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On bubble and spike oscillations in a dusty gas Rayleigh-Taylor instability

Published online by Cambridge University Press:  02 October 2012

Kaushik Balakrishnan
Kaushik Balakrishnan*
Affiliation:
Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California
*
Address correspondence and reprint requests to: K. Balakrishnan, Computational Research Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, E-mail: kaushikb@lbl.gov
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Abstract

The Multiphase Buoyancy-Drag model recently formulated in Balakrishnan & Menon, Laser and Particle Beams, 2011 is applied to investigate the (1) rise of dusty gas Rayleigh-Taylor bubbles into a pure gas and (2) fall of pure gas Rayleigh-Taylor spikes into a region of particles. It is demonstrated that for these two scenarios, the bubble or spike amplitude oscillates about the dusty gas/pure gas interface. The ratio of the bubble or spike amplitudes on the pure gas side to the dusty gas side, asymptotes to a constant that depends only on the initial Atwood number, A, the multiphase Atwood number, Am, and the initial wavelength of the perturbation, λo. For the same Am, the ratio decreases with A for oscillating bubbles, and vice versa for oscillating spikes.

Type
Research Article
Information
Laser and Particle Beams , Volume 30 , Issue 4 , December 2012 , pp. 633 - 638
Copyright
Copyright © Cambridge University Press 2012

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References

REFERENCES

Alon, U., Hecht, J., Mukamel, D. & Shvarts, D. (1994). Scale invariant mixing rates of hydrodynamically unstable interfaces . Phys. Rev. Lett. 72, 2867–2870.CrossRefGoogle ScholarPubMed
Alon, U., Hecht, J., Ofer, D. & Shvarts, D. (1995). Power laws and similarity of Rayleigh-Taylor and Richtmyer-Meshkov mixing fronts at all density ratios. Phys. Rev. Lett. 74, 534–537.CrossRefGoogle ScholarPubMed
Balakrishnan, K. & Menon, S. (2010). On turbulent chemical explosions into dilute aluminum particle clouds. Combus. Theor. Mod. 14, 583–617.CrossRefGoogle Scholar
Balakrishnan, K. (2010). On the high fidelity simulations of chemical explosions and their interaction with solid particle clouds. PhD Thesis, Georgia Institute of Technology.Google Scholar
Balakrishnan, K. & Menon, S. (2011). A multiphase buoyancy-drag model for the study of Rayleigh-Taylor and Richtmyer-Meshkov instabilities in dusty gases. Laser Part. Beams 29, 201–217.CrossRefGoogle Scholar
Dalziel, S.B. (1993). Rayleigh-Taylor instability: Experiments with image analysis. Dyn. Atmosph. Oceans 20, 127–153.CrossRefGoogle Scholar
Dimonte, G. & Schneider, M. (2000). Density ratio dependence of Rayleigh-Taylor mixing for sustained and impulsive acceleration histories. Phys. Fluids 12, 304–321.CrossRefGoogle Scholar
Frost, D., Gregoire, Y., Goroshin, S., Ripley, R. & Zhang, F. (2011). Particle jet formation during explosive dispersal of solid particles. 64th annual meeting of the APS division of fluid dynamics, November 20–22, Baltimore, Maryland.Google Scholar
Layzer, D. (1955). On the instability of superposed fluids in a gravitational field. Astrophys. J. 122, 1–12.CrossRefGoogle Scholar
Oron, D., Arazi, L., Kartoon, D., Rikanati, A., Alon, U. & Shvarts, D. (2001). Dimensionality dependence of the Rayleigh-Taylor and Richtmyer-Meshkov instability late-time scaling laws. Phys. Plasmas 8, 2883–2889.CrossRefGoogle Scholar
Ramshaw, J.D., (1998). Simple model for linear and nonlinear mixing at unstable fluid interfaces with variable acceleration. Phys. Rev. E 58, 5834–5840.CrossRefGoogle Scholar
Lord Rayleigh, . (1883). Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proceedings of the London Mathematical Society 14, 170–177.Google Scholar
Richtmyer, R.D. (1960). Taylor instability in a shock acceleration of compressible fluids. Commun on Pure and App Math 13, 297–319.CrossRefGoogle Scholar
Sharp, D.H. (1984). An overview of Rayleigh-Taylor instability. Phys. D 12, 3–18.CrossRefGoogle Scholar
Srebro, Y., Elbaz, Y., Sadot, O., Arazi, L. & Shvarts, D. (2003). A general buoyancy-drag model for the evolution Rayleigh-Taylor and Richtmyer-Meshkov instabilities. Laser Parti. Beams 21, 347–353.CrossRefGoogle Scholar
Taylor, G.I. (1950). The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. Proceedings of the Royal Society of London. Series A, Math and Phys Sci 201, 192–196.Google Scholar
Ukai, S., Balakrishnan, K. & Menon, S. (2010). On Richtmyer-Meshkov instability in dilute gas-particle mixtures. Phys. Fluids 22, 104103.CrossRefGoogle Scholar
Youngs, D.L. (1984). Numerical simulation of turbulent mixing by Rayleigh-Taylor instability. Phys. D 12, 32–44.CrossRefGoogle Scholar
Youngs, D.L. (1989). Modelling turbulent mixing by Rayleigh-Taylor instability . Phys. D 37, 270–287.CrossRefGoogle Scholar
Youngs, D.L. (1991). Three-dimensional numerical simulation of turbulent mixing by Rayleigh-Taylor instability. Phys. Fluids A 3, 1312–1320.CrossRefGoogle Scholar
Youngs, D.L. (1994). Numerical simulation of mixing by Rayleigh-Taylor and Richtmyer-Meshkov instabilities. Laser Part. Beams 12, 725–750.CrossRefGoogle Scholar