Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-19T08:22:05.611Z Has data issue: false hasContentIssue false
  • English
  • Français

Three-dimensional multimode Rayleigh–Taylor and Richtmyer–Meshkov instabilities at all density ratios

Published online by Cambridge University Press:  03 March 2004

D. KARTOON ,
D. ORON ,
L. ARAZI  and
D. SHVARTS
D. KARTOON
Affiliation:
Department of Physics, Nuclear Research–Center Negev, Beer-Sheva, Israel Department of Physics, Ben Gurion University, Beer-Sheva, Israel
D. ORON
Affiliation:
Faculty of Physics, The Weizmann Institute of Science, Rehovot, Israel
L. ARAZI
Affiliation:
School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv, Israel
D. SHVARTS
Affiliation:
Department of Physics, Nuclear Research–Center Negev, Beer-Sheva, Israel Department of Physics, Ben Gurion University, Beer-Sheva, Israel Department of Mechanical Engineering, Ben Gurion University, Beer-Sheva, Israel
Get access Rights & Permissions [Opens in a new window]

Abstract

The three-dimensional (3D) turbulent mixing zone (TMZ) evolution under Rayleigh–Taylor and Richtmyer–Meshkov conditions was studied using two approaches. First, an extensive numerical study was made, investigating the growth of a random 3D perturbation in a wide range of density ratios. Following that, a new 3D statistical model was developed, similar to the previously developed two-dimensional (2D) statistical model, assuming binary interactions between bubbles that are growing at a 3D asymptotic velocity. Confirmation of the theoretical model was gained by detailed comparison of the bubble size distribution to the numerical simulations, enabled by a new analysis scheme that was applied to the 3D simulations. In addition, the results for the growth rate of the 3D bubble front obtained from the theoretical model show very good agreement with both the experimental and the 3D simulation results. A simple 3D drag–buoyancy model is also presented and compared with the results of the simulations and the experiments with good agreement. Its extension to the spike-front evolution, made by assuming the spikes' motion is governed by the single-mode evolution determined by the dominant bubbles, is in good agreement with the experiments and the 3D simulations. The good agreement between the 3D theoretical models, the 3D numerical simulations, and the experimental results, together with the clear differences between the 2D and the 3D results, suggest that the discrepancies between the experiments and the previously developed models are due to geometrical effects.

Keywords

Numerical simulationsRayleigh–Taylor instabilityRichtmyer–Meshkov instabilityStatistical modelThree-dimensional
Type
Research Article
Information
Laser and Particle Beams , Volume 21 , Issue 3 , July 2003 , pp. 327 - 334
Copyright
© 2003 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

