Ablation effects in weakly nonlinear stage of the ablative Rayleigh-Taylor instability

1996 ◽  
Author(s):  
Susumu Hasegawa ◽  
Katsunobu Nishihara
Keyword(s):  
Taylor Instability ◽  
Weakly Nonlinear ◽  
Nonlinear Stage ◽  
Rayleigh Taylor Instability

scholarly journals Ablation effects in weakly nonlinear stage of the ablative Rayleigh–Taylor instability

1996 ◽  
Vol 14 (1) ◽  
pp. 45-54
Author(s):  
Susumu Hasegawa ◽  
Katsunobu Nishihara
Keyword(s):  
Perturbation Theory ◽  
Mode Coupling ◽  
Wave Amplitude ◽  
Taylor Instability ◽  
Weakly Nonlinear ◽  
Effective Gravity ◽  
Nonlinear Stage ◽  
Excited Wave ◽  
Wave Numbers ◽  
Rayleigh Taylor Instability

Weakly nonlinear stage of the ablative Rayleigh-Taylor instability has been studied by the perturbation theory. Mode coupling of linear growing waves with wave numbers kA and kB drives new excited waves with wave numbers k0 (= kA ± kB, 2kA, 2kB). We have investigated time evolution of the excited waves and found that the ablation effect plays an important role even in the nonlinear stage to reduce amplitude of the excited waves. Differences between an ablation surface and a classical contact surface have been discussed. Dependence of the excited wave amplitude on the wavenumber k0, the ablation velocity va, and the effective gravity g is also investigated.

scholarly journals Phase-field model for the Rayleigh–Taylor instability of immiscible fluids

2009 ◽  
Vol 622 ◽  
pp. 115-134 ◽  
Author(s):  
ANTONIO CELANI ◽  
ANDREA MAZZINO ◽  
PAOLO MURATORE-GINANNESCHI ◽  
LARA VOZELLA
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Stokes Equations ◽  
Phase Field Model ◽  
Terminal Velocity ◽  
Immiscible Fluids ◽  
Taylor Instability ◽  
Upper And Lower Bounds ◽  
Weakly Nonlinear ◽  
Rayleigh Taylor Instability

The Rayleigh–Taylor instability of two immiscible fluids in the limit of small Atwood numbers is studied by means of a phase-field description. In this method, the sharp fluid interface is replaced by a thin, yet finite, transition layer where the interfacial forces vary smoothly. This is achieved by introducing an order parameter (the phase-field) continuously varying across the interfacial layers and uniform in the bulk region. The phase-field model obeys a Cahn–Hilliard equation and is two-way coupled to the standard Navier–Stokes equations. Starting from this system of equations we have first performed a linear analysis from which we have analytically rederived the known gravity–capillary dispersion relation in the limit of vanishing mixing energy density and capillary width. We have performed numerical simulations and identified a region of parameters in which the known properties of the linear phase (both stable and unstable) are reproduced in a very accurate way. This has been done both in the case of negligible viscosity and in the case of non-zero viscosity. In the latter situation, only upper and lower bounds for the perturbation growth rate are known. Finally, we have also investigated the weakly nonlinear stage of the perturbation evolution and identified a regime characterized by a constant terminal velocity of bubbles/spikes. The measured value of the terminal velocity is in agreement with available theoretical prediction. The phase-field approach thus appears to be a valuable technique for the dynamical description of the stages where hydrodynamic turbulence and wave-turbulence come into play.

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

scholarly journals Efficient perturbation methods for Richtmyer–Meshkov and Rayleigh–Taylor instabilities: Weakly nonlinear stage and beyond

2003 ◽  
Vol 21 (3) ◽  
pp. 321-325 ◽  
Author(s):  
M. VANDENBOOMGAERDE ◽  
C. CHERFILS ◽  
D. GALMICHE ◽  
S. GAUTHIER ◽  
P.A. RAVIART
Keyword(s):  
Growth Rate ◽  
Perturbation Method ◽  
Numerical Simulations ◽  
Perturbation Methods ◽  
High Order ◽  
Standard Approach ◽  
Weakly Nonlinear ◽  
Nonlinear Stage ◽  
Selection Mode ◽  
Rayleigh Taylor Instability

The simplified perturbation method of Vandenboomgaerdeet al.(2002) is applied to both the Richtmyer–Meshkov and the Rayleigh–Taylor instabilities. This theory is devoted to the calculus of the growth rate of the perturbation of the interface in the weakly nonlinear stage. In the standard approach, expansions appear to be series in time. We build accurate approximations by retaining only the terms with the highest power in time. This simplifies and accelerates the solution. High order expressions are then easily reachable. For the Richtmyer–Meshkov instability, multimode configurations become tractable and the selection mode process can be studied. Inferences for the intermediate nonlinear regime are also proposed. In particular, a class of homothetic configurations is inferred; its validity is verified with numerical simulations even as vortex structures appear at the interface. This kind of method can also be used for the Rayleigh–Taylor instability. Some examples are presented.

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.

Cylindrical effects in weakly nonlinear Rayleigh–Taylor instability

2015 ◽  
Vol 24 (1) ◽  
pp. 015202 ◽  
Author(s):  
Wan-Hai Liu ◽  
Wen-Fang Ma ◽  
Xu-Lin Wang
Keyword(s):  
Taylor Instability ◽  
Weakly Nonlinear ◽  
Rayleigh Taylor Instability
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