Mechanism of the Large Surface Deformation Caused by Rayleigh-Taylor Instability at Large Atwood Number


Studying the dynamical behaviors of the liquid spike formed by Rayleigh-Taylor instability is important to understand the mechanisms of liquid atomization process. In this paper, based on the information on the velocity and pressure fields obtained by the coupled-level-set and volume-of- fluid (CLSVOF) method, we describe how a freed spike can be formed from a liquid layer under falling at a large Atwood number. At the initial stage when the surface deformation is small, the amplitude of the surface deformation increases exponentially. Nonlinear effect becomes dominant when the amplitude of the surface deformation is comparable with the surface wavelength (~0.1λ). The maximum pressure point, which results from the impinging flow at the spike base, is essential to generate a liquid spike. The spike region above the maximum pressure point is dynamically free from the bulk liquid layer below that point. As the descending of the maximum pressure point, the liquid elements enter the freed region and elongate the liquid spike to a finger-like shape.

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Li, Y. and Umemura, A. (2014) Mechanism of the Large Surface Deformation Caused by Rayleigh-Taylor Instability at Large Atwood Number. Journal of Applied Mathematics and Physics, 2, 971-979. doi: 10.4236/jamp.2014.210110.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Arnett, W.D., Bahcall, J.N., Kirshner, R.P. and Woosley, S.E. (1989) Supernova 1987A. Annual Review of Astronomy and Astrophysics, 27, 629-700.
[2] Norman, M., Smarr, L., Smith, M. and Wilson, J. (1981) Hydrodynamic Formation of Twin-Exhaust Jets. Astrophysical Journal, 247, 52-58.
[3] Evans, R., Bennett, A. and Pert, G. (1982) Rayleigh-Taylor Instabilities in Laser-Accelerated Targets. Physical Review Letters, 49, 1639-1642.
[4] Lindl, J.D., McCrory, R.L. and Campbell, E.M. (1992) Progress toward Ignition and Burn Propagation in Inertial Confinement Fusion. Physics Today, 45, 32-40.
[5] Beale, J.C. and Reitz, R.D. (1999) Modeling Spray Atomization with the Kelvin-Helmholtz /Rayleigh-Taylor Hybrid Model. Atomization Sprays, 9, 623-650.
[6] Kong, S., Senecal, P. and Reitz, R. (1999) Developments in Spray Modeling in Diesel and Direct-Injection Gasoline Engines. Oil & Gas Science and Technology, 54, 197-204.
[7] Rayleigh, L. (1883) Investigation of the Character of the Equilibrium of an Incompressible Heavy Fluid of Variable Density. Proceedings of the London Mathematical Society, 14, 170-177.
[8] Taylor, G.I. (1950) The Instability of Liquid Surfaces When Accelerated in a Direction Perpendicular to Their Planes. I. Proceedings of the Royal Society A, 201, 192-196.
[9] Lewis, D. (1950) The Instability of Liquid Surfaces When Accelerated in a Direction Perpendicular to Their Planes. II. Proceedings of the Royal Society A, 202, 81-96.
[10] Layzer, D. (1955) On the Instability of Superposed Fluids in a Gravitational Field. Astrophysical Journal, 122, 1-12.
[11] Goncharov, V. (2002) Analytical Model of Nonlinear, Single-Mode, Classical Rayleigh-Taylor Instability at Arbitrary Atwood Numbers. Physical Review Letters, 88, Article ID: 134502.
[12] Andrews, M.J. and Dalziel, S.B. (2010) Small Atwood Number Rayleigh-Taylor Experiments. Philosophical Transactions of the Royal Society A: Mathematical Physical and Engineering Sciences, 368, 1663-1679.
[13] Dimonte, G., Ramaprabhu, P., Youngs, D., Andrews, M. and Rosner, R. (2005) Recent Advances in the Turbulent Rayleigh-Taylor Instability. Physics of Plasmas, 12, Article ID: 056301.
[14] Ramaprabhu, P. and Andrews, M. (2004) Experimental Investigation of Rayleigh-Taylor Mixing at Small Atwood Numbers. Journal of Fluid Mechanics, 502, 233-271.
[15] Waddell, J., Niederhaus, C. and Jacobs, J. (2001) Experimental Study of Rayleigh-Taylor Instability: Low Atwood Number Liquid Systems with Single-Mode Initial Perturbations. Physics of Fluids (1994-Present), 13, 1263-1273.
[16] Baker, G.R., Meiron, D.I. and Orszag, S.A. (1980) Vortex Simulations of the Rayleigh-Taylor Instability. Physics of Fluids (1958-1988), 23, 1485-1490.
[17] Ramaprabhu, P., Dimonte, G. and Andrews, M. (2005) A Numerical Study of the Influence of Initial Perturbations on the Turbulent Rayleigh-Taylor Instability. Journal of Fluid Mechanics, 536, 285-320.
[18] Ramaprabhu, P., Dimonte, G., Woodward, P., Fryer, C., Rockefeller, G., Muthuraman, K., Lin, P. and Jayaraj, J. (2012) The Late-Time Dynamics of the Single-Mode Rayleigh-Taylor Instability. Physics of Fluids (1994-Present), 24, Article ID: 074107.
[19] Youngs, D.L. (1984) Numerical Simulation of Turbulent Mixing by Rayleigh-Taylor Instability. Physica D: Nonlinear Phenomena, 12, 32-44.
[20] Baker, G., Verdon, C., McCrory, R. and Orszag, S. (1987) Rayleigh-Taylor Instability of Fluid Layers. Journal of Fluid Mechanics, 178, 161-175.
[21] Brackbill, J., Kothe, D.B. and Zemach, C. (1992) A Continuum Method for Modeling Surface Tension. Journal of Computational Physics, 100, 335-354.
[22] Piriz, A., Cortázar, O., Cela, J.L. and Tahir, N. (2006) The Rayleigh-Taylor Instability. American Journal of Physics, 74, 1095-1098.
[23] Harlow, F.H. and Welch, J.E. (1965) Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface. Physics of Fluids (1958-1988), 8, 2182-2189.
[24] Sussman, M. and Puckett, E.G. (2000) A Coupled Level Set and Volume-of-Fluid Method for Computing 3D and Axisymmetric Incompressible Two-Phase Flows. Journal of Computational Physics, 162, 301-337.
[25] Van der Pijl, S., Segal, A., Vuik, C. and Wesseling, P. (2005) A Mass-Conserving Level-Set Method for Modelling of Multi-Phase Flows. International Journal for Numerical Methods in Fluids, 47, 339-361.
[26] Ramaprabhu, P. and Dimonte, G. (2005) Single-Mode Dynamics of the Rayleigh-Taylor Instability at Any Density Ratio. Physical Review E, 71, Article ID: 036314.
[27] He, X., Zhang, R., Chen, S. and Doolen, G.D. (1999) On the Three-Dimensional Rayleigh-Taylor Instability. Physics of Fluids (1994-Present), 11, 1143-1152.

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