Cylindrical effects in weakly nonlinear Rayleigh–Taylor instability

doi:10.1088/1674-1056/24/1/015202

›› 2015, Vol. 24 ›› Issue (1): 15202-015202.doi: 10.1088/1674-1056/24/1/015202

• PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES • 上一篇下一篇

Cylindrical effects in weakly nonlinear Rayleigh–Taylor instability

刘万海^{a b}, 马文芳^a, 王绪林^a

a Research Center of Computational Physics, Mianyang Normal University, Mianyang 621000, China;
b HEDPS and CAPT, Peking University, Beijing 100871, China

收稿日期:2014-04-01 修回日期:2014-05-13 出版日期:2015-01-05 发布日期:2015-01-05
基金资助:
Project supported by the National Basic Research Program of China (Grant No. 10835003), the National Natural Science Foundation of China (Grant No. 11274026), the Scientific Research Foundation of Mianyang Normal University, China (Grant Nos. QD2014A009 and 2014A02), and the National High-Tech ICF Committee.

Cylindrical effects in weakly nonlinear Rayleigh–Taylor instability

Liu Wan-Hai (刘万海)^{a b}, Ma Wen-Fang (马文芳)^a, Wang Xu-Lin (王绪林)^a

a Research Center of Computational Physics, Mianyang Normal University, Mianyang 621000, China;
b HEDPS and CAPT, Peking University, Beijing 100871, China

Received:2014-04-01 Revised:2014-05-13 Online:2015-01-05 Published:2015-01-05
Contact: Wang Xu-Lin E-mail:wxln177@163.com
Supported by:
Project supported by the National Basic Research Program of China (Grant No. 10835003), the National Natural Science Foundation of China (Grant No. 11274026), the Scientific Research Foundation of Mianyang Normal University, China (Grant Nos. QD2014A009 and 2014A02), and the National High-Tech ICF Committee.

摘要/Abstract

摘要： The classical Rayleigh-Taylor instability (RTI) at the interface between two variable density fluids in the cylindrical geometry is explicitly investigated by the formal perturbation method up to the second order. Two styles of RTI, convergent (i.e., gravity pointing inward) and divergent (i.e., gravity pointing outwards) configurations, compared with RTI in Cartesian geometry, are taken into account. Our explicit results show that the interface function in the cylindrical geometry consists of two parts: oscillatory part similar to the result of the Cartesian geometry, and non-oscillatory one contributing nothing to the result of the Cartesian geometry. The velocity resulting only from the non-oscillatory term is followed with interest in this paper. It is found that both the convergent and the divergent configurations have the same zeroth-order velocity, whose magnitude increases with the Atwood number, while decreases with the initial radius of the interface or mode number. The occurrence of non-oscillation terms is an essential character of the RTI in the cylindrical geometry different from Cartesian one.

关键词: cylindrical effect, Rayleigh-Taylor instability, variable density fluid

Abstract: The classical Rayleigh-Taylor instability (RTI) at the interface between two variable density fluids in the cylindrical geometry is explicitly investigated by the formal perturbation method up to the second order. Two styles of RTI, convergent (i.e., gravity pointing inward) and divergent (i.e., gravity pointing outwards) configurations, compared with RTI in Cartesian geometry, are taken into account. Our explicit results show that the interface function in the cylindrical geometry consists of two parts: oscillatory part similar to the result of the Cartesian geometry, and non-oscillatory one contributing nothing to the result of the Cartesian geometry. The velocity resulting only from the non-oscillatory term is followed with interest in this paper. It is found that both the convergent and the divergent configurations have the same zeroth-order velocity, whose magnitude increases with the Atwood number, while decreases with the initial radius of the interface or mode number. The occurrence of non-oscillation terms is an essential character of the RTI in the cylindrical geometry different from Cartesian one.

Key words: cylindrical effect, Rayleigh-Taylor instability, variable density fluid

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, 马文芳, 王绪林. Cylindrical effects in weakly nonlinear Rayleigh–Taylor instability[J]. , 2015, 24(1): 15202-015202.

