is driven by impulsive acceleration such as a shock wave [1]. This instability is typically investigated in shock tube experiments. Any perturbations initially presented on the interface will, in most cases, be amplified following the passage of the shock. The physical mechanism for the amplification of perturbations on the interface is the baroclinic vorticity production as a result of the misalignment of the pressure gradient (∇p) of the shock and the local density gradient (∇ρ) at the interface. Nonlinearities come into play when the interface between two fluids becomes more distorted, and secondary baroclinic or shear-driven instabilities [2], such as the Kelvin-Helmholtz instability (KHI), also start developing. This combi...

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The late-time development of the Richtmyer–Meshkov instability

Cited by 45 publications

References 19 publications

Vortex-accelerated secondary baroclinic vorticity deposition and late-intermediate time dynamics of a two-dimensional Richtmyer–Meshkov interface

Vortex-accelerated secondary baroclinic vorticity deposition and late-intermediate time dynamics of a two-dimensional Richtmyer–Meshkov interface

Growth of shocked gaseous interfaces in a conical geometry

Large-eddy simulations of the Richtmyer-Meshkov instability of rectangular interfaces accelerated by shock waves

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