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In order to better understand and predict the complex interface instability phenomena induced by non-uniform shock waves in practical engineering and scientific applications, a detailed investigation has been conducted on the interaction between a Mach reflection wave configuration and a planar gas interface. Particular attention is paid to the role of the Mach stem scale in governing the evolution of interface instability and the associated mechanisms of perturbation growth. Numerical simulations show that when the Mach reflection wave configuration interacts with the interface, the complex wave structures impart initial velocity perturbations onto the interface, thereby triggering instability. This process is further influenced by the non-uniform post-shock flow field, under which the initially perturbed interface gradually evolves into a concave cavity and subsequently into jet-like bubble structures. These patterns are notably different from the spike and bubble morphologies observed in classical Richtmyer-Meshkov instability. A systematic quantitative analysis of the perturbation amplitude reveals that the instability growth can be divided into two different stages: an initial linear growth stage and a nonlinear development stage. The transition between these stages is governed by interface deformation mechanisms, particularly the bending of the slip line intersecting the interface and the subsequent formation of the curl-up jet. When the shock strength and incidence angle of the Mach reflection configuration are kept constant, the Mach stem scale emerges as the decisive parameter controlling the characteristic time of slip line curling and jet development. The results show that during the linear stage, perturbation growth is primarily determined by shock strength and incidence angle, and is insensitive to the Mach stem scale. In contrast, during the nonlinear stage, the perturbation growth rate increases with the augmentation of Mach stem scales, highlighting the scale-dependent nature of the nonlinear stage. Furthermore, theoretical models are critically examined against numerical simulation results. While existing models can reasonably capture the initial velocity perturbations imprinted on the interface by the Mach reflection configuration, they are unable to combine the effects of Mach stem scale and the sustained driving influence of post-shock flow non-uniformities. This limitation underscores the need for improved theoretical descriptions. Overall, these findings provide new insights into the intrinsic coupling among shock strength, incidence angle, and Mach stem scale in determining the evolution of shock-induced interface instability. These insights not only deepen the fundamental understanding of Richtmyer-Meshkov-type instabilities in non-classical regimes but also provide valuable references for the development of predictive theoretical models and also for engineering applications such as inertial confinement fusion and high-speed propulsion systems.
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Keywords:
- Richtmyer-Meshkov instability /
- shock wave /
- Mach reflection /
- jet
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图 1 计算域示意图
Figure 1. Schematic of the computational domain.
图 2 (a) 实验与数值模拟圆柱绕射波系结构对比; (b) 实验与数值模拟圆柱绕射波系三波点轨迹对比
Figure 2. (a) Comparison of the wave configuration of the diffracted shock; (b) comparison of the triple point trajectories of the diffracted shock.
图 3 数值模拟和实验结果对比 (a) 界面演化图像; (b) 界面纵向高度h
Figure 3. Comparison of the numerical and experimental results: (a) The interface morphology; (b) the interface height h.
图 4 平面激波绕射刚体圆柱波系结构示意图
Figure 4. Schematic diagram of the planar shock diffracting around the cylinder.
图 5 三种情形入射马赫反射波系
Figure 5. Incident Mach reflection wave configuration for three cases.
图 6 马赫反射波系与平面界面作用过程的数值纹影图(左)和波系示意图(右) (a) t = –4 μs; (b) t = –1 μs; (c) t = 0 μs; (d) t = 5 μs
Figure 6. Numerical schlieren images (left) and wave configuration diagrams (right) of the flow field resulting from the interaction between a Mach reflection wave configuration and an interface: (a) t = –4 μs; (b) t = –1 μs; (c) t = 0 μs; (d) t = 5 μs.
图 7 马赫反射波系冲击诱导的界面法向速度沿界面分布规律
Figure 7. Longitudinal velocity along the interface imparted by the Mach reflection wave configuration.
图 8 情形Ⅰ界面演化图像
Figure 8. Evolution of the interface for case Ⅰ.
图 9 情形Ⅰ界面演化定量分析 (a) 界面扰动振幅; (b) 界面扰动增长率; (c) 气泡头部速度; (d) 凹腔肩部和底部的高度
Figure 9. Quantitative analysis of interface evolution for case Ⅰ: (a) Interface perturbation amplitude; (b) interface perturbation growth rate; (c) the velocity of the bubble head; (d) the height of the cavity shoulder and cavity bottom.
