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Based on ideal compressible magnetohydrodynamics (MHD) equations, the interface instabilities induced by the interaction between planar shock wave and the light gas (Helium) cylinder under the influence of the magnetic fields with different directions are investigated numerically by using the CTU(corner transport upwind)+CT (constrained transport) algorithm. The numerical results elucidate the evolution of flow field characteristics and wave structures with and without magnetic field. Moreover, we examine the influence of the magnetic field direction on a characteristic scales (including the length, height and width of the central axis of gas cylinder), as well as the volume compressibility. Then, the mechanism of the magnetic field direction affecting the interface instability is studied in depth by integrating the analyses of the circulation, energy, velocity and magnetic force distribution within the flow field. The core of this study, is to explore the suppression mechanism of interface instability by magnetic field force. The results show that the magnetic pressure plays a crucial role in driving vorticity away from the interface, thereby reducing its deposition on the density interface. Simultaneously, it adheres to the divided vortex layer, thereby effectively isolating the influence of Richtmyer-Meshkov instability on the interface. On the other hand, the magnetic tension adheres to the separated vortex layer, and its direction is opposite to that of the vorticity generated by the shear of interface velocity. This action effectively suppresses the Kelvin-Helmholtz instability and the rolling-up of vortices on the density interface. Additionally, under the control of a longitudinal magnetic field, the direction of magnetic tension is opposite to the direction of the central jet, effectively suppressing the development of Rayleigh-Taylor instability.
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Google Scholar
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表 1 气体参数
Table 1. Gas parameters.
Gas Density
ρ/(kg·m–3)Specific-heat ratio γ Molar mass
M/(g·mol–1)Speed of sound
cA/(m·s–1)Air 1.176 1.40 28.96 347 He 0.162 1.67 4.00 1021 表 2 不同工况下的初始条件
Table 2. The initial conditions of different cases.
Case a $\beta^{-1}$ Magnetic field direction 1 0.8 0 — 2 0.8 0.0005 Transverse 3 0.8 0.0005 Longitudinal -
[1] Richtmyer R D 1960 Commun. Pure Appl. Math. 13 297
Google Scholar
[2] Meshkov E E 1969 Fluid Dyn. 4 101
[3] Kelvin L 1871 Philos. Mag. 42 362
Google Scholar
[4] Helmholtz H V 1868 Monthly Reports of the Royal Prussian Academy of Philosophy in Berlin 23 215
[5] Rayleigh L 1882 Proc. R. Math. Soc. s1-14 170
Google Scholar
[6] Taylor S G 1950 Proc. R Soc. London Ser. A 201 192
Google Scholar
[7] Zheng C, Zhang H H, Chen Z H, Wu W T, Sha S 2019 Phys. Fluids 31 086104
Google Scholar
[8] 林震亚, 张焕好, 陈志华, 刘 迎 2017 爆炸与冲击 37 748
Google Scholar
Lin Z Y, Zhang H H, Chen Z H, Liu Y 2017 Explo. Shock Waves 37 748
Google Scholar
[9] Haas J F, Sturtevant B 1987 J. Fluid Mech. 181 41
Google Scholar
[10] Jacobs J 1993 Phys. Fluids 5 2239
Google Scholar
[11] Layes G, Metayer O L 2007 Phys. Fluids 19 042105
Google Scholar
[12] Jacobs J and Krivets V 2005 Phys. Fluids 17 034105
Google Scholar
