Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-26T20:43:16.118Z Has data issue: false hasContentIssue false
  • English
  • Français

Thin plate effects in the Rayleigh–Taylor instability of elastic solids

Published online by Cambridge University Press:  08 June 2006

A. R. PIRIZ ,
J. J. LÓPEZ CELA ,
M. C. SERNA MORENO ,
N. A. TAHIR  and
D. H. H. HOFFMANN
A. R. PIRIZ
Affiliation:
E.T.S.I. Industriales, Universidad de Castilla-La Mancha, Ciudad Real, Spain
J. J. LÓPEZ CELA
Affiliation:
E.T.S.I. Industriales, Universidad de Castilla-La Mancha, Ciudad Real, Spain
M. C. SERNA MORENO
Affiliation:
E.T.S.I. Industriales, Universidad de Castilla-La Mancha, Ciudad Real, Spain
N. A. TAHIR
Affiliation:
Gesellschaft für Schwerionenforschung, Darmstadt, Germany
D. H. H. HOFFMANN
Affiliation:
Institut für Kernphysik, Technishe Universität Darmstadt, Darmstadt, Germany and Gesellschaft für Schwerionenforschung, Darmstadt, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

We perform the analysis of the Rayleigh–Taylor instability of thin perfectly elastic solid plates using the analytical approach recently developed by Piriz and coworkers. The model describes the evolution of the perturbation amplitude from the initial conditions and at relatively long times it yields the asymptotic growth rate. It applies to solid/inviscid fluid interfaces. For the particular case of solid/vacuum interface, the model has been compared with the exact results by Plohr and Sharp and an excellent agreement has been found. In general, thinner plates are found to be more unstable and, in the presence of a fluid below the elastic plate, the growth rate is reduced.

