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任意Atwood数Rayleigh-Taylor和 Richtmyer-Meshkov 不稳定性气泡速度研究

陶烨晟 王立锋 叶文华 张广财 张建成 李英骏

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Citation:

任意Atwood数Rayleigh-Taylor和 Richtmyer-Meshkov 不稳定性气泡速度研究

陶烨晟, 王立锋, 叶文华, 张广财, 张建成, 李英骏

The bubble velocity research of Rayleigh-Taylor and Richtmyer-Meshkov instabilities at arbitrary Atwood numbers

Tao Ye-Sheng, Wang Li-Feng, Ye Wen-Hua, Zhang Guang-Cai, Zhang Jian-Cheng, Li Ying-Jun
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  • 本文将Layzer气泡模型推广到任意界面Atwood数情形,得到了自洽的微分方程组.该模型描述了气泡从早期的指数增长阶段到气 泡以渐近速度上升的非线性阶段的发展过程,给出了Rayleigh-Taylor(RT)和Richtmyer-Meshkov(RM)不稳定性的二维和 三维气泡速度渐近解,还求出了二维和三维RT不稳定性气泡顶点附近速度的解析解.
    We generalize the Layzer's bubble model to the cases of two-dimensional and three-dimensional analytical models of an arbitrary interface Atwood number and obtain self-consistent equations. The generalized model provides a continuous bubble evolution from the earlier exponential growth to the nonlinear regime. The asymptotic bubble velocities are obtained for the Rayleigh-Taylor(RT) and Richtmyer-Meshkov(RM) instabilities. We also report on the two-dimensional and the three-dimensional analytical expressions for the evolution of the RT bubble velocity.
    • 基金项目: 国家重点基础研究发展计划(973项目) (批准号: 2007CB815100)和国家自然科学基金(批准号: 10935003, 10775020, 11074300, 10874242和11075024)资助的课题.
    • Funds: Project supported by the National Basic Research Program of China(973 Program)(Grant No. 2007CB815100), and The National Natural Science Foundation of China (Grant No. 10935003, 10775020, 11074300, 10874242, 11075024).
    [1]

    Lord Rayleigh 1900 Scientific Papers (Vol. Π) (Cambridge, England: Cambridge University Press) p200

    [2]

    Richtmyer R D 1960 Commum Pure Appl. Math. 13 297

    [3]

    Ye W H, Zhang W Y, He X T 2002 Phys. Rev. E 65 57401

    [4]

    Lindl J D, Amendt P, Berger R L, Glendinning S G, Glenzer S H, Haan S W, Kauffman R L, Landen O L, Suter L J 2004 Phys. Plasmas 11 339

    [5]

    Committee on High Energy Density Plasma Physics Plasma Science Committee Board on Physics and Astronomy Division on Engineering and Physical Sciences 2001 Frontiers in High Energy Density Physics (Washington DC: Academic)

    [6]

    Wang L F, Ye W H, Li Y J 2010 Chin. Phys. Lett. 27 025202

    [7]

    Ye W H, Zhang W Y, He X T 2000 Acta Phys. Sin. 49 762 (in Chinese) [叶文华, 张维岩, 贺贤土 2000 物理学报 49 726]

    [8]

    Wang L F, Ye W H , Li Y J 2008 Acta Phys. Sin. 57 3038 (in Chinese) [王立锋, 叶文华, 李英骏 2008 物理学报 57 3038]

    [9]

    Wang L F, Ye W H, Li Y J, Meng L M 2008 Chin. Phys. B 17 3792

    [10]

    Wang L F, Ye W H, Sheng Z M, Don W S, Li Y J, He X T 2010 Physics of Plasmas 17 122706

    [11]

    Goncharov V N 2002 Phys. Rev. Lett. 88 134502

    [12]

    Stefano Atzeni 2003 Inertial Fusion Beam plasma interaction, hydrodynamics, dense plasma physics (Oxford: Clarendon Press) p286

    [13]

    Sung-Ik Sohn 2003 Phys. Rev. E 67 26301

    [14]

    Wang L F, Ye W H, Fan Z F, Li Y J 2010 EPL 90 15001

    [15]

    Jacobs J W, Catton I 1988 J. Fluid Mech. 187 329

    [16]

    Wang L F, Ye W H, Li Y J 2010 Physics of Plasmas 17 042103

    [17]

    Wang Li Feng, Ye W H, Li Y J 2010 Chin. Phys. Lett. 27 025203

    [18]

    Wang L F, Ye W H, Li Y J 2010 Physics of Plasmas 17 052305

    [19]

    Layzer D 1955 Astrophys. J. 122 1

    [20]