[13] Zhai Z G, Wang M H, Si T, Luo X S 2014 J. Fluid Mech. 757 800
Google Scholar
[14] Wang X S, Yang D G, Wu J Q, Luo X S 2015 Phys. Fluids 27 064104
Google Scholar
[15] Bai J S, Zou L Y, Wang T, Liu K, Huang W B, Liu J G, Li P, Tan D W, Liu C L 2010 Phys. Rev. E 82 056318
Google Scholar
[16] Si T, Long T, Zhai Z G, Luo X S 2015 J. Fluid Mech. 784 225
Google Scholar
[17] Luo X S, Ding J C, Wang M H, Zhai Z G, Si T 2015 Phys. Fluids 27 091702
Google Scholar
[18] Lei F, Ding J C, Si T, Zhai Z G, Luo X S 2017 J. Fluid Mech. 826 819
Google Scholar
[19] Ding J C, Si T, Yang J M, Lu X Y, Zhai Z G, Luo X S 2017 Phys. Rev. Lett. 119 014501
Google Scholar
[20] Liang Y, Ding J C, Zhai Z G, Si T, Luo X S 2017 Phys. Fluids 29 086101
Google Scholar
[21] 李冬冬, 王革, 张斌 2018 物理学报 67 184702
Google Scholar
Li D D, Wang G, Zhang B 2018 Acta Phys. Sin. 67 184702
Google Scholar
[22] Guo X, Zhai Z G, Si T, Luo X S 2019 Phys. Rev. Fluids 4 092001(R
[23] 王显圣, 司廷, 罗喜盛, 杨基明 2012 力学学报 44 664
Google Scholar
Wang X S, Si T, Luo X S, Yang J M 2012 Acta Mech. Sin. 44 664
Google Scholar
[24] 张升博, 张焕好, 陈志华, 郑纯 2023 物理学报 72 105202
Google Scholar
Zhang S B, Zhang H H, Chen Z H, Zheng C 2023 Acta Phys. Sin. 72 105202
Google Scholar
[25] Zhang S B, Zhang H H, Chen Z H, Zheng C 2023 Phys. Plasmas 30 022107
Google Scholar
[26] Samtaney R 2003 Phys. Fluids 15 53
Google Scholar
[27] Wheatley V, Samtaney R, Pullin D I, Gehre R M 2014 Phys. Fluids 26 016102
Google Scholar
[28] Sano T 2021 Astrophys. J. 920 29
Google Scholar
[29] 李源, 罗喜胜 2014 计算物理 31 659
Google Scholar
Li Y, Luo X S 2014 Chin. J. Comput. Phys. 31 659
Google Scholar
[30] Qiu Z Y, Wu Z W, Cao J T, Li D 2008 Phys. Plasmas 15 042305
Google Scholar
[31] Tapinou K C, Wheatley V, Bond D, Jahn I 2023 Phys. Plasmas 30 022707
Google Scholar
[32] Tapinou K C, Wheatley V, Bond D 2023 J. Fluid Mech. 977 A19
Google Scholar
[33] Rinderknecht H G, Amendt P, Wilks S, Collins G 2018 Plasma Phys. Controlled Fusion 60 064001
Google Scholar
[34] Xu A G, Zhang G C, Gan Y B, Chen F, Yu X J 2012 Front. Phys. 7 582
Google Scholar
[35] Gan Y B, Xu A G, Lai H L, Li W, Sun G L, Succi S 2022 J. Fluid Mech. 951 A8
Google Scholar
[36] Zhang D J, Xu A G, Zhang Y D, Gan Y B, Li Y J 2022 Phys. Fluids 34 086104
Google Scholar
[37] Zhang Y D, Xu A G, Chen F, Lin C D, Wei Z H 2022 AIP Adv. 12 035347
Google Scholar
[38] Song J H, Xu A G, Miao l, Chen F, Liu Z P, Wang L F, Wang N F, Hou X 2024 Phys. Fluids 36 016107
Google Scholar
[39] 沙莎, 张焕好, 陈志华, 郑纯, 吴威涛, 石启陈 2020 物理学报 69 184701
Google Scholar
Sha S, Zhang H H, Chen Z H, Zheng C, Wu W T, Shi Q C 2020 Acta Phys. Sin. 69 184701
Google Scholar
[40] Zhang H H, Zheng C, Aubry N, Wu W T, Chen Z H 2020 Phys. Fluids 32 116104
Google Scholar
[41] Colella P 1990 J. Comput. Phys. 87 171
Google Scholar
[42] Londrillo P, Zanna L D 2004 J. Comput. Phys. 195 17
Google Scholar
[43] Shin M, Stone J M, Snyder G F 2008 Astrophys. J. 680 336
Google Scholar
[44] Saltzman J 1994 J. Comput. Phys. 115 153
Google Scholar
[45] Colella P, Woodward P 1984 J. Comput. Phys. 54 17
[46] Evans C, Hawley J 1988 Astrophys J. 322 659
[47] Lin Z Y, Zhang H H, Chen Z H, Liu Y, Hong Y J 2017 Int. J. Comput. Fluid D. 31 21
Google Scholar
[48] Giordano J, Burtschell Y 2006 Phys. Fluids. 18 036102
Google Scholar
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