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摘要: 固体界面的不稳定性增长是武器内爆物理、惯性约束聚变点火和材料动力学行为研究等工程和科学领域中的关键物理过程, 它可能导致固体表面出现轻重介质相互侵入、物质微喷射乃至湍流混合等复杂的物理现象, 对其发展规律的研究具有重要的意义. 本文在第二、三章分别介绍了对固体界面Richtmyer-Meshkov (RM) 和Rayleigh-Taylor (RT) 不稳定性发展规律的研究现状, 总结了现有的不稳定性增长理论模型并探讨了其局限性. 与纯流体界面不稳定性增长所不同的是, 由于固体材料存在强度, 其界面不稳定性发展过程中扰动增长的部分能量会被强度这一耗散因素转化为晶格的热能, 从而降低扰动增长速率乃至抑制扰动增长, 因此如何衡量动态加载过程中固体的强度效应成为认识其不稳定增长规律的关键. 另一方面, 由于固体界面不稳定性的发展结果蕴含着材料的本构、状态方程等信息, 人们提出可以应用不稳定性的增长规律来获取材料的动态屈服强度、校验材料的高压本构模型和抑制不稳定性的增长, 本文在第四章中对这部分内容进行了介绍, 并指出建立能精确描述不稳定性增长现象与材料性质间“关联性机制”的理论模型是成功进行应用的关键. 在这些基础上, 本文于第五章展望了该领域存在的机遇和挑战.Abstract: The growth of interface instability in solids is a critical phenomenon affecting various fields of engineering and science, including implosion physics, inertial confinement fusion ignition, and the dynamic behavior of materials. This instability can lead to complex phenomena such as the interpenetration of light and heavy media at solid surfaces, material micro-jetting, and turbulent mixing, highlighting the significance of understanding its underlying mechanisms. This paper reviews the current research status of Richtmyer-Meshkov (RM) and Rayleigh-Taylor (RT) instabilities at solid interfaces in Chapters 2 and 3. We summarize existing theoretical models of instability growth and discuss their limitations. Unlike the instability growth observed in pure fluid interfaces, solid materials possess inherent strength, which enables some of the energy from perturbation growth to be transformed into lattice thermal energy through dissipative mechanisms. This energy conversion reduces the rate of perturbation growth and may even suppress the development of instabilities. Consequently, understanding the effects of material strength under dynamic loading conditions is crucial for comprehending instability growth behavior. Moreover, the outcomes of solid interface instability are indicative of various material properties, including constitutive relationships and equations of state. Researchers have proposed that instability growth can be leveraged to determine the dynamic yield strength of materials, validate high-pressure constitutive models, and mitigate instability growth. Chapter 4 focuses on this aspect, emphasizing the need to establish a theoretical model that accurately describes the "correlation mechanism" between instability phenomena and material properties for effective applications. Building on these foundations, Chapter 5 explores future opportunities and challenges in this field.
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图 1 典型的流动不稳定性现象. (a) 平面激波作用下空气/SF6界面的演化(Collins & Jacobs, 2002); (b) 水杯中轻重流体间的混合; (c) 火箭发动机推进剂喷注与燃烧; (d) 大气中环流的云涡
图 3 高爆炸药 (HE) 产生的平面冲击波加载到初始有正弦型扰动的样品前 (a) 和加载后 (b) 界面的几何构型示意图 (Buttler et al. 2012)
图 4 冲击波加载到两个理想弹性固体分界面后, (a) 界面无量纲扰动周期T/T0随材料密度比ρ2/ρ1变化,不同符号代表不同材料性质组合, 实线代表公式 (5) 的理论预测 (α=1.55); (b) 振荡振幅η (圆圈)、v0T/2π (三角形)、最大振荡速度 (正方形) 随振荡周期T的变化, 实线代表经典情况 (G=0) 时扰动速度随T的演化
图 5 理想弹性固体在冲击加载后界面振荡周期T/T0随材料密度比ρ2/ρ1变化. 实线代表数值结果, 长虚线代表公式 (8) 的理论预测, 短虚线代表公式 (5) 理论预测, 点划线通过在复平面内定位极点计算极点频率得到.
图 6 PAGOSA模拟得到的Cu界面RM扰动增长结果. (a) 界面随时间演化图, 黄色为Cu材料, 黑色为气体, 从上至下四组图像的初始扰动分别为kη0=0.125, 0.18, 0.22和0.4; (b) 无量纲的尖钉极值振幅 (实心符号)、气泡极值振幅 (空心符号) 随无量纲尖钉极值增长速度的变化, 虚线代表CD=0.24时公式 (13) 理论预测
图 7 (a) 真空与弹塑性固体界面RM扰动增长问题初始构型示意图; (b) 模拟得到的尖钉极值振幅随极值增长速率变化图, 实线代表Cp=0.29时公式 (11) 理论预测
图 12 PBX9501炸药爆轰驱动Cu靶后 (a) 殷建伟模拟得到的尖钉相对自由面速度随时间发展结果 (b) Prime模拟 (实线) 和Piriz 理论预测 (虚线) 得到的尖钉绝对速度随时间发展结果
图 13 炸药爆轰加载下柱面金属的RM扰动增长研究. (a) 实验和计算构型示意图, (b) 钢壳内爆过程中的实验结果照相图像, (c) 扰动振幅随时间发展的数值和实验结果对比图 (d) 钢壳内爆过程中数值模拟图像
图 15 基于PHELIX平台开展的磁驱柱面RM扰动增长研究. (a) 实验构型示意图, (b) 锡靶内爆过程中质子照相图像, 其内界面预制有不同的初始扰动 (kη0=0.1,0.2,0.3), (c) 锡靶内爆过程中扰动振幅随时间的变化, 实线代表Flag程序模拟结果, 实心点代表质子照相实验结果, (d) Flag程序模拟得到的锡靶界面扰动增长图像 (kη0=0.3)
图 17 炸药爆轰加载钢体球壳后的界面扰动增长结果: (a) 实验回收得到的样品照相图像, 上方为外层球壳, 下方为内层球壳, h0代表球壳的初始厚度; (b) 钢体球壳在两个不同时刻的伽玛断层成像结果, 上方为t=2 μs时刻, 下方为内半径汇聚到20 mm的时刻, (c) 数值模拟得到的1/8球壳随时间演化示意图, 其中t=0 μs图像代表初始计算构型示意图, (b) 球壳内界面速度随时间演化图, 其中黑线代表实验结果, 红线和蓝线分别代表采用Glushak和Mises弹塑性本构模型的计算结果
图 18 物质界面处RT扰动发展示意图. (a) 物质界面处RT扰动发展几何构型示意图, (b) PBX-9404炸药爆轰加载Al板的实验装置示意图, (c) Al板界面RT不稳定性发展过程示意图
图 21 弹塑性厚平板与理想流体界面的RT扰动发展过程中 (A=1, Kh>>1), (a) 临界发生弹塑性转变和不稳定增长时, 无量纲初始扰动振幅
