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Title: Heuristic model of the nonlinear Rayleigh-Taylor instability

Abstract

A simple model is derived heuristically for the nonlinear evolution of the Rayleigh-Taylor instability. Ordinary differential equations for time evolution of the spike and bubble amplitudes are found by constructing terms that smoothly connect the regimes of small and large amplitude behavior. The results apply to arbitrarily varying acceleration fields, including shock-induced instabilities. The model predicts amplitudes accurate to better than 20% (velocity predictions are more accurate), in comparisons with published experimental data and two-dimensional numerical simulations with hydrocodes. A limitation in the present model is that the density ratio of the two fluids should not be close to one for accurate modeling.

Authors:
;
Publication Date:
Research Org.:
Particle Beam Fusion Dept., 4240 Sandia National Laboratories, Albuquerque, New Mexico 87185
OSTI Identifier:
6788131
Resource Type:
Journal Article
Journal Name:
J. Appl. Phys.; (United States)
Additional Journal Information:
Journal Volume: 52:2
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; RAYLEIGH-TAYLOR INSTABILITY; NONLINEAR PROBLEMS; ACCELERATION; COMPARATIVE EVALUATIONS; DIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; SHOCK WAVES; SIMULATION; TWO-DIMENSIONAL CALCULATIONS; VELOCITY; EQUATIONS; INSTABILITY; 658000* - Mathematical Physics- (-1987)

Citation Formats

Baker, L, and Freeman, J R. Heuristic model of the nonlinear Rayleigh-Taylor instability. United States: N. p., 1981. Web. doi:10.1063/1.328793.
Baker, L, & Freeman, J R. Heuristic model of the nonlinear Rayleigh-Taylor instability. United States. https://doi.org/10.1063/1.328793
Baker, L, and Freeman, J R. 1981. "Heuristic model of the nonlinear Rayleigh-Taylor instability". United States. https://doi.org/10.1063/1.328793.
@article{osti_6788131,
title = {Heuristic model of the nonlinear Rayleigh-Taylor instability},
author = {Baker, L and Freeman, J R},
abstractNote = {A simple model is derived heuristically for the nonlinear evolution of the Rayleigh-Taylor instability. Ordinary differential equations for time evolution of the spike and bubble amplitudes are found by constructing terms that smoothly connect the regimes of small and large amplitude behavior. The results apply to arbitrarily varying acceleration fields, including shock-induced instabilities. The model predicts amplitudes accurate to better than 20% (velocity predictions are more accurate), in comparisons with published experimental data and two-dimensional numerical simulations with hydrocodes. A limitation in the present model is that the density ratio of the two fluids should not be close to one for accurate modeling.},
doi = {10.1063/1.328793},
url = {https://www.osti.gov/biblio/6788131}, journal = {J. Appl. Phys.; (United States)},
number = ,
volume = 52:2,
place = {United States},
year = {Sun Feb 01 00:00:00 EST 1981},
month = {Sun Feb 01 00:00:00 EST 1981}
}