Keywords

Elastic solidsPerturbation amplitudeRayleigh-Taylor instabilitySemi-infinite apporximationSymmetry constraints
Type
Research Article
Information
Laser and Particle Beams , Volume 24 , Issue 2 , June 2006 , pp. 275 - 282
Copyright
© 2006 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Arnold, R.C., Colton, E., Fenster, S., Foss, M., Magelssen, G. & Moretti, A. (1982). Utilization of high-energy, small emittance accelerators for ICF target experiments. Nucl. Instrum. Methods Phys. Res. 199, 557.CrossRefGoogle Scholar
Bakhrakh, S.M., Drennov, O.B., Kovalev, N.P., Lebedev, A.I., Meshkov, E.E., Mikhailov, A.L., Nevmerzhitsky, N.V., Nizovtsev, P.N., Rayevsky, V.A., Simonov, G.P., Solovyev, V.P. & Zhidov, I.G. (1997). Hydrodynamic instability in strong media. Lawrence Livermore National Laboratory Report No. UCRL-CR-126710.CrossRef
Breil, J., Hallo, L., Maire, P.H. & Olazabal-Loume, M. (2005). Hydrodynamic instabilities in axisymmetric geometry self-similiar models and numerical simulations. Laser Part. Beams. 23, 47.CrossRefGoogle Scholar
Henning, W.F. (2004). The future GSI facility. Nucl. Instrum. Methods Phys. Res. B. 214, 155.CrossRefGoogle Scholar
Hoffmann, D.H.H., Blazevic, A., Ni, P., Rosmej, O., Roth, M., Tahir, N.A., Tauschwitz, A., Udrea, S., Varentsov, D. Weyrich, K., &Maron, Y. (2005). Present and future perspectives for high energy density physics with intense heavy ion and laser beams. Laser Part. Beams. 23, 47.CrossRefGoogle Scholar
Landau, L.D. & Lifshits, E.M. (1986). Theory of Elasticity. 3rd. Edition. Oxford: Pergamon.
Miles, J.W. (1966). Taylor instability of a plate plate. General Dynamics Report No. GAMD-7335, AD643161.
Piriz, A.R., Lopez Cela, J.J., Cortazar, O.D., Tahir, N.A. & Hoffmann, D.H.H. (2005). Rayleigh-Taylor instability in elastic solids. Phys. Rev. E. 72, 056313.CrossRefGoogle Scholar
Piriz, A.R., Portugues, R.F., Tahir, N.A. & Hoffmann, D.H.H. (2002). Implosion of multilayered cylindrical targets driven by intense heavy ion beams. Phys. Rev. E. 66, 056403.CrossRefGoogle Scholar
Piriz, A.R., Portugues, R.F., Tahir, N.A. & Hoffmann, D.H.H. (2002). Analytic model for studying heavy-ion-imploded cylindrical targets. Laser Part. Beams. 20, 427.CrossRefGoogle Scholar
Piriz, A.R., Sanz, J. & Ibanez, L.F. (1997). Rayleigh-Taylor instability of steady ablation fronts: The discontinuity model revisited. Phys. Plasmas. 4, 1117.CrossRefGoogle Scholar
Piriz, A.R., Tahir, N.A., Hoffmann, D.H.H. & Temporal, M. (2003a). Generation of a hollow ion beam: Calculation of the rotation frequency required to accommodate symmetry constraint. Phys. Rev. E. 67, 017501.Google Scholar
Piriz, A.R., Temporal, M., Lopez Cela, J.J., Tahir, N.A. & Hoffmann, D.H.H. (2003b). Symmetry analysis of cylindrical implosions driven by high-frequency rotating ion beams. Plasma Phys. Contr. Fusion. 45, 1733.Google Scholar
Plohr, B.J. & Sharp, D.H. (1998). Instability of accelerated elastic metal plates. ZAMP. 49, 786.CrossRefGoogle Scholar
Steinberg, D.J., Cochran, S.G. & Guinan, M.W. (1980). A constitutive model for metals applicable at high-strain rate. J. Appl. Phys. 51, 1498.CrossRefGoogle Scholar
Robinson, A.C. & Swegle, J.W. (1989). Acceleration instability in elastic-platic solids: Analytical techniques. J. Appl. Phys. 66, 2859.CrossRefGoogle Scholar
Tahir, N.A., Adonin, A., Deutsch, C., Fortov, V.E., Grandjouan, N., Geil, B., Grayaznov, V., Hoffmann, D.H.H., Kulish, M., Lomonosov, I.V., Mintsev, V., Ni, P., Nikolaev, D., Piriz, A.R., Shilkin, N., Spiller, P., Shutov, A., Temporal, M., Ternovoi, V., Udrea, S. & Varentsov, D. (2005). Studies of heavy ion-induced highenergy density states in matter at the GSI Darmstadt SIS-18 and future FAIR facility. Nucl. Instrum. Methods Phys. Res. A. 544, 16.CrossRefGoogle Scholar
Tahir, N.A., Hoffmann, D.H.H., Kozyreva, A., Shutov, A., Maruhn, J.A., Neuner, U., Tauschwitz, A., Spiller, P. & Bock, R. (2001). Designing future heavy-ion-matter interaction experiments for the GSI Darmstadt heavy ion synchrotron. Nucl. Instrum. Methods Phys. Res. A. 464, 211.CrossRefGoogle Scholar
Tahir, N.A., Juranek H., Shutov A., Redmer R., Piriz A.R., Temporal M., Varentsov D., Udrea S., Hoffmann D.H.H., Deutsch C., Lomonosov I. & Fortov V.E. (2003). Influence of the equation of state on the compression and heating of hydrogen. Phys. Rev. B. 67, 184101.CrossRefGoogle Scholar
Tahir, N.A., Udrea, S., Deutsch, C., Fortov, V.E., Grandjouan, G., Gryaznov, V., Hoffmann, D.H.H., Hulsmann, P., Kirk, M., Lomonosov, I.V., Piriz, A.R., Shutov, A., Spiller, P., Temporal, M. & Varentsov, D. (2004). Target heating in high-energy-density matter experiments at the proposed GSI FAIR facility: Non-linear bunch rotation in SIS 100 and optimization of spot size and pulse length. Laser Part. Beams. 22, 485.CrossRefGoogle Scholar
Taylor, G.I. (1950). The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I. Proc. R. Soc. London. A 201, 192.Google Scholar
Temporal, M., Lopez-Cela, J.J., Piriz, A.R., Grandjouan, N., Tahir, N.A. & Hoffmann, D.H.H. (2005). Compression of a cylindrical hydrogen sample driven by an intense co-axial heavy ion beam. Laser Part. Beams. 23, 137.CrossRefGoogle Scholar
Temporal, M., Piriz, A.R., Grandjouan, N., Tahir, N.A. & Hoffmann, D.H.H. (2003). Numerical analysis of a multilayered cylindrical target compression driven by a rotating intense heavy ion beam. Laser Part. Beams. 21, 609.CrossRefGoogle Scholar
Terrones, G. (2005). Fastest growing linear Rayleigh-Taylor modes at solid/fluid and solid/solid interfaces. Phys. Rev. E. 71, 036306.CrossRefGoogle Scholar
White, G.N. (1973). A one-degree-of-freedom model for the taylor instability of an ideally plastic metal plate. Los Alamos National Laboratory Report LA-5225-MS.
Wouchuk, J.G. & Piriz, A.R. (1995). Growth rate reduction of the Rayleigh-Taylor instability by ablative convection. Phys. Plasmas. 2, 493.CrossRefGoogle Scholar