$ \widehat{\mathrm{\xi }} $ 随无量纲波长$ \widehat{\mathrm{\lambda }} $ 的变化. (b) 不同初始扰动条件下, 无量纲扰动振幅z随无量纲时间τ的演化
图 23 (a) 电磁加载“铝飞层—聚乙烯夹层—铜靶”三层套筒结构后产生的RTI现象. 前两幅图分别为5微秒和8.5微秒时的数值模拟结果, 后两幅图为x光照相结果, (b) 电磁直接加载外表面预制有扰动的套筒X光照相结果
图 24 基于FP-1平台的磁驱柱面RTI实验结果与计算结果对比, (a) 套筒内、外界面位置随时间变化, (b) 界面扰动振幅随时间变化, 其中虚线代表不含强度效应的理论预测 (公式), 实线为考虑固体强度效应后的理论预测 (公式)
图 26 气炮驱动Cu飞片撞击Ce样品后的 (a) X光照相图像, F0代表初始静态图像, F1到F5代表时间间隔为153.4 ns的动态图像, (b) 尖钉和自由面的速度剖面, 黑线代表实验PDV测速结果, 蓝线代表FLAG程序数值模拟结果 (Y=0.13 GPa)
图 27 采用FLAG程序模拟Cu飞片撞击Ce样品得到的界面扰动图像 (t=950 ns), 其中Ce样品采用理想弹塑性本构模型. (a) 初始计算构型示意图, (b) Y=0.26 GPa计算结果, (c) Y=0.13 GPa计算结果, (d) Y=0.065 GPa计算结果
图 28 PBX9501炸药爆轰加载Cu样品后的RM扰动增长结果. (a) 采用FLAG程序模拟得到的尖钉速度随时间变化结果 (kη0=0.39), 不同线型代表模拟中对Cu材料预设不同的屈服强度 (Y=0.4−1.6 GPa), (b) 当取Y=0.53 GPa, 尖钉极值增长速度随初始扰动变化的模拟 (实线) 与实验结果 (红点) 对比图
图 29 (a) 基于Omega激光实验得到的6061-T6铝合金界面RT扰动增长因子随时间变化, 五个黑色圆点代表不同时刻的实验结果, 不同线型代表模拟中对材料预设不同屈服强度 (Y=0−1.2 GPa) 的计算结果, (b) 基于VNIIEF柱面内爆实验得到的Cu界面RT扰动增长因子随时间变化, 红色圆圈代表不同时刻的实验结果, 绿色虚线和黑色实线代表分别代表取Y=0.15 GPa和0.18 GPa时的数值模拟结果
图 30 气炮驱动 Cu界面RM扰动增长后的尖钉位移随时间演化结果, 符号代表实验结果, 线型代表对Cu材料采用不同本构模型时的数值模拟结果. (a) 采用理想弹塑性本构模型, Y=0.1, 0.5, 1 GPa时的数值与实验结果对比图, (b) 采用ZA、JC、PTW、SGL本构模型时的数值与实验结果对比图
图 31 (a) Omega激光器准等熵驱动钒样品RT不稳定增长实验装置示意图, (b) 扰动增长因子随时间的变化, 其中方框代表Omega实验数据, 从上到下的棕色、绿色、蓝色、紫色虚线分别代表采用理想流体、SG、PTW和多尺度本构模型进行二维数值模拟的计算结果, 绿色和蓝色实线分别代表调整原始输入参数后的SG和PTW模型预测结果
图 32 (a) 爆轰加载后金属Sn样品的熔化破碎密度图像 (陈永涛等 2013), (b) 磁驱动柱面Sn样品汇聚过程中的组分分布 (t=11.42 μs), 红色为液相, 绿色为伽马相, 蓝色为β相 (Rousculp et al. 2016)
图 34 : 对数坐标系下三种材料的
$\bar{\varepsilon}_p^{\max }$ 随$ k\eta _{sp}^{{\text{max}}} $ 的变化及定标关系. (a) Cu, (b) Al, (c) 钢, 图中紫色实线代表$ \overline \varepsilon _{_{\text{p}}}^{{\text{max}}} = 1.08{({\text{k}}\eta _{sp}^{\max })^{0.65425}} $ 表 1 : 固体界面RM扰动增长理论模型总结
理论模型 无量纲尖钉极值振幅与无量纲尖钉极值增长速度关系 斜率(拟合系数) 截距 Piriz2008 $ {{k}}\eta _{{\text{sp}}}^{\max } = {{k}}{\eta _0} + {C_p}\dfrac{{{\rho _0}\mathop {\eta _0^2}\limits^ \cdot }}{Y} $ $ {C_p} = 0.29 $ $ {\text{k}}{\eta _0} $ Dimonte2011 $ {{k}}\eta _{{\text{sp}}}^{\max } = 0.08 + {C_D}\dfrac{{{\rho _0}{{{\text{(v}}_{{\mathrm{sp}}}^{\max })}^2}}}{Y} $ $ {C_D} = 0.24 $ 0.08 Buttler2012 $ {k}{\eta }_{\text{sp}}^{\mathrm{max}}={k}{\eta }_{0} + {C}_{B} \left(\dfrac{1{-}\Delta \text{V/(2D)}}{1-\Delta \text{V/D}}\right)^{2}\dfrac{{\rho }_{\text{0}}\stackrel{\cdot }{{\eta }_{0}^{2}}}{Y} $ $ {C_B} = 0.29 $ $ {\text{k}}{\eta _0} $ Mikaelian2013 $ {{k}}\eta _{{\text{sp}}}^{\max } = {{k}}{\eta _0} + {C_M}\dfrac{{({\rho ^{\text{h}}} + {\rho ^{\text{l}}})\mathop {\eta _0^2}\limits^ \cdot }}{{{Y^{\text{h}}} + {Y^{\text{l}}}}} $ $ {C_M} = 0.33 $ $ {\text{k}}{\eta _0} $ 殷建伟2018 $ {{k}}\eta _{{\text{sp}}}^{\max } = {C_Y}\dfrac{{{\rho _0}{{({\text{v}}_{{\mathrm{sp}}}^{\max })}^2}}}{Y} $ $ {C_Y} = 0.3 $ 0 陈潜2019 $ {{k}}\eta _{{\mathrm{sp}}}^{{\text{max}}} = \dfrac{Y}{{4\sqrt 3 kG}} + {C_C}\dfrac{{{\rho _S}\mathop {\eta _0^2}\limits^ \cdot }}{Y} $ $ {C_C} = {\text{f}}(A) $ $ \dfrac{Y}{{4\sqrt 3 kG}} $ 
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表 2 : 固体界面 RT 扰动增长理论模型总结
模型 界面运动方程/色散关系 渐进界面扰动增长率 (t$ \to \mathrm{\infty } $) Remington2004: 任意A, 任意kh, 显含应变率 $ \begin{gathered} {\gamma ^2} + 2{k^2}{\nu _{{\mathrm{eff}}}}\gamma + k \times \tanh (kh)\times \left(\dfrac{{kG}}{\rho } - Ag\right) = 0 \\ {{\text{v}}_{{\mathrm{eff}}}} = Y/(\sqrt 6 \rho \mathop \varepsilon \limits^ \cdot ) \\ \end{gathered} $ $ \gamma = {\nu _{{\mathrm{eff}}}}{{{k}}^2}\left[{\left(1 - \dfrac{{\tanh (kh)\times (kG/\rho - Ag)}}{{\nu _{_{eff}}^2{k^3}}}\right)^{1/2}} - 1\right] $ Piriz 2009: 固体/理想流体界面, A=1,kh>>1 $ \mathop \eta \limits^{ \cdot \cdot } = \left\{ \begin{gathered} {{k}}g(\eta + {\eta _0})- 2{k^2}G\eta /\rho \begin{array}{*{20}{c}} ,&{\eta \leqslant {\eta _p}} \end{array} \\ {{k}}g(\eta + {\eta _0})- \alpha Yk/\rho \sqrt 3 \begin{array}{*{20}{c}} ,&{\eta \geqslant {\eta _p}} \end{array} \\ \end{gathered} \right. $