Alon, U., Shvarts, D., & Mukamel, D. (1993). Scale-invariant regime in Rayleigh–Taylor bubble-front dynamics. Phys. Rev. E 48, 1008–1014.Google Scholar
Alon, U., Hecht, J., Mukamel, D., & Shvarts, D. (1994). Scale invariant mixing rates of hydrodynamically unstable interfaces. Phys. Rev. Lett. 72, 2867–2870.Google Scholar
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.Google Scholar
Arazi, L. (2001). A Drag–Buoyancy Based Study of the Late-Time RT and RM Scaling Laws. MSc Thesis. Israel: Tel-Aviv University.
Bernal, L.P. (1988). The statistics of the organized vortical structure in turbulent mixing layers. Phys. Fluids 31, 2533–2543.Google Scholar
Gardner, C.L., Glimm, J., McBryan, O., Menikoff, R., Sharp, D.H., & Zhang, Q. (1988). The dynamics of bubble growth for Rayleigh–Taylor unstable interfaces. Phys. Fluids 31, 447–465.Google Scholar
Dimonte, E., & Schneider, M.B. (1996). Turbulent Rayleigh–Taylor instability experiments with variable acceleration. Phys. Rev. E 54, 3740–3743.Google Scholar
Dimonte, E. (1999). Nonlinear evolution of the Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Phys. Plasmas 6, 2009–2015.Google Scholar
Dimonte, E., & Schneider, M.B. (2000). Density ratio dependence of Rayleigh–Taylor mixing for sustained and impulsive acceleration histories. Phys. Fluids 12, 304–321.Google Scholar
Glimm, J., & Sharp, D.H. (1990). Chaotic mixing as a renormalization-group fixed point. Phys. Rev. Lett. 64, 2137–2139.Google Scholar
Haan, S.W. (1989). Onset of nonlinear saturation for Rayleigh–Taylor growth in the presence of a full spectrum of modes. Phys. Rev. A 39, 5812–5825.Google Scholar
Haan, S.W. (1991). Weakly nonlinear hydrodynamic instabilities in inertial fusion. Phys. Fluids B 3, 2349–2355.CrossRefGoogle Scholar
Haan, S.W. (1995). Design and modeling of ignition targets for the National Ignition Facility. Phys. Plasmas 2, 2480–2487.Google Scholar
Hecht, J., Alon, U., & Shvarts, D. (1994). Potential flow models of Rayleigh–Taylor and Richtmyer–Meshkov bubble fronts. Phys. Fluids 6, 4019–4030.Google Scholar
Kartoon, D. (2000). Evolution of a Three-Dimensional Random Perturbation under RT and RM Instabilities. M.Sc. Thesis. Israel: Ben-Gurion University.
Layzer, D. (1955). On the instability of superimposed fluids in a gravitational field. Astrophys. J. 122, 1–12.Google Scholar
Ofer, D., Alon, U., Shvarts, D., McCrory, R.L., & Verdon, C.P. (1996). Modal model for the nonlinear multimode Rayleigh–Taylor instability. Phys. Plasmas 3, 3073–3090.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.Google Scholar
Read, K.I. (1984). Experimental investigation of turbulent mixing by Rayleigh–Taylor instability. Physica D 12, 45–58.Google Scholar
Remington, B.A., Kane, J, Drake, R.P., Glendinning, S.G., Estabrook, K., London, R., Castor, J., Wallace, R.J., Arnett, D., Liang, E., McCray, R., Rubenchik, A., & Fryxell, B. (1997). Supernova hydrodynamics experiments on the Nova laser. Phys. Plasmas 4, 1994–2003.CrossRefGoogle Scholar
Rikanati, A., Alon, U., & Shvarts, D. (1998). Vortex model for the nonlinear evolution of the multimode Richtmyer–Meshkov instability at low Atwood numbers. Phys. Rev. E 58, 7410–7418.Google Scholar
Schneider, M.B., Dimonte, G., & Remington, B. (1998). Large and small scale structure in Rayleigh–Taylor mixing. Phys. Rev. Lett. 80, 3507–3510.Google Scholar
Sharp, D.H. (1984). An overview of Rayleigh–Taylor instability. Physica D 12, 3–10.Google Scholar
Shvarts, D., Alon, U., Ofer, D., McCrory, R.L., & Verdon, C.P. (1995). Nonlinear evolution of multimode Rayleigh–Taylor instability in two and three dimensions. Phys. Plasmas 2, 2465–2472.CrossRefGoogle Scholar
Shvarts, D., Oron, D., Kartoon, D., Rikanati, A., Sadot, O., Srebro, Y., Yedvab, Y., Ofer, D., Levin, A., Sarid, E., Ben-Dor, G., Erez, L., Erez, G., Yosef-Hai, A., Alon, U., & Arazi, L. (2000). Scaling laws of nonlinear Rayleigh–Taylor and Richtmyer–Meshkov instabilities in two and three dimensions. In Inertial Fusion Science and Applications 99—State of the Art 1999, (Labaune, C., Hogan, W.J. & Tanaka, K.A., Eds.). Amsterdam: Elsevier.
Youngs, D.L. (1984). Numerical simulation of turbulent mixing by Rayleigh–Taylor instability. Physica D 12, 32–44.Google Scholar
Youngs, D.L. (1991). Three-dimensional numerical simulation of turbulent mixing by Rayleigh–Taylor instability. Phys. Fluids A 3, 1312–1320.CrossRefGoogle Scholar