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Wavelength Selection in a Vibrated Granular Layer

Published online by Cambridge University Press:  01 February 2011

Eric Clément
Affiliation:
Laboratoire des Milieux Désordonnés et Hétérogènes – UMR 7603, Université Pierre et Marie Curie- Boîte 86, 4, Place Jussieu, F-75252 Paris, France
Laurent Labous
Affiliation:
Laboratoire des Milieux Désordonnés et Hétérogènes – UMR 7603, Université Pierre et Marie Curie- Boîte 86, 4, Place Jussieu, F-75252 Paris, France
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Abstract

We present a numerical study of a surface instability occurring in a bidimensional vibrated granular layer. The driving mechanism for the formation of stationary waves is closely followed. Two regimes of wavelength selection are identified : a dispersive regime and a saturation regime. For the saturation regime, a connection is established between the pattern formation and an intrinsic instability occurring spontaneously in dissipative gases. We also address the importance of the detailed dissipation laws determining the wavelength values.

Type
Research Article
Copyright
Copyright © Materials Research Society 2000

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References

REFERENCES

[1] Melo, F., Ubanhovar, P. and Swinney, H., Phys. Rev. Lett. 72, 172 (1994);Google Scholar
Melo, F., Ubanhovar, P. and Swinney, H., Phys. Rev. Lett. 75, 3838 (1995).Google Scholar
[2] Umbanhowar, P., Ph.D. dissertation The University of Texas in Austin (1996); P. Umbanhowar and H. Swinney, preprint (2000).Google Scholar
[3] Faraday, M., Philos. Trans. R. Soc. 121, 299 (1831).Google Scholar
[4] Clément, E., Vanel, L., Duran, J. and Rajchenbach, J., Phys. Rev. E 53, 2972 (1996).Google Scholar
[5] Luding, S., Clément, E., Rajchenbach, J. and Duran, J., Europhys. Lett, 36, 247 (1996).Google Scholar
[6] Bizon, C., Shatuck, M.D., Swift, J.B., McCormick, W.D. and Swinney, H., Phys. Rev. Lett. 80, 57 (1998)Google Scholar
[7] Bizon, C., Shattuck, M. D., and Swift, J. B., Phys. Rev. E 60, 7210 (1999).Google Scholar
[8] Labous, L., Thèse de Doctorat, Université Paris VI (1998); E. Clément, L. Labous preprint, submitted to Phys. Rev. E (2000).Google Scholar
[9] Walton, O. et al., J. Rheol. 30, 949 (1983).Google Scholar
[10] Bernu, B. and Mazighi, R., J. Phys. A 23, 5745 (1990);Google Scholar
MacNamara, S., Young, W.R., Phys. Fluid A 5, 34 (1993).Google Scholar
[11] Goldhirsch, I. and Zanetti, G., Phys. Rev. Lett. 70, 1619 (1993);Google Scholar
MacNamara, S. and Young, W.R., Phys. Rev. E 50, R28 (1994).Google Scholar