图 10 情形Ⅰ不同时刻的界面涡量云图 (a) t = 70 μs; (b) t = 200 μs; (c) t = 300 μs; (d) t = 400 μs
Figure 10. Contour of vorticity at different evolution time for case Ⅰ: (a) t = 70 μs; (b) t = 200 μs; (c) t = 300 μs; (d) t = 400 μs.
图 11 三种情形不同时刻的涡量云图
Figure 11. Contour of vorticity at different evolution time for three cases.
图 12 (a) 三种情形界面扰动振幅变化; (b) 三种情形无量纲扰动振幅变化
Figure 12. (a) Time variations of amplitude for three cases; (b) time variations of dimensionless amplitude for three cases.
图 13 三种情形界面形态对比 (a) τ = 8.85; (b) τ = 17.70; (c) τ = 26.62; (d) τ = 35.82
Figure 13. Comparison of the interface morphologies at different times for case I, II and III: (a) τ = 8.85; (b) τ = 17.70; (c) τ = 26.62; (d) τ = 35.82.
图 14 三种情形τ = 17.70时刻流场对称面速度分布
Figure 14. Velocity distribution in cavity symmetric plane at τ = 17.70 for three cases.
图 15 凹腔肩部、底部的高度变化与理论模型预测对比
Figure 15. Comparison of the height variations of the cavity shoulder and cavity bottom with the theoretical model predictions.
图 16 情形Ⅰ波后流场的速度非均匀性 (a) 滑移线内外侧速度分布; (b) 波后高速三角区对称面压力分布
Figure 16. Velocity non-uniformity in the post-wave flow field for case Ⅰ: (a) Velocity distribution on both sides of the slip line; (b) pressure distribution on the symmetry axis of the high-speed triangular area.
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[1] Richtmyer R D 1960 Commun. Pure. Appl. Math. 13 297
Google Scholar
[2] Meshkov E E 1969 Fluid Dyn. 4 101
[3] Smalyuk V A, Weber C R, Landen O L, et al. 2020 Plasma Phys. Controlled Fusion 62 014007
Google Scholar
[4] Chen Z, Yuan Y T, Wang L F, Tu S Y, Miao W Y, Wu J F, Ye W H, Deng K L, Hou L F, Wei M X, Li Y J, Yin C S, Dai Z S, Han X Y, Li Y S, Li Z Y, Zhang C, Pu Y D, Dong Y S, Yang D, Yang J M, Zheng W D, Zou S Y, Wang M, Ding Y K, Zhu S P, Zhang W Y, He X T 2024 Phys. Rev. Lett. 133 135101
Google Scholar
[5] 孙锦山 2009 力学进展 39 460
Sun J S 2009 Adv. Mech. 39 460
[6] 王裴, 何安民, 邵建立, 孙海权, 陈大伟, 刘文斌, 刘军 2018 中国科学: 物理学 力学 天文学 48 094608
Google Scholar
Wang P, He A M, Shao J L, Sun H Q, Chen D W, Liu W B, Liu J 2018 Sci. Sin. -Phys. Mech. Astron. 48 094608
Google Scholar
[7] Ren Z, Wang B, Xiang G, Zhao D, Zhang L 2019 Prog. Aeronaut. Sci. 105 40
Google Scholar
[8] Dimotakis P E 2005 Annu. Rev. Fluid Mech. 37 329
Google Scholar
[9] 邹立勇, 吴强, 李欣竹 2020 中国科学: 物理学 力学 天文学 50 104702
Google Scholar
Zou L Y, Wu Q, Li X Z 2020 Sci. Sin. -Phys. Mech. Astron. 50 104702
Google Scholar
[10] Zhang E L, Liao S F, Zou L Y, Zhai Z G, Liu J H, Li X Z 2024 J. Fluid Mech. 984 A49
Google Scholar
[11] Zhou Y, Sadler J D, Hurricane O A 2025 Annu. Rev. Fluid Mech. 57 197
Google Scholar
[12] Zhou Y 2017 Phys. Rep. 720–722 1
[13] 孙贝贝, 叶文华, 张维岩 2023 72 194701
Google Scholar
Sun B B, Ye W H, Zhang W Y 2023 Acta Phys. Sin. 72 194701
Google Scholar
[14] 张升博, 张焕好, 陈志华, 郑纯 2023 72 105202
Google Scholar