$ \gamma = \sqrt {{{k}}g} $Piriz 2014: 固体/粘性流体界面, 任意A, kh>>1 $ \begin{gathered} \mathop \eta \limits^{ \cdot \cdot } + \dfrac{{2\mu {k^2}}}{{{\rho _2} + {\rho _1}}}\mathop \eta \limits^ \cdot = \\ \left\{ \begin{gathered} {\text{Ak}}g(\eta + {\eta _0})- 2{k^2}G\eta /({\rho _2} + {\rho _1})\begin{array}{*{20}{c}} ,&{\eta \leqslant {\eta _p}} \end{array} \\ {\text{Ak}}g(\eta + {\eta _0})- \sqrt 3 Yk/({\rho _2} + {\rho _1})\begin{array}{*{20}{c}} ,&{\eta \geqslant {\eta _p}} \end{array} \\ \end{gathered} \right. \\ \end{gathered} $ $ \gamma = \sqrt {\dfrac{{{\mu ^2}{k^4}}}{{{{({\rho _2} + {\rho _1})}^2}}} + A{\text{k}}g} - \dfrac{{\mu {k^2}}}{{({\rho _2} + {\rho _1})}} $ Piriz 2019: 固体/理想流体界面, 任意A,任意kh $ {\left(\dfrac{{kg}}{{{\gamma ^2}}}\right)^2} - 1 = \left(\dfrac{{kg}}{{{\gamma ^2}}} + 1\right)\dfrac{{1 - A}}{{1 + A}}[\dfrac{{kg}}{{{\gamma ^2}}} + \coth (kh)] $ $ \begin{gathered} {\gamma _{1,2}} = \pm \sqrt {\dfrac{{2A{\text{kg}}}}{{1 + A + (1 - A)\coth (kh)}}} \\ {\gamma _{3,4}} = \pm \sqrt { - kg} \\ \end{gathered} $
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4 附录 表3: 符号-物理量对照表
符号 对应物理量 符号 对应物理量 η 界面扰动振幅 G 剪切模量 η0 界面初始扰动振幅 Y 屈服强度 η0* 界面在受到冲击波加载后刚开始进行不稳定增长时的振幅 μ 动力学粘性系数 $ \eta _{{\text{s}}p}^{\max } $ 尖钉的极值振幅 ν 界面两侧流体的平均粘性系数 λ 界面扰动波长 νeff 固体的等效晶格粘度 λ0 界面初始扰动波长 μ0 真空磁导率 λc RT不稳定增长的临界波长 I 电流强度 k 扰动波数 γ 界面扰动增长率 kc RT不稳定增长的临界波数 γ0 格林艾森系数 A Atwood数 cv 等容比热容 ρ0 材料初始密度 σ 表面张力系数 ρ 冲击波作用后的材料密度 c0 零压下的体波声速 Fy 作用于界面法向方向上的力 Dij 应变率张量 ω 振荡频率 Sij 偏应力张量 T 振荡周期 ΔV 冲击波经过后物质界面的速度增量 p 压力 D 冲击波的传播速度 ε 应变 R 套筒外半径 $ \mathop \varepsilon \limits^ \cdot $ 应变率 h 平板的厚度 C 数值拟合常数 g 重力加速度
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[1] 陈永涛, 洪仁楷, 汤铁钢, 等. 2016. 熔化状态下锡样品微喷射现象的诊断. 高压物理学报, 30(4): 323-327. doi: 10.11858/gywlxb.2016.04.009 [2] 陈永涛, 任国武, 汤铁钢, 等. 2013. 爆轰加载下金属样品的熔化破碎现象诊断. 物理学报, 62(11): 116202. doi: 10.7498/aps.62.116202 [3] 郝鹏程, 冯其京, 胡晓棉. 2016. 内爆加载金属界面不稳定性的数值分析. 爆炸与冲击, 36(6): 739-744. doi: 10.11883/1001-1455(2016)06-0739-06 [4] 经福谦, 胡思得. 1991. 核武器研制中的若干物理问题. 20 (8): 0-0. [5] 李碧勇, 彭建祥, 谷岩, 等. 2020. 爆轰加载下高纯铜界面 Rayleigh-Taylor 不稳定性实验研究. 物理学报, . [6] 罗喜胜, 翟志刚, 司廷, 等. 2014. 激波诱导下的气体界面不稳定性实验研究. 力学进展, 44(1): 260-290. doi: 10.6052/1000-0992-14-028 [7] 刘军, 冯其京, 周海兵. 2014. 柱面内爆驱动金属界面不稳定性的数值模拟研究. 物理学报, 63(15): 155201. doi: 10.7498/aps.63.155201 [8] 叶雁, 李军, 朱鹏飞, 等. 2013. 脉冲X光照相在微物质喷射诊断中的应用. 高压物理学报, 27(3): 398-402. doi: 10.11858/gywlxb.2013.03.013 [9] 陆逸然, 王晋军. 2024. 高效合成射流激励器研究进展及展望. 力学进展, 54(1): 61-85. doi: 10.6052/1000-0992-23-038 [10] 潘昊, 胡晓棉, 吴子辉, 等. 2012. 铈低压冲击相变数值模拟研究. 物理学报, 61(20): 351-357. doi: 10.7498/aps.61.206401 [11] 任九生, 程昌钧. 2009. 超弹性材料的不稳定性问题. 力学进展, 39(5): 566-575. doi: 10.3321/j.issn:1000-0992.2009.05.006 [12] 汤文辉, 张若棋. 2008. 物态方程理论及计算概论(第二版). 北京: 高等教育出版社. [13] 谭华. 2007. 实验冲击波物理导引. 国防工业出版社. [14] 王洪建, 冯永祯, 罗笔瀚, 等. 2023. 强激光加载下金属材料微喷诊断实验研究进展. 强激光与粒子束, 35(10): 5-16. doi: 10.11884/HPLPB202335.230225 [15] 王立锋, 叶文华, 陈竹, 等. 2021. 激光聚变内爆流体不稳定性基础问题研究进展, 33 (1): 012001-012001. [16] 王涛, 汪兵, 林健宇, 等. 2020. 柱形汇聚几何中内爆驱动金属界面不稳定性. 爆炸与冲击, 40(5): 1-12. doi: 10.11883/bzycj-2019-0150 [17] 殷建伟, 潘昊, 吴子辉, 郝鹏程, 段卓平, 胡晓棉. 2017. 爆轰驱动Cu界面的Richtmyer-Meshkov 扰动增长稳定性. 物理学报, 66(20): 204701 doi: 10.7498/aps.66.204701 [18] 殷建伟. 2018. 强度介质界面的 Richtmyer-Meshkov 扰动增长规律研究. 北京理工大学博士论文. [19] 叶雁, 李军, 朱鹏飞, 等. 2013. 脉冲X光照相在微物质喷射诊断中的应用. 高压物理学报, 27(3): 398-402. doi: 10.11858/gywlxb.2013.03.013 [20] 朱建士, 胡晓棉, 王裴, 等. 2010. 爆炸与冲击动力学若干问题研究进展. 力学进展, 40(4): 400-423. doi: 10.6052/1000-0992-2010-4-J2009-144 [21] 郑宇轩, 周风华, 胡时胜, 等. 2016. 固体的冲击拉伸碎裂. 力学进展, 46(1): 506-540. doi: 10.6052/1000-0992-16-004 [22] 张维岩, 叶文华, 吴俊峰, 等. 2014. 激光间接驱动聚变内爆流体不稳定性研究. 中国科学: 物理学力学天文学, 1-23. [23] 章征伟. 2020. 磁驱动固体套筒内爆理论与实验研究. 中国工程物理研究院. [24] 章征伟, 魏懿, 孙奇志, 等. 2016. 材料强度对电磁驱动固体套筒内爆过程的影响. 强激光与粒子束, 28(4): 156-160. doi: 10.11884/HPLPB201628.125017 [25] Aglitskiy Y, Velikovich A L, Karasik M, et al. 2010. Basic hydrodynamics of Richtmyer-Meshkov-type growth and oscillations in the inertial confinement fusionrelevant conditions. Phil TransR Soc A, 368: 1739-1768. doi: 10.1098/rsta.2009.0131 [26] Al’tshuler L V, Il’kaev R I, Fortov V E. 2021. Use of powerful shock and detonation waves to study extreme states of matter. Physics-Uspekhi, 64(11): 1167. [27] Arinin V A, Baltakov F N, Burenkov O M. 2004. A series of joint VNIIEF/LANL experiments on radiographic studies of perturbation growth at the interface of a polyethylene liner with polyethylene or water. Proc. MG-X, 348-353. [28] Atchison W L, Zocher M A, Kaul A M. 2008. Studies of material constitutive behavior using perturbation growth in explosive and magnetically