Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-17T13:59:45.807Z Has data issue: false hasContentIssue false
  • English
  • Français

Intuitive calculation of the relativistic Rayleigh-Taylor instability linear growth rate

Published online by Cambridge University Press:  04 May 2011

Antoine Bret
Antoine Bret*
Affiliation:
ETSI Industriales, Universidad de Castilla-La Mancha, Ciudad Real, Spain
*
Address correspondence and reprint requests to: Antoine Bret, Universidad Castilla La Mancha, ETSI Industriales, Avda Camillo Jose Cela, s/n 13 071 Ciudad Real, Spain. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The Rayleigh-Taylor instability is a key process in many fields of Physics ranging from astrophysics to inertial confinement fusion. It is usually analyzed deriving the linearized fluid equations, but the physics behind the instability is not always clear. Recent works on this instability allow for an very intuitive understanding of the phenomenon and for a straightforward calculation of the linear growth rate. In this Letter, it is shown that the same reasoning allows for a direct derivation of the relativistic expression of the linear growth rate for an incompressible fluid.

Keywords

Inertial confinement fusionLinearized fluid equationsRayleigh-Taylor instability
Type
Research Article
Information
Laser and Particle Beams , Volume 29 , Issue 2 , June 2011 , pp. 255 - 257
Copyright
Copyright © Cambridge University Press 2011

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

Allen, A.J., Hughes, P.A. (1984) The Rayleigh-Taylor instability in astrophysical fluids. Royal Astronom. Soc. 208, 609–621.Google Scholar
Chandrasekhar, S. (1961), Hydrodynamics and Hydromagnetic Stability. New York: Dover.Google Scholar
Douglas, M., De Groot, J. & Spielman, R. (2001) The magneto-rayleigh-taylor instability in dynamic z pinches. Laser Part. Beams 15, 527.Google Scholar
Fried, B.D. (1959) Mechanism for Instability of Transverse Plasma Waves. Phys. Fluids 2, 337.CrossRefGoogle Scholar
Hester, J.J., Stone, J.M., Scowen, P.A., Jun, B., Gallagher, J.S. III, Norman, M.L., Ballester, G.E., Burrows, C.J., Casertano, S., Clarke, J.T., Crisp, D., Griffiths, R.E., Hoessel, J.G., Holtzman, J.A., Krist, J., Mould, J.R., Sankrit, R., Stapelfeldt, K.R., Trauger, J.T., Watson, A. & Westphal, J.A. (1996) WFPC2 studies of the Crab Nebula. III. magnetic Rayleigh-Taylor instabilities and the origin of the filaments. Astrophys. J. 456, 225–233.Google Scholar
Kawata, S., Sato, T., Teramoto, T., Bandoh, E., Masubichi, Y. & Takahashi, I. (1993) Radiation effect on pellet implosion and rayleigh-taylor instability in light-ion beam inertial confinement fusion. Laser Part. Beams 11, 757.CrossRefGoogle Scholar
Landau, L. & Lifschitz, E. (1987 a) Course of theoretical physics: Fluid Mechanics. Oxford: Butterworth-Heinemann.Google Scholar
Landau, L. & Lifschitz, E. (1987 b) Course of theoretical physics: The classical theory of fields. Oxford: Butterworth-Heinemann.Google Scholar
Levinsona, A. (2010) Relativistic Rayleigh-Taylor instability of a decelerating shell and its implications for gamma-ray bursts. J. Geophys. & Astrophys. Fluid Dyn. 104, 85–111.CrossRefGoogle Scholar
Lopez Cela, J.J., Piriz, A.R., Serna Moreno, M.C. & Tahir, N.A. (2006) Numerical simulations of rayleigh-taylor instability in elastic solids. Laser Part. Beams 24, 427.Google Scholar
Piriz, A.R., Cortázar, O.D., López Cela, J.J. & Tahir, N.A. (2006) The Rayleigh-Taylor instability. Am. J. Phys. 74 1095–1098.Google Scholar
Piriz, A.R., Lopez Cela, J.J., Serena Moreno, M.C., Tahir, N.A. & Hoffmann, D.H.H. (2006) Thin plate effects in the Rayleigh-Taylor instability of elastic solids. Laser Part. Beams 24, 275.Google Scholar
Piriz, A.R., Sanz, J. & Ibañez, L.F. (1997) Rayleigh-Taylor instability of steady ablation fronts: The discontinuity model revisited. Phys. Plasmas 4, 1117–1126.CrossRefGoogle Scholar
Pomraning, G. (1990) Radiative-transfer in rayleigh-taylor unstable icf pellets. Laser Part. Beams 8, 741.Google Scholar
Rayleigh, L. (1900) Scientific Papers. Vol. II. Cambridge: Cambridge.Google Scholar
Taylor, G. (1950) The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I. Roy. Soc. London Proc. Series A 201, 192–196.Google Scholar
Waxman, E. & Piran, T. (1994) Stability of fireballs and gamma-ray bursts. Astrophys. J. Lett. 433, L85–L88.CrossRefGoogle Scholar