The three-dimensional weakly nonlinear Rayleigh–Taylor instability in spherical geometry

2020 ◽  
Vol 27 (2) ◽  
pp. 022707
Keyword(s):  
Three Dimensional ◽  
Spherical Geometry ◽  
Taylor Instability ◽  
Weakly Nonlinear ◽  
Rayleigh Taylor Instability

Simulation of the Weakly Nonlinear Rayleigh-Taylor Instability in Spherical Geometry

2020 ◽  
Vol 37 (5) ◽  
pp. 055201
Author(s):  
Yun-Peng Yang ◽  
Jing Zhang ◽  
Zhi-Yuan Li ◽  
Li-Feng Wang ◽  
Jun-Feng Wu ◽  
...  
Keyword(s):  
Spherical Geometry ◽  
Taylor Instability ◽  
Weakly Nonlinear ◽  
Rayleigh Taylor Instability

Three-dimensional Rayleigh-Taylor instability Part 1. Weakly nonlinear theory

1988 ◽  
Vol 187 ◽  
pp. 329-352 ◽  
Author(s):  
J. W. Jacobs ◽  
I. Catton
Keyword(s):  
Aspect Ratio ◽  
Three Dimensional ◽  
Taylor Instability ◽  
Initial Surface ◽  
Surface Slope ◽  
Cross Sectional ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
Rayleigh Taylor Instability ◽  
The Stability

Three-dimensional weakly nonlinear Rayleigh-Taylor instability is analysed. The stability of a confined inviscid liquid and an overlying gas with density much less than that of the liquid is considered. An asymptotic solution for containers of arbitrary cross-sectional geometry, valid up to order ε3 (where ε is the root-mean-squared initial surface slope) is obtained. The solution is evaluated for the rectangular and circular geometries and for various initial modes (square, hexagonal, axisymmetric, etc.). It is found that the hexagonal and axisymmetric instabilities grow faster than any other shapes in their respective geometries. In addition it is found that, sufficiently below the cutoff wavenumber, instabilities that are equally proportioned in the lateral directions grow faster than those with longer, thinner shape. However, near the cutoff wavenumber this trend reverses with instabilities having zero aspect ratio growing faster than those with aspect ratio near 1.

Interface Width Effect on the Weakly Nonlinear Rayleigh–Taylor Instability in Spherical Geometry

2020 ◽  
Vol 37 (7) ◽  
pp. 075201
Author(s):  
Yun-Peng Yang ◽  
Jing Zhang ◽  
Zhi-Yuan Li ◽  
Li-Feng Wang ◽  
Jun-Feng Wu ◽  
...  
Keyword(s):  
Spherical Geometry ◽  
Taylor Instability ◽  
Weakly Nonlinear ◽  
Interface Width ◽  
Width Effect ◽  
Rayleigh Taylor Instability

Three-dimensional Rayleigh-Taylor instability Part 2. Experiment

1988 ◽  
Vol 187 ◽  
pp. 353-371 ◽  
Author(s):  
J. W. Jacobs ◽  
I. Catton
Keyword(s):  
High Speed ◽  
Small Volume ◽  
Circular Tube ◽  
Three Dimensional ◽  
Vertical Tube ◽  
Taylor Instability ◽  
Gravitational Acceleration ◽  
Lateral Direction ◽  
Weakly Nonlinear ◽  
Rayleigh Taylor Instability

Three-dimensional Rayleigh-Taylor instability, induced by accelerating a small volume of water down a vertical tube using air pressure, is investigated. Two geometries are studied: a 15.875 cm circular tube and a 12.7 cm square tube. Runs were made with initial disturbances in the form of standing waves forced by shaking the test section in a lateral direction. Accelerations ranging from 5 to 10 times gravitational acceleration and wavenumbers from 1 cm−1 to 8 cm−1 are studied. The resulting instability was recorded and later analysed using high-speed motion picture photography. Measurements of the growth rate are found to agree well with linear theory. In addition, good qualitative agreement between photographs and three-dimensional surface plots of the weakly nonlinear solution of Part 1 of this series (Jacobs & Catton 1988) is obtained.

scholarly journals Three-dimensional simulations and analysis of the nonlinear stage of the Rayleigh-Taylor instability

1995 ◽  
Vol 13 (3) ◽  
pp. 423-440 ◽  
Author(s):  
J. Hecht ◽  
D. Ofer ◽  
U. Alon ◽  
D. Shvarts ◽  
S.A. Orszag ◽  
...  
Keyword(s):  
Initial Conditions ◽  
Three Dimensional ◽  
Spherical Geometry ◽  
Taylor Instability ◽  
Three Dimensions ◽  
Type Model ◽  
Late Time ◽  
Nonlinear Stage ◽  
Rayleigh Taylor Instability ◽  
Atwood Number

The nonlinear stage in the growth of the Rayleigh-Taylor instability in three dimensions (3D) is studied using a 3D multimaterial hydrodynamic code. The growth of a single classical 3D square and rectangular modes is compared to the growth in planar and cylindrical geometries and found to be close to the corresponding cylindrical mode, which is in agreement with a new Layzer-type model for 3D bubble growth. The Atwood number effect on the final shape of the instability is demonstrated. Calculations in spherical geometry of the late deceleration stage of a typical ICF pellet have been performed. The different late time shapes obtained are shown to be a result of the initial conditions and the high Atwood number. Finally, preliminary results of calculations of two-mode coupling and random perturbations growth in 3D are presented.

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