Vortex morphologies on reaccelerated interfaces: Visualization, quantification and modeling of one- and two-mode compressible and incompressible environments

Kotelnikov, Alexei D.; Ray, Jaideep; Zabusky, Norman J.

doi:10.1063/1.1321264

Cited by 31 publications

(20 citation statements)

References 29 publications

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“…This mechanism reminds us of the mixing enhancement resulting from reshock of an interface, where opposite sign vorticity are generated by the oppositely directed acceleration. 30 A similar sketch arises when considering slow-fast Richtmyer-Meshkov environments.…”

Section: Vorticity and Circulation: Vavd And Density Gradient Intementioning

confidence: 83%

“…9, we see that the two lowest A* curves are nested, whereas the largest A* curve oscillates strongly and settles down to a near-steady value which is lower than that for A*ϭ0.635. These large A* phenomena are most likely due to waves in Soon after the shock passage, the fluid motion becomes nearly incompressible as demonstrated by Kotelnikov et al 30 and Meiron and Meloon. 31 The evolution of the vorticity in Eq.…”

Section: Vorticity and Circulation: Vavd And Density Gradient Intementioning

confidence: 87%

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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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Section: Vorticity and Circulation: Vavd And Density Gradient Intementioning

confidence: 83%

Section: Vorticity and Circulation: Vavd And Density Gradient Intementioning

confidence: 87%

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

2003

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“…This equation and the vortex method (Krasny 1987;Kotelnikov et al 2000;Sohn 2004;Matsuoka & Nishihara 2006a) enable us to calculate the roll-up of the interface. The velocity of the interface (x, y) = (X (b, t), Y (b, t)) is given as (Baker et al 1982;Matsuoka & Nishihara 2006a)…”

Section: (C) Arbitrary Amplitude Theory In Planar Geometrymentioning

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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“…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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Vortex morphologies on reaccelerated interfaces: Visualization, quantification and modeling of one- and two-mode compressible and incompressible environments

Cited by 31 publications

References 29 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

Richtmyer–Meshkov instability: theory of linear and nonlinear evolution

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

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