Weakly nonlinear multi-mode Rayleigh-Taylor instability in two-dimensional spherical geometry

2018 ◽  
Vol 25 (8) ◽  
pp. 082713 ◽  
Keyword(s):  
Spherical Geometry ◽  
Taylor Instability ◽  
Two Dimensional ◽  
Weakly Nonlinear ◽  
Rayleigh Taylor Instability ◽  
Multi Mode

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 A Relaxation Filtering Approach for Two-Dimensional Rayleigh–Taylor Instability-Induced Flows

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 78 ◽  
Author(s):  
Sk. Mashfiqur Rahman ◽  
Omer San
Keyword(s):  
High Resolution ◽  
Numerical Experiments ◽  
Single Mode ◽  
Taylor Instability ◽  
Two Dimensional ◽  
Reconstruction Scheme ◽  
Rayleigh Taylor Instability ◽  
Multi Mode ◽  
Filtering Approach ◽  
Point Stencil

In this paper, we investigate the performance of a relaxation filtering approach for the Euler turbulence using a central seven-point stencil reconstruction scheme. High-resolution numerical experiments are performed for both multi-mode and single-mode

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

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.

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