Nonlinear saturation amplitude of cylindrical Rayleigh–Taylor instability

doi:10.1088/1674-1056/23/9/094502

›› 2014, Vol. 23 ›› Issue (9): 94502-094502.doi: 10.1088/1674-1056/23/9/094502

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

Nonlinear saturation amplitude of cylindrical Rayleigh–Taylor instability

刘万海^{a b}, 于长平^c, 叶文华^{b d e}, 王立峰^{b d}

a Research Center of Computational Physics, Mianyang Normal University, Mianyang 621000, China;
b Key Laboratory of High Energy Density Physics Simulation (HEDPS), and Center for Applied Physics and Technology, Peking University, Beijing 100871, China;
c Key Laboratory of High Temperature Gas Dynamics (LHD), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China;
d Institute of Applied Physics and Computational Mathematics, Beijing 100194, China;
e Department of Physics, Zhejiang University, Hangzhou 310027, China

收稿日期:2013-12-30 修回日期:2014-02-27 出版日期:2014-09-15 发布日期:2014-09-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10835003 and 11274026) and the Scientific Research Foundation of Mianyang Normal University, China (Grant No. 07165411).

Nonlinear saturation amplitude of cylindrical Rayleigh–Taylor instability

Liu Wan-Hai (刘万海)^{a b}, Yu Chang-Ping (于长平)^c, Ye Wen-Hua (叶文华)^{b d e}, Wang Li-Feng (王立峰)^{b d}

a Research Center of Computational Physics, Mianyang Normal University, Mianyang 621000, China;
b Key Laboratory of High Energy Density Physics Simulation (HEDPS), and Center for Applied Physics and Technology, Peking University, Beijing 100871, China;
c Key Laboratory of High Temperature Gas Dynamics (LHD), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China;
d Institute of Applied Physics and Computational Mathematics, Beijing 100194, China;
e Department of Physics, Zhejiang University, Hangzhou 310027, China

Received:2013-12-30 Revised:2014-02-27 Online:2014-09-15 Published:2014-09-15
Contact: Yu Chang-Ping E-mail:champion-yu@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10835003 and 11274026) and the Scientific Research Foundation of Mianyang Normal University, China (Grant No. 07165411).

摘要/Abstract

摘要： The nonlinear saturation amplitude (NSA) of the fundamental mode in the classical Rayleigh-Taylor instability with a cylindrical geometry for an arbitrary Atwood number is analytically investigated by considering the nonlinear corrections up to the third order. The analytic results indicate that the effects of the initial radius of the interface (r₀) and the Atwood number (A) play an important role in the NSA of the fundamental mode. The NSA of the fundamental mode first increases gently and then decreases quickly with increasing A. For a given A, the smaller the r₀/λ (λ is the perturbation wavelength), the larger the NSA of the fundamental mode. When r₀/λ is large enough (r₀ λ), the NSA of the fundamental mode is reduced to the prediction in the previous literatures within the framework of the third-order perturbation theory.

关键词: nonlinear saturation amplitude, Rayleigh-Taylor instability, cylindrical interface

Abstract: The nonlinear saturation amplitude (NSA) of the fundamental mode in the classical Rayleigh-Taylor instability with a cylindrical geometry for an arbitrary Atwood number is analytically investigated by considering the nonlinear corrections up to the third order. The analytic results indicate that the effects of the initial radius of the interface (r₀) and the Atwood number (A) play an important role in the NSA of the fundamental mode. The NSA of the fundamental mode first increases gently and then decreases quickly with increasing A. For a given A, the smaller the r₀/λ (λ is the perturbation wavelength), the larger the NSA of the fundamental mode. When r₀/λ is large enough (r₀ λ), the NSA of the fundamental mode is reduced to the prediction in the previous literatures within the framework of the third-order perturbation theory.

Key words: nonlinear saturation amplitude, Rayleigh-Taylor instability, cylindrical interface

中图分类号: (Implosion symmetry and hydrodynamic instability (Rayleigh-Taylor, Richtmyer-Meshkov, imprint, etc.))

52.57.Fg

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.)) 52.65.Vv (Perturbative methods)

刘万海, 于长平, 叶文华, 王立峰. Nonlinear saturation amplitude of cylindrical Rayleigh–Taylor instability[J]. , 2014, 23(9): 94502-094502.

Liu Wan-Hai (刘万海), Yu Chang-Ping (于长平), Ye Wen-Hua (叶文华), Wang Li-Feng (王立峰). Nonlinear saturation amplitude of cylindrical Rayleigh–Taylor instability[J]. Chin. Phys. B, 2014, 23(9): 94502-094502.

