| PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES |
|
|
|
|
Weakly Nonlinear Rayleigh–Taylor Instability in Incompressible Fluids with Surface Tension |
| Hong-Yu Guo1,2, Li-Feng Wang2,3, Wen-Hua Ye2,3**, Jun-Feng Wu2, Wei-Yan Zhang2 |
1Graduate School, China Academy of Engineering Physics, Beijing 100088
2Institute of Applied Physics and Computational Mathematics, Beijing 100094
3HEDPS, Center for Applied Physics and Technology, Peking University, Beijing 100871
|
|
| Cite this article: |
|
Hong-Yu Guo, Li-Feng Wang, Wen-Hua Ye et al 2017 Chin. Phys. Lett. 34 045201 |
|
|
|
|
Abstract A weakly nonlinear model is established for incompressible Rayleigh–Taylor instability with surface tension. The temporal evolution of a perturbed interface is explored analytically via the third-order solution. The dependence of the first three harmonics on the surface tension is discussed. The amplitudes of bubble and spike are greatly affected by surface tension. The saturation amplitude of the fundamental mode versus the Atwood number $A$ is investigated with surface tension into consideration. The saturation amplitude decreases with increasing $A$. Surface tension exhibits a stabilizing phenomenon. It is shown that the asymmetrical development of the perturbed interface occurs much later for large surface tension effect.
|
|
|
Received: 12 November 2016
Published: 21 March 2017
|
|
| PACS: |
52.57.Fg
|
(Implosion symmetry and hydrodynamic instability (Rayleigh-Taylor, Richtmyer-Meshkov, imprint, etc.))
|
| |
47.20.Ma
|
(Interfacial instabilities (e.g., Rayleigh-Taylor))
|
| |
52.35.Py
|
(Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.))
|
|
|
| Fund: Supported by the National Natural Science Foundation of China under Grant Nos 11275031, 11475034, 11575033 and 11274026, and the National Basic Research Program of China under Grant No 2013CB834100. |
|
|
|
| [1] | Rayleigh L 1883 Proc. London Math. Soc. 14 170 | | [2] | Taylor G 1950 Proc. R. Soc. London Ser. A 201 192 | | [3] | Nuckolls J, Wood L, Thiessen A and Zimmerman G 1972 Nature 239 139 | | [4] | Gamezo V N, Khokhlov A M, Oran E S, Chtchelkanova A Y and Rosenberg R O 2003 Science 299 77 | | [5] | Remington B A, Drake R P and Ryutov D D 2006 Rev. Mod. Phys. 78 755 | | [6] | Wang L F, Ye W H and Li Y J 2010 Chin. Phys. Lett. 27 025203 | | [7] | Guo H Y et al 2014 Chin. Phys. Lett. 31 044702 | | [8] | Yang B L, Wang L F, Ye W H and Xue C 2011 Phys. Plasmas 18 072111 | | [9] | Piriz A R et al 1997 Phys. Plasmas 4 1117 | | [10] | Ye W H, Zhang W Y and He X T 2002 Phys. Rev. E 65 057401 | | [11] | Wang L F, Ye W H and Li Y J 2010 Chin. Phys. Lett. 27 025202 | | [12] | Wang L F et al 2012 Phys. Plasmas 19 100701 | | [13] | Bellman R and Pennington R H 1954 Quart. Appl. Math. 12 151 | | [14] | Chandrasekhar S 1961 Hydrodynamic and Hydromagnetic Stability (London: Oxford University) chap X | | [15] | Mikaelian K O 1990 Phys. Rev. A 42 7211 | | [16] | Jacobs J W and Catton I 1988 J. Fluid Mech. 187 329 | | [17] | Velikovich A L and Dimonte G 1996 Phys. Rev. Lett. 76 3112 | | [18] | Wang L F, Wu J F, Guo H Y, Ye W H, Liu J, Zhang W Y and He X T 2015 Phys. Plasmas 22 082702 | | [19] | Liu W H, Wang L F, Ye W H and He X T 2012 Phys. Plasmas 19 042705 | | [20] | Wang L F, Guo H Y, Wu J F, Ye W H, Liu J, Zhang W Y and He X T 2014 Phys. Plasmas 21 122710 | | [21] | Wang L F et al 2012 Phys. Plasmas 19 112706 |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