driven liner systems. Russian Journal of Physical Chemistry B, 2(3): 387-401. doi: 10.1134/S199079310803010X [29] Avdeev P A, Artamonov M V, Bakhrakh S M. 2001. LEGAK program complex aimed to compute nonsteady-state flows of multi-component continuum media and the principles for realization of this complex on the distributed-memory multiprocessor computer. Ser. : Math. modeling physical processes, 3: 14. [30] Bakhrakh S M, Drennov O B, Kovalev N P, et al. 1997. Hydrodynamic instability in strong media. UCRL-CR-126710. [31] Bakhrakh S M, Velichko S V, Spiridonov V F, et al. 2004. LEGAK-3D technique aimed to compute 3D nonsteady-state flows of multi-component continuum media and the principles for its realization on the distributed-memory multiprocessor computer. Ser. : Math. modeling physical processes, 4: 41. [32] Barnes J F, Blewett P J, Mc Queen R G, el al. 1974. Taylor instability in solids. Journal of Applied Physics, 45(2): 727-732. doi: 10.1063/1.1663310 [33] Bell G I. 1951. Taylor instability on cylinders and spheres in the small amplitude approximation. Report No. LA-1321, LANL,1321: 91873-9. [34] Bellman R, Pennington R H. 1954. Effects of surface tension and viscosity on Taylor instability. Quarterly of Applied Mathematics, 12(2): 151-162. doi: 10.1090/qam/63198 [35] Betti R, Hurricane O A. 2016. Inertial-confinement fusion with lasers. Nature Physics, 12(5): 435-448. [36] Buttler W T, Oró D M, Preston D L, et al. 2012. Unstable Richtmyer–Meshkov growth of solid and liquid metals in vacuum. Journal of Fluid Mechanics, 703: 60-84. doi: 10.1017/jfm.2012.190 [37] Buyko A M, Zmushko V V, Mokhov V N, et al. 2005. Dynamic copper and polyethylene strengths in shockless loading to 15 GPa according to the data of explosive magnetic experiments with cylindrical three-layer liner systems//2005 IEEE Pulsed Power Conference. IEEE, : 1242-1245. [38] Buyko A M, Gorbachev Y N, Zmushko V V, et al. 2002. Study of dynamic strength of copper in joint VNIIEF/LANL liner experiments on capacitor bank ATLAS (RUS-6 7). Proc. Int. Conf. Megagauss-9. 718-724. [39] Buyko A M, Zmushko V V, Atchison W L, et al. 2008. Results and prospects of material strength studies on electrophysical facilities based on perturbation growth in liner systems. IEEE transactions on plasma science, 36(1): 104-111. [40] Casner A, Masse L, Delorme B, et al. 2014. Progress in indirect and direct-drive planar experiments on hydrodynamic instabilities at the ablation front. Phys Plasmas, 21: 122702. doi: 10.1063/1.4903331 [41] Casner A, Smalyuk V A, Masse L. 2012. Designs for highly nonlinear ablative Rayleigh-Taylor experiments on the National Ignition Facility. Physics of Plasmas, 19(08): 2708-2717. [42] Casner A, Galmiche D, Huser G, et al. 2009. Indirect drive ablative Rayleight-Taylor experiments with rugby hohlraums on OMEGA. Phys Plasmas, 16: 092701. doi: 10.1063/1.3224027 [43] Casey D T, Woods D T, Smalyuk V A, et al. 2015. Performance and mix measurements of indirect drive Cu-doped Be implosions. Physical Review Letters, 114(20): 205002. doi: 10.1103/PhysRevLett.114.205002 [44] Chandrasekhar S. 2013. Hydrodynamic and hydromagnetic Stability. Courier Corporation. [45] Chen Q, Li L, Zhang Y, et al. 2019. Effects of the Atwood number on the Richtmyer-Meshkov instability in elastic-plastic media. Physical Review E, 99(5): 053102. [46] Collins B D, Jacobs J W. 2002. PLIF flow visualization and measurements of the Richtmyer–Meshkov instability of an air/SF6 interface. Journal of Fluid Mechanics, 464: 113-136. doi: 10.1017/S0022112002008844 [47] Colvin J D, Legrand M, Remington B A, et al. 2003. A model for instability growth in accelerated solid metals. Journal of applied physics, 93(9): 5287-5301. doi: 10.1063/1.1565188 [48] De Resseguier T, Prudhomme G, Roland C, et al. 2020. Material ejection from surface defects in laser shock-loaded metallic foils. AIP Conference Proceedings, 2272 (1). [49] Dimonte G, Gore R, Schneider M. 1998. Rayleigh-Taylor instability in elastic-plastic materials. Physical review letters, 80(6): 1212. doi: 10.1103/PhysRevLett.80.1212 [50] Dimonte G, Terrones G, Cherne F J, et al. 2011. Use