参考文献 41

[1]	Rayleigh L 1883 Proc. London Math. Soc. 14 170
[2]	Taylor G 1950 Proc. R. Soc. London Ser. A 201 192
[3]	Zhang Q 1998 Phys. Rev. Lett. 81 3391
[4]	Mikaelian K O 2003 Phys. Rev. E 67 026319
[5]	Goncharov V N 2002 Phys. Rev. Lett. 88 134502
[6]	Ramaprabhu P, Dimonte G, Young Y N, Calder A C and Fryxell B 2006 Phys. Rev. E 74 066308
[7]	Layzer D 1955 Astrophys. J. 122 1
[8]	Jacobs J W and Catton I 1988 J. Fluid Mech. 187 329
[9]	Haan S W 1991 Phys. Fluids B 3 2349
[10]	Berning M and Rubenchik A M 1998 Phys. Fluids 10 1564
[11]	Liu W H, Wang L F, Ye W H and He X T 2012 Phys. Plasmas 19 042705
[12]	Zhang W Y, Ye W H, He X T and Wu J F 2003 Acta Phys. Sin. 52 1688 (in Chinese)
[13]	Ye W H and He X T 2010 Chin. Phys. Lett. 27 125203
[14]	Wang L F, Li Y J and Ye W H 2010 Chin. Phys. Lett. 27 025203
[15]	Tao Y S, Wang L F, Ye W H, Zhang G, Zhang J C and Li Y J 2012 Acta Phys. Sin. 61 075207 (in Chinese)
[16]	Hasegawa S and Nishihara K 1995 Phys. Plasmas 2 4606
[17]	Sanz J, Ramírez J, Ramis R, Betti R and TownR P J 2002 Phys. Rev. Lett. 89 195002
[18]	Ikegawa T and Nishihara K 2002 Phys. Rev. Lett. 89 115001
[19]	Garnier J and Masse L 2005 Phys. Plasmas 12 062707
[20]	Sohn S I 2003 Phys. Rev. E 67 026301
[21]	Goncharov V N and Li D 2005 Phys. Rev. E 71 046306
[22]	Lafay M A, Le C B and Gauthier S 2007 Europhys. Lett. 79 64002
[23]	Remington B A, Weber S V, Marinak M M, Haan S W, Kilkenny J D, Wallace R J and Dimonte G 1995 Phys. Plasmas 2 241
[24]	Smalyuk V A, Goncharov V N, Boehly T R, Knauer J P, Meyerhofer D D and Sangster T C 2004 Phys. Plasmas 11 5083
[25]	Jing L F, Huang T X, Jiang S E, Chen B L, Pu Y D, Hu F and Cheng S B 2012 Acta Phys. Sin. 61 105205 (in Chinese)
[26]	Cao Z R, Miao W Y, Dong J J, Yuan Y T, Yang Z H, Yuan Z, Zhang H Y, Liu S Y, Jiang S E and Ding Y K 2012 Acta Phys. Sin. 61 075213 (in Chinese)
[27]	Dunning M J and Haan S W 1995 Phys. Plasmas 2 1669
[28]	Wang L F, Ye W H, Fan Z F and Li Y J 2010 Europhys. Lett. 90 15001
[29]	Wang L F, Ye W H and Li Y J 2010 Phys. Plasmas 17 052305
[30]	Mügler C and Gauthier S 1998 Phys. Rev. E 58 4548
[31]	Rikanati A, Alon U and Shvarts D 1998 Phys. Rev. E 58 7410
[32]	Wang L F, Ye W H, Fan Z F, Li Y J, He X T and Yu M Y 2009 Europhys. Lett. 86 15002
[33]	Zhang Q and Graham M J 1998 Phys. Fluids 10 974
[34]	Sweeney M A and Perry F C 1981 J. Appl. Phys. 52 4487
[35]	Weir S T, Chandler E A and Goodwin B T 1998 Phys. Rev. Lett. 80 3763
[36]	Fan Z F, Zhu S P, Pei W B, Ye W H, Li M, Xu X W, Wu J F, Dai Z Z and Wang L F 2012 Europhys. Lett. 99 65003
[37]	Gamezo V N, Khokhlov A M, Oran E S, Chtchelkanova A Y and Rosenberg R O 2003 Science 299 77
[38]	Remington B A, Drake R P and Ryutov D D 2006 Rev. Mod. Phys. 78 755
[39]	Ebisuzaki T, Shigeyama T and Nomoto K 1989 Astrophys. J. 344 L65
[40]	Ye W H, Zhang W Y and He X T 2002 Phys. Rev. E 65 057401
[41]	He X T and Zhang W Y 2007 Eur. Phys. J. D 44 227

Nonlinear saturation amplitude of cylindrical Rayleigh–Taylor instability

Nonlinear saturation amplitude of cylindrical Rayleigh–Taylor instability

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