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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, IsraelDepartment 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, IsraelDepartment of Physics, Ben Gurion University, Beer-Sheva, IsraelDepartment of Mechanical Engineering, Ben Gurion University, Beer-Sheva, Israel
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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

Information

Type
Research Article
Information
Laser and Particle Beams , Volume 21 , Issue 3 , July 2003, pp. 327 - 334
Copyright
© 2003 Cambridge University Press

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