Liu Wan-Hai (刘万海), Ma Wen-Fang (马文芳), Wang Xu-Lin (王绪林). Cylindrical effects in weakly nonlinear Rayleigh–Taylor instability[J]. Chin. Phys. B, 2015, 24(1): 15202-015202.

参考文献 34

[1]	Rayleigh L 1883 Proc. London Math. Soc. 14 170
[2]	Taylor G 1950 Proc. R. Soc. Lond. A 201 192
[3]	Ataeni S and Guerrieri A 1993 Europhys. Lett. 22 603
[4]	Lafay M A, Creurer B L and Gauthier S 2007 Europhys. Lett. 79 64002
[5]	Abarzhi S I 2010 Europhys. Lett. 91 35001
[6]	Layzer D 1955 Astrophys. J. 122 1
[7]	Zhang Q 1998 Phys. Rev. Lett. 81 3391
[8]	Goncharov V N 2002 Phys. Rev. Lett. 88 134502
[9]	Mikaelian K O 2003 Phys. Rev. E 67 026319
[10]	Sohn S I 2003 Phys. Rev. E 67 026301
[11]	Wang L F, Ye W H, Fan Z F and Li Y J 2010 Europhys. Lett. 90 15001
[12]	Jacobs J W and Catton I 1988 J. Fluid Mech. 187 329
[13]	Haan S W 1991 Phys. Fluids B 3 2349
[14]	Liu W H, Wang L F, Ye W H and He X T 2012 Phys. Plasmas 19 042705
[15]	Liu W H, Wang L F, Ye W H and He X T 2013 Phys. Plasmas 20 062101
[16]	Li Y J, Ye W H and Wang L F 2010 Chin. Phys. Lett. 27 025203
[17]	Huo X H, Wang L F, Tao Y S, et al. 2013 Acta Phys. Sin. 62 144705 (in Chinese)
[18]	Xia T J, Cao Y G and Dong Y Q 2013 Acta Phys. Sin. 62 214702 (in Chinese)
[19]	Ye W H, Li Y J and Wang L F 2010 Chin. Phys. Lett. 27 025202
[20]	Remington B A, Arnett D, Drake R P and Takabe H 1999 Science 284 1488
[21]	Kifonidis K, Plewa T, Scheck L, Janka H T and Müller E 2006 Astron. Astrophys. 453 661
[22]	Remington B A, Arnett D, Drake R P and Takabe H 2006 Rev. Mod. Phys. 78 755
[23]	Drake R P 2006 High-Energy-Density Physics: Fundamentals, Inertial Fusion and Experimental Astrophysics (New York: Springer)
[24]	Bodner S 1974 Phys. Rev. Lett. 33 761
[25]	Sanz J, Ramírez J, Ramis R, Betti R and Town R P J 2002 Phys. Rev. Lett. 89 195002
[26]	Garnier J, Raviart P A, Cherfils-Clérouin C and Masse L 2003 Phys. Rev. Lett. 90 185003
[27]	Ye W H, Zhang W Y and He X T 2002 Phys. Rev. E 65 057401
[28]	He X T and Zhang W Y 2007 Eur. Phys. J. D 44 227
[29]	Wang L F, Ye W H, Sheng Z M, Don W S, Li Y J and He X T 2010 Phys. Plasmas 17 122706
[30]	Ye W H, Wang L F and He X T 2010 Phys. Plasmas 17 122704
[31]	Yu H and Livescu D 2008 Phys. Fluids 20 104103
[32]	Zhang Q and Graham M J 1998 Phys. Fluids 10 974
[33]	Sweeney M A and Perry F C 1981 J. Appl. Phys. 52 4487
[34]	Weir S T, Chandler E A and Goodwin B T 1998 Phys. Rev. Lett. 80 3763

Cylindrical effects in weakly nonlinear Rayleigh–Taylor instability

Cylindrical effects in weakly nonlinear Rayleigh–Taylor instability

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