of the Richtmyer-Meshkov instability to infer yield stress at high-energy densities. Physical review letters, 107(26): 264502. [51] Dimonte G, Remington B. 1993. Richtmyer-Meshkov experiments on the Nova laser at high compression. Physical review letters, 70(12): 1806. doi: 10.1103/PhysRevLett.70.1806 [52] Drucker D C. 1980. Taylor instability of the surface of an elasticplastic plate, Mechanics Today. [53] Fermi E. 1962. The Collected Papers of Enrico Fermi, edited by E. Amaldi et al. [54] Frachet V, Geleznikoff F, Guix R, et al. 1989. Rayleigh Taylor instability in cylindrical configuration. Proceedings of 2nd International Workshop on the Physics of Compressible Turbulent Mixing. : 862−849. [55] Gao C Y, Zhang L C. 2012. Constitutive modelling of plasticity of fcc metals under extremely high strain rates. International Journal of Plasticity, 32: 121-133. [56] Goldstein W, Rosner R. 2012. Workshop on the science of fusion ignition on NIF. LLNL-TR-570412, [57] Goncharov V N, McKenty P, Skupsky S, et al. 2000. Modeling hydrodynamic instabilities in inertial confinement fusion targets. Physics of Plasmas, 7(12): 5118-5139. doi: 10.1063/1.1321016 [58] Grady D. 2007. Fragmentation of rings and shells: the legacy of NF Mott. Springer Science & Business Media. [59] Grigoryev S Y, Dyachkov S A, Parshikov A N, et al. 2022. Limited and unlimited spike growth from grooved free surface of shocked solid. Journal of Applied Physics, 131 (6). [60] Guo H Y, Wang L F, Ye W H, et al. 2018. Weakly nonlinear Rayleigh–Taylor instability in cylindrically convergent geometry. Chinese Physics Letters, 35(5): 055201. doi: 10.1088/0256-307X/35/5/055201 [61] Haan S W, Huang H, Johnson M A, et al. 2015. Instability growth seeded by oxygen in CH shells on the National Ignition Facility. Physics of Plasmas, 22 (3). [62] Hao P C, Feng Q J, Hu X M. 2016. A numerical study of the instability of the metal shell in the implosion. Explosion and Shock Waves, 36(6): 739-744. [63] Henry de Frahan M T, Belof J L, Cavallo R M, et al. 2015. Experimental and numerical investigations of beryllium strength models using the Rayleigh-Taylor instability. Journal of Applied Physics, 117 (22). [64] Hide R. 1955. The character of the equilibrium of an incompressible heavy viscous fluid of variable density: an approximate theory. Mathematical Proceedings of the Cambridge Philosophical Society. Cambridge University Press, 51(1): 179-201. [65] Huntington C M, Belof J L, Blobaum K J M, et al. 2017. Investigating iron material strength up to 1 Mbar using Rayleigh-Taylor growth measurements. AIP Conference Proceedings. AIP Publishing, 1793 (1). [66] Jensen B J, Cherne F J, Prime M B, et al. 2015. Jet formation in cerium metal to examine material strength. Journal of Applied Physics, 118 (19). [67] Karkhanis V, Ramaprabhu P, Cherne F J, et al. 2018. A numerical study of bubble and spike velocities in shock-driven liquid metals. Journal of Applied Physics, 123 (2). [68] Kozlov E A, Ol'Khov O V, Shuvalova E V. 2014. Numerical 3D-modeling of spall and shear fractures in shells of austenitic 12Kh18N10T steel and 30KhGSA steel under their spherical and quasi-spherical explosive loading. Journal of Physics: Conference Series (см. в книгах). Institute of Physics and IOP Publishing Limited, 490 (1): 012192-012192. [69] Kozlov E A, Petrovtsev A V. 2014. Cumulation of a spherically converging shock wave in metals and its dependence on elastic-plastic properties, phase transitions, spall and shear fractures. Journal of Physics: Conference Series. IOP Publishing, 490 (1): 012191. [70] Kozlov E A. 2012. 