    Abarzhi S I, Nishihara K, Glimm J 2003 Phys. Lett. A 317 470

    [21]

    Ramaprabhu P, Guy Dimonte 2005 Phys. Rev. E 71 036314

    [22]

    Karning O. Mikaelian 2003 Phys. Rev. E 67 026319

    [23]

    Ramaprabhu P, Guy Dimonte, Young Y N, Calder A C, Fryxell B 2006 Phys. Rev. E 74 066308

  • [1]

    Lord Rayleigh 1900 Scientific Papers (Vol. Π) (Cambridge, England: Cambridge University Press) p200

    [2]

    Richtmyer R D 1960 Commum Pure Appl. Math. 13 297

    [3]

    Ye W H, Zhang W Y, He X T 2002 Phys. Rev. E 65 57401

    [4]

    Lindl J D, Amendt P, Berger R L, Glendinning S G, Glenzer S H, Haan S W, Kauffman R L, Landen O L, Suter L J 2004 Phys. Plasmas 11 339

    [5]

    Committee on High Energy Density Plasma Physics Plasma Science Committee Board on Physics and Astronomy Division on Engineering and Physical Sciences 2001 Frontiers in High Energy Density Physics (Washington DC: Academic)

    [6]

    Wang L F, Ye W H, Li Y J 2010 Chin. Phys. Lett. 27 025202

    [7]

    Ye W H, Zhang W Y, He X T 2000 Acta Phys. Sin. 49 762 (in Chinese) [叶文华, 张维岩, 贺贤土 2000 物理学报 49 726]

    [8]

    Wang L F, Ye W H , Li Y J 2008 Acta Phys. Sin. 57 3038 (in Chinese) [王立锋, 叶文华, 李英骏 2008 物理学报 57 3038]

    [9]

    Wang L F, Ye W H, Li Y J, Meng L M 2008 Chin. Phys. B 17 3792

    [10]

    Wang L F, Ye W H, Sheng Z M, Don W S, Li Y J, He X T 2010 Physics of Plasmas 17 122706

    [11]

    Goncharov V N 2002 Phys. Rev. Lett. 88 134502

    [12]

    Stefano Atzeni 2003 Inertial Fusion Beam plasma interaction, hydrodynamics, dense plasma physics (Oxford: Clarendon Press) p286

    [13]

    Sung-Ik Sohn 2003 Phys. Rev. E 67 26301

    [14]

    Wang L F, Ye W H, Fan Z F, Li Y J 2010 EPL 90 15001

    [15]

    Jacobs J W, Catton I 1988 J. Fluid Mech. 187 329

    [16]

    Wang L F, Ye W H, Li Y J 2010 Physics of Plasmas 17 042103

    [17]

    Wang Li Feng, Ye W H, Li Y J 2010 Chin. Phys. Lett. 27 025203

    [18]

    Wang L F, Ye W H, Li Y J 2010 Physics of Plasmas 17 052305

    [19]

    Layzer D 1955 Astrophys. J. 122 1

    [20]

    Abarzhi S I, Nishihara K, Glimm J 2003 Phys. Lett. A 317 470

    [21]

    Ramaprabhu P, Guy Dimonte 2005 Phys. Rev. E 71 036314

    [22]

    Karning O. Mikaelian 2003 Phys. Rev. E 67 026319

    [23]

    Ramaprabhu P, Guy Dimonte, Young Y N, Calder A C, Fryxell B 2006 Phys. Rev. E 74 066308

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  • PDF下载量:  875
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出版历程
  • 收稿日期:  2010-12-22
  • 修回日期:  2012-04-05
  • 刊出日期:  2012-04-05

任意Atwood数Rayleigh-Taylor和 Richtmyer-Meshkov 不稳定性气泡速度研究

  • 1. 中国矿业大学(北京)深部岩土力学与地下工程国家重点实验室, 北京 100083;
  • 2. 北京应用物理与计算数学研究所, 北京 100088;
  • 3. 北京大学应用物理与技术研究中心, 北京 100871;
  • 4. 北京林业大学, 北京 100083
    基金项目: 国家重点基础研究发展计划(973项目) (批准号: 2007CB815100)和国家自然科学基金(批准号: 10935003, 10775020, 11074300, 10874242和11075024)资助的课题.

摘要: 本文将Layzer气泡模型推广到任意界面Atwood数情形,得到了自洽的微分方程组.该模型描述了气泡从早期的指数增长阶段到气 泡以渐近速度上升的非线性阶段的发展过程,给出了Rayleigh-Taylor(RT)和Richtmyer-Meshkov(RM)不稳定性的二维和 三维气泡速度渐近解,还求出了二维和三维RT不稳定性气泡顶点附近速度的解析解.

English Abstract

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