Zhang S B, Zhang H H, Chen Z H, Zheng C 2023 Acta Phys. Sin. 72 105202
Google Scholar
[15] Zhai Z G, Zou L Y, WU Q, Luo X S 2018 Proc. Inst. Mech. Eng. , Part C 232 2830
Google Scholar
[16] Xu A G, Zhang D J, Gan Y B 2024 Front. Phys 19 42500
Google Scholar
[17] 袁永腾, 涂绍勇, 尹传盛, 李纪伟, 戴振生, 杨正华, 侯立飞, 詹夏宇, 晏骥, 董云松, 蒲昱东, 邹士阳, 杨家敏, 缪文勇 2021 70 205203
Google Scholar
Yuan Y T, Tu S Y, Yin C S, Li J W, Dai Z S, Yang Z H, Hou L F, Zhan X Y, Yan J, Dong Y S, Pu Y D, Zou S Y, Yang J M, Miao W Y 2021 Acta Phys. Sin. 70 205203
Google Scholar
[18] Zhou Y 2024 Hydrodynamic Instabilities and Turbulence: Rayleigh-Taylor, Richtmyer-Meshkov, and Kelvin-Helmholtz Mixing (Cambridge: Cambridge University Press) pp242–246
[19] Thomas V A, Kares R J 2012 Phys. Rev. Lett. 109 075004
Google Scholar
[20] Ishizaki R, Nishihara K, Sakagami H, Ueshima Y 1996 Phys. Rev. E 53 R5592
Google Scholar
[21] Wang H, Zhai Z G, Luo X S 2022 J. Fluid Mech. 947 A42
Google Scholar
[22] 刘金宏, 邹立勇, 曹仁义, 廖深飞, 王彦平 2014 力学学报 46 475
Liu J H, Zou L Y, Cao R Y, Liao S F, Wang Y P 2014 Chin. J. Theor. Appl. Mech. 46 475
[23] Zou L Y, Liu J H, Liao S F, Zheng X X, Zhai Z G, Luo X S 2017 Phys. Rev. E 95 013107
Google Scholar
[24] Liao S F, Zhang W B, Chen H, Zou L Y, Liu J H, Zheng X X 2019 Phys. Rev. E 99 013103
Google Scholar
[25] Wang Z, Wang T, Bai J S, Xiao J X 2019 J. Turbul. 20 481
[26] He Y F, Peng N F, Li H F, Tian B L, Yang Y 2023 Phys. Rev. Fluids 8 63402.1
[27] “BlastFoam: A Solver for Compressible Multi-Fluid Flow with Application to High-Explosive Detonation. ” Synthetik Applied Technologies LLC. 2020
[28] Toro E F, Spruce M, Speares W 1994 Shock Waves 4 25
Google Scholar
[29] Li L F, Jin T, Zou L Y, Luo K, Fan J R 2023 Phys. Fluids 35 026104
Google Scholar
[30] Chen Y F, Jin T, Liang Z H, Zou L Y 2023 Phys. Fluids 35 114103
Google Scholar
[31] Bryson A E, Gross R W 1961 J. Fluid Mech. 10 1
Google Scholar
[32] 张恩来, 廖深飞, 邹立勇, 刘金宏, 李欣竹, 梁正虹 2024 中国科学: 物理学 力学 天文学 54 104704
Google Scholar
Zhang E L, Liao S F, Zou L Y, Liu J H, Li X Z, Liang Z H 2024 Sci. Sin. Phys. Mech. Astron 54 104704
Google Scholar
[33] 霍新贺, 王立锋, 陶烨晟, 李英骏 2013 62 144705
Google Scholar
Huo X H, Wang L F, Tao Y S, Li Y J 2013 Acta Phys. Sin. 62 144705
Google Scholar
[34] Gao Y L, Jiang Z L 2009 Explosion and Shock Waves 29 143
[35] Winkler K A, Chalmers J W, Hodson S W, Woodward P R, Zabusky N J 1987 Phys. Today 40 28
[36] Henderson L F, Vasilev E I, Ben-Dor G, Elperin T 2003 J. Fluid Mech. 479 259
Google Scholar
[37] Liang Y, Ding J C, Zhai Z G, Si T, Luo X S 2017 Phys. Fluids 29 086101
Google Scholar
[38] Zhai Z G, Liang Y, Liu L L, Ding J C, Luo X S, Zou L Y 2018 Phys. Fluids 30 046104
Google Scholar
[39] Zou L Y, Al-Marouf M, Cheng W, Samtaney R, Ding J C, Luo X S 2019 J. Fluid Mech. 879 448
Google Scholar
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