2D-and 3D-explosive experiments for verification of spall and shear strength models for some steels. AIP Conference Proceedings. American Institute of Physics, 1426(1): 945-948. [71] Krygier A, Powell P D, McNaney J M, et al. 2019. Extreme hardening of Pb at high pressure and strain rate. Physical Review Letters, 123(20): 205701. doi: 10.1103/PhysRevLett.123.205701 [72] Landau L D, Lifshitz E M. 1987. Fluid Mechanics. [73] Lebedev A I, Nisovtsev P N, Rayevsky V A. 1993. Rayleigh-Taylor Instability in Solids. Proceedings of the 4th International Workshop on the Physics of Compressible Turbulent Mixing, Cambridge, UK, Cambridge University Press: 81-93. [74] Lebedev A I, Nizovtsev P N, Raevskii V A, et al. 1996. Rayleigh-Taylor instability in firm substances. Physics-Doklady, 41(7): 328-330. [75] Lim H, Battaile C C, Brown J L, et al. 2016. Physically-based strength model of tantalum incorporating effects of temperature, strain rate and pressure. Modelling and Simulation in Materials Science and Engineering, 24(5): 055018. doi: 10.1088/0965-0393/24/5/055018 [76] Linhart J G. 1961. Dynamic stability of a conducting, cylindrical shell in a magnetic field. Journal of Applied Physics, 32(3): 500-505. doi: 10.1063/1.1736032 [77] Liu J, Feng Q J, Zhou H B. 2014. Simulation study of interface instability in metals driven by cylindrical implosion. Acta Physica Sinica, 63(15): 155201. doi: 10.7498/aps.63.155201 [78] Lorenz K T, Edwards M J, Glendinning S G, et al. 2005. Accessing ultrahigh-pressure, quasi-isentropic states of matter. Physics of plasmas, 12 (5). [79] Marsh S P. 1980. LASL shock Hugoniot data. Univ of California Press. [80] McGlaun J M, Thompson S L, Elrick M G. 1990. CTH: A three-dimensional shock wave physics code. International Journal of Impact Engineering, 10(1-4): 351-360. doi: 10.1016/0734-743X(90)90071-3 [81] Mikaelian K O. 1996. Rayleigh-Taylor instability in finite-thickness fluids with viscosity and surface tension. Physical Review E, 54(4): 3676. doi: 10.1103/PhysRevE.54.3676 [82] Meshkov E E. 1969. Instability of the interface of two gases accelerated by a shock wave. Fluid Dynamics, 4(5): 101-104. [83] Mikaelian K O. 2013. Shock-induced interface instability in viscous fluids and metals. Physical Review E, 87(3): 031003. doi: 10.1103/PhysRevE.87.031003 [84] Mikaelian K O. 1993. Effect of viscosity on Rayleigh-Taylor and Richtmyer-Meshkov instabilities. Physical Review E, 47(1): 375. [85] Miles J W. 1966. Taylor instability of a flat plate. General Dynamics Report No. GAMD-7335, AD643161. San Diego, CA: General Dynamics. [86] Monfared S K, Oró D M, Grover M, et al. 2014. Experimental observations on the links between surface perturbation parameters and shock-induced mass ejection. Journal of Applied Physics, 116 (6). [87] Nishihara K, Ishizaki R, Wouchuk J G, et al. 1998. Hydrodynamic perturbation growth in start-up phase in laser implosion. Physics of Plasmas, 5(5): 1945-1952. doi: 10.1063/1.872864 [88] Olles J D, Hudspeth M C, Tilger C F, et al. 2021. The effect of liquid tamping media on the growth of Richtmyer-Meshkov instability in copper. Journal of Dynamic Behavior of Materials, 7(2): 338-351. doi: 10.1007/s40870-021-00305-8 [89] Olles J D, Hudspeth M, Tilger C F, et al. 2020. Hydrodynamic Richtmyer-Meshkov instability of metallic solids used to assess material deformation at high strain-rates. Dynamic Behavior of Materials, Volume 1: Proceedings of the 2019 Annual Conference on Experimental and Applied Mechanics. Springer International Publishing, : 149-155. [90] Opie S, Loomis E, Peralta P, et al. 2017. Strength and viscosity effects on perturbed shock front stability in metals. Physical Review Letters, 118(19): 195501. [91] Ortega A L, Hill D J, Pullin D I, et al. 2010. Linearized Richtmyer-Meshkov flow analysis for impulsively accelerated incompressible solids. Physical Review E, 81(6): 066305. doi: 10.1103/PhysRevE.81.066305 [92] Ortega A L, Lombardini M, Barton P T, et al. 2015. Richtmyer-Meshkov instability for elastic-plastic solids in converging geometries. Journal of the Mechanics and Physics of Solids, 76: 291-324. doi: 10.1016/j.jmps.2014.12.002 [93] Ortega A L, Lombardini M, Pullin D I, et al. 2014. Numerical simulations of the Richtmyer-Meshkov instability in solid-vacuum interfaces using calibrated plasticity laws. Physical Review E, 89(3): 033018. [94] Park H S, Lorenz K T, Cavallo R M. 2010. Viscous Rayleigh-Taylor instability experiments at high pressure and strain rate. Physical Review Letter, 104(13): 5504-5507. [95] Park H S, Remington B A, Becker R C, et al. 2010. Strong stabilization of the Rayleigh-Taylor instability by material strength at megabar pressures. Physics of Plasmas, 17 (5). [96] Plesset M S. 1954. On the stability of fluid flows with spherical symmetry. Journal of Applied Physics, 25(1): 96-98. doi: 10.1063/1.1721529 [97] Plohr J N, Plohr B J. 2005. Linearized analysis of Richtmyer–Meshkov flow for elastic materials. Journal of Fluid Mechanics, 537: 55-89. doi: 10.1017/S0022112005004647 [98] Plohr B J, Sharp D H. 1998. Instability of accelerated elastic metal plates. Zeitschrift für angewandte Mathematik und Physik ZAMP, 49: 786-804. [99] Piriz A R, Cela J J L, Cortazar O D, et al. 2005. Rayleigh-Taylor instability in elastic solids. Physical Review E, 72(5): 056313. doi: 10.1103/PhysRevE.72.056313 [100] Piriz A R, Cela J J L, Tahir N A, et al. 2006. Richtmyer-Meshkov flow in elastic solids. Physical Review E, 74(3): 037301. [101] Piriz A R, Cela J J L, Tahir N A. 2009. Linear analysis of incompressible Rayleigh-Taylor instability in solids. Physical Review E, 80(4): 046305. doi: 10.1103/PhysRevE.80.046305 [102] Piriz A R, Cela J J L, Tahir N A, et al. 2008. Richtmyer-Meshkov instability in elastic-plastic media. Physical Review E, 78(5): 056401. doi: 10.1103/PhysRevE.78.056401 [103] Piriz A R, Cela J J L, Tahir N A. 2010. Comment on“Viscous Rayleigh-Taylor Instability Experiments at High Pressure and Strain Rate”. Physical review letters, 105(17): 179601. doi: 10.1103/PhysRevLett.105.179601 [104] Piriz A R, Cortazar O D, Lopez Cela J J, et al. 2006. The rayleigh-taylor instability. American journal of physics, 74(12): 1095-1098. [105] Piriz A R, Piriz S A, Tahir N A. 2021. Elastic-plastic Rayleigh-Taylor instability at a cylindrical interface. Physical Review E, 104(3): 035102. doi: 10.1103/PhysRevE.104.035102 [106] Piriz A R, Sun Y B, Tahir N A. 2013. Rayleigh-Taylor stability boundary at solid-liquid interfaces. Physical Review E, 88(2): 023026. doi: 10.1103/PhysRevE.88.023026 [107] Piriz A R, Sun Y B, Tahir N A. 2014. Rayleigh-Taylor linear growth at an interface between an elastoplastic solid and a viscous liquid. Physical Review E, 89(6): 063022. [108] Piriz S A, Piriz A R, Tahir N A. 2019. Magneto-Rayleigh–Taylor instability in an elastic finite-width medium overlying an ideal fluid. Journal of Fluid Mechanics, 867: 1012-1042. doi: 10.1017/jfm.2019.193 [109] Preston D L, Tonks D L, Wallace D C. 2003. Model of plastic deformation for extreme loading conditions. Journal of applied physics, 93(1): 211-220. doi: 10.1063/1.1524706 [110] Prime M B, Buttler W T, Buechler M A, et al. 2017. Estimation of metal strength at very high rates using free-surface Richtmyer–Meshkov instabilities. Journal of Dynamic Behavior of Materials, 3: 189-202. doi: 10.1007/s40870-017-0103-9 [111] Prime M B, Buttler W T, Fensin S J, et al. 2019. Tantalum strength at extreme strain rates from impact-driven Richtmyer-Meshkov instabilities. Physical Review E, 100(5): 053002. [112] Prudhomme G, De Rességuier T, Roland C, et al. 2020. Velocity and mass density of the ejecta produced from sinusoidal grooves in laser shock-loaded tin. Journal of Applied Physics, 128 (15). [113] Remington B A, Bazan G, Belak J et al. 2004. Materials Science Under Extreme Conditions of Pressure and Strain Rate9. Metal lurgical and Materials Transactions A, : 2587-2607. [114] Reinovsky R E, Atchison W L, Dimonte G, et al. 2008. Pulsed-power hydrodynamics: An application of pulsed-power and high magnetic fields to the exploration of material properties and problems in experimental hydrodynamics. IEEE transactions on plasma science, 36(1): 112-124. doi: 10.1109/TPS.2007.914708 [115] Richtmyer R D. 1954. Taylor instability in shock acceleration of compressible fluids. Los Alamos Scientific Lab. , N. Mex. [116] Roberts M S. 2012. Experiments and simulations on the incompressible, Rayleigh-Taylor instability with small wavelength initial perturbations. The University of Arizona. [117] Robinson A C, Swegle J W. 1989. Acceleration instability in elastic‐plastic solids. II. Analytical techniques. Journal of applied physics, 66(7): 2859-2872. doi: 10.1063/1.344191 [118] Rousculp C L, Oro D M, Griego J R, et al. 2016. Investigation of Surface Phenomena in Shocked Tin in Converging Geometry. Los Alamos National Lab. (LANL), Los Alamos, NM (United States). [119] Ruden E L, Bell D E. 1997. Rayleigh–Taylor stability criteria for elastic-plastic solid plates and shells. Journal of applied physics, 82(1): 163-170. doi: 10.1063/1.365795 [120] Sheppard M G, Atchison W L, Anderson W E, et al. 1997. Rayleigh-Taylor mix experiment on Pegasus. Digest of Technical Papers. 11th IEEE International Pulsed Power Conference (Cat. No. 97CH36127). IEEE, 2: 1399-1404. [121] Smalyuk V A, Weber C R, Landen O L, et al. 2020. Review of hydrodynamic instability experiments in inertially confined fusion implosions on National Ignition Facility. Plasma Phys Control Fusion, 62: 014007. doi: 10.1088/1361-6587/ab49f4 [122] Stebner A P, Wehrenberg C E, Li B, et al. 2018. Strength of tantalum shocked at ultrahigh pressures. Materials Science and Engineering: A, 732 : 220-227. [123] Steinberg D J, Cochran S G, Guinan M W. 1980. A constitutive model for metals applicable at high‐strain rate. Journal of applied physics, 51(3): 1498-1504. doi: 10.1063/1.327799 [124] Sun Q, Jia Y, Zhang Z, et al. 2022. Cylindrical metal liner implosion at extremes of pressure and material velocity on an intense pulsed power facility-FP-2. Review of Scientific Instruments, 93 (1). [125] Sun Y B, Zeng R H, Tao J J. 2021. Effects of viscosity and elasticity on Rayleigh-Taylor instability in a cylindrical geometry. Physics of Plasmas, 28 (6). [126] Swegle J W, Robinson A C. 1989. Acceleration instability in elastic‐plastic solids. I. Numerical simulations of plate acceleration. Journal of Applied Physics, 66(7): 2838-2858. doi: 10.1063/1.344190 [127] Taylor G I. 1950. The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 201(1065): 192-196. [128] Terrones G. 2005. Fastest growing linear Rayleigh-Taylor modes at solid/fluid and solid/solid interfaces. Physical Review E, 71(3): 036306. [129] Terrones G, Carrara M D. 2015. Rayleigh-Taylor instability at spherical interfaces between viscous fluids: Fluid/vacuum interface. Physics of Fluids, 27 (5). [130] Terrones G, Heberling T. 2020. Rayleigh–Taylor instability at spherical interfaces between viscous fluids: The fluid/fluid interface. Physics of Fluids, 32 (9). [131] Velikovich A L. 1996. Analytic theory of Richtmyer–Meshkov instability for the case of reflected rarefaction wave. Physics of Fluids, 8(6): 1666-1679. doi: 10.1063/1.868938 [132] Vogler T J, Hudspeth M C. 2021. Tamped Richtmyer–Meshkov instability experiments to probe high-pressure material strength. Journal of Dynamic Behavior of Materials, 7: 262-278. [133] Wang L F, Ye W H, He X T, et al. 2017. Theoretical and simulation research of hydrodynamic instabilities in inertial-confinement fusion implosions. Sci China Phys Mech Astron, 60: 055201. doi: 10.1007/s11433-017-9016-x [134] Wang Pei, He Anmin, Shao Jianli, et al. 2018. Numerical and theoretical investigations of shock-induced material ejection and ejecta-gas mixing. Scientia Sinica, 48(9): 106-116. [135] Weinwurm M, Bland S N, Chittenden J P. 2014. Metal liner-driven cylindrically convergent isentropic compression of cryogenic deuterium. Journal of Physics: Conference Series. IOP Publishing, 500(8): 082002. doi: 10.1088/1742-6596/500/8/082002 [136] White G N. 1973. Los Alamos National Laboratory Report No. LA-5225-MS (unpublished [137] Wouchuk J G. 2001. Growth rate of the linear Richtmyer-Meshkov instability when a shock is reflected. Physical Review E, 63(5): 056303. doi: 10.1103/PhysRevE.63.056303 [138] Zhang Q, Graham M J. 1997. Scaling laws for unstable interfaces driven by strong shocks in cylindrical geometry. Physical review letters, 79(14): 2674. doi: 10.1103/PhysRevLett.79.2674 [139] Zhang S, Liu W, Wang G, et al. 2019. Investigation of convergent Richtmyer–Meshkov instability at tin/xenon interface with pulsed magnetic driven imploding. Chinese Physics B, 28(4): 044702. [140] Zhao Z, Wang P, Liu N, et al. 2020. Analytical model of nonlinear evolution of single-mode Rayleigh–Taylor instability in cylindrical geometry. Journal of Fluid Mechanics, 900: A24. doi: 10.1017/jfm.2020.526 -
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