COLE R H . Underwater explosion [M ] . Princeton,NJ , US : Princeton University Press , 1948 .

ZAMYSHLYAEV B V . Dynamic loads in underwater explosion:AD 757183 [R ] . Washington, DC , US : Naval Intelligence Support Center ,1973.

RAMAJEYATHILAGAM K , VENDHAN C P . Deformation and rupture of thin rectangular plates subjected to underwater shock [J ] . International Journal of Impact Engineering , 2004 , 30 ( 6 ): 699 - 719 . DOI: 10.1016/j.ijimpeng.2003.01.001 http://doi.org/10.1016/j.ijimpeng.2003.01.001 https://linkinghub.elsevier.com/retrieve/pii/S0734743X04000132 https://linkinghub.elsevier.com/retrieve/pii/S0734743X04000132

BRETT J M , YANNAKAPOLOUS G . A study of explosive effects in close proximity to a submerged cylinder [J ] . International Journal of Impact Engineering , 2008 , 35 ( 4 ): 206 - 225 . DOI: 10.1016/j.ijimpeng.2007.01.007 http://doi.org/10.1016/j.ijimpeng.2007.01.007 https://linkinghub.elsevier.com/retrieve/pii/S0734743X07000115 https://linkinghub.elsevier.com/retrieve/pii/S0734743X07000115

崔杰 , 张阿漫 , 郭君 , 等 . 舱段结构在气泡射流作用下的毁伤效果 [J ] . 爆炸与冲击 , 2012 , 32 ( 4 ): 355 - 361 .

CUIJ , ZHANG A M , GUO J , et al. Damage effect of cabin structure subjected to bubble jet [J ] . Explosion and Shock Waves , 2012 , 32 ( 4 ): 355 - 361 . (in Chinese)

BRUJAN E A , NAHEN K , SCHMIDT P , et al. Dynamics of laser-induced cavitation bubbles near elastic boundaries: influence of the elastic modulus [J ] . Journal of Fluid Mechanics , 2001 , 433 : 251 - 281 . DOI: 10.1017/S0022112000003347 http://doi.org/10.1017/S0022112000003347 https://www.cambridge.org/core/product/identifier/S0022112000003347/type/journal_article https://www.cambridge.org/core/product/identifier/S0022112000003347/type/journal_article The interaction of a laser-induced cavitation bubble with an elastic boundary and \nits dependence on the distance between bubble and boundary are investigated experimentally. \nThe elastic boundary consists of a transparent polyacrylamide (PAA) \ngel with 80% water concentration with elastic modulus E = 0.25 MPa. At this E-value, \nthe deformation and rebound of the boundary is very pronounced providing \nparticularly interesting features of bubble dynamics. It is shown by means of high-speed photography with up to 5 million frames s−1 that bubble splitting, formation \nof liquid jets away from and towards the boundary, and jet-like ejection of the \nboundary material into the liquid are the main features of this interaction. The maximum \nliquid jet velocity measured was 960 m s−1. Such high-velocity jets penetrate \nthe elastic boundary even through a water layer of 0.35 mm thickness. The jetting \nbehaviour arises from the interaction between the counteracting forces induced by \nthe rebound of the elastic boundary and the Bjerknes attraction force towards the \nboundary. General principles of the formation of annular and axial jets are discussed \nwhich allow the interpretation of the complex dynamics. The concept of the Kelvin \nimpulse is examined with regard to bubble migration and jet formation. The results \nare discussed with respect to cavitation erosion, collateral damage in laser surgery, \nand cavitation-mediated enhancement of pulsed laser ablation of tissue.

LINDAU O , LAUTERBORN W . Cinematographic observation of the collapse and rebound of a laser-produced cavitation bubble near a wall [J ] . Journal of Fluid Mechanics , 2003 , 479 : 327 - 348 . DOI: 10.1017/S0022112002003695 http://doi.org/10.1017/S0022112002003695 http://www.journals.cambridge.org/abstract_S0022112002003695 http://www.journals.cambridge.org/abstract_S0022112002003695

ZHANG A M , CUI P , WANG Y . Experiments on bubble dynamics between a free surface and a rigid wall [J ] . Experiments in Fluids , 2013 , 54 : 1602 :. DOI: 10.1007/s00348-013-1602-7 http://doi.org/10.1007/s00348-013-1602-7 http://link.springer.com/10.1007/s00348-013-1602-7 http://link.springer.com/10.1007/s00348-013-1602-7

ZHANG A M , CUI P , CUI J . Experimental study on bubble dynamics subject to buoyancy [J ] . Journal of Fluid Mechanics , 2015 , 776 : 137 - 160 . DOI: 10.1017/jfm.2015.323 http://doi.org/10.1017/jfm.2015.323 https://www.cambridge.org/core/product/identifier/S0022112015003237/type/journal_article https://www.cambridge.org/core/product/identifier/S0022112015003237/type/journal_article This paper is concerned with the dynamics of large bubbles subject to various strengths of buoyancy effects, which are associated with applications for underwater explosion. The bubble is produced by electric discharge in a low-pressure tank to enhance the buoyancy effects. Experiments are carried out for a bubble in an infinite field, below a free surface and above a rigid boundary. The effects of buoyancy are reflected by the dimensionless parameter ${\\it\\delta}=\\sqrt{{\\it\\rho}gR_{m}/(p_{amb}-p_{v})}$, where $R_{m}$, $p_{amb}$, $p_{v}$, ${\\it\\rho}$ and $g$ are the maximum bubble radius, ambient pressure, saturated vapour pressure, density of water and the acceleration of gravity respectively. A systematic study of buoyancy effects is carried out for a wide range of ${\\it\\delta}$ from 0.034 to 0.95. A series of new phenomena and new features is observed. The bubbles recorded are transparent, and thus we are able to display and study the jet formation, development and impact on the opposite bubble surface as well as the subsequent collapsing and rebounding of the ring bubble. Qualitative analyses are carried out for the bubble migration, jet velocity and jet initiation time, etc. for different values of ${\\it\\delta}$. When a bubble oscillates below a free surface or above a rigid boundary, the Bjerknes force due to the free surface (or rigid boundary) and the buoyancy are in opposite directions. Three situations are studied for each of the two configurations: (i) the Bjerknes force being dominant, (ii) the buoyancy force being dominant and (iii) the two forces being approximately balanced. For case (iii), we further consider two subcases, where both the balanced Bjerknes and buoyancy forces are weak or strong. When the Bjerknes and buoyancy forces are approximately balanced over the pulsation, some representative bubble behaviours are observed: the bubble near free surface is found to split into two parts jetting away from each other for small ${\\it\\delta}$, or involutes from both top and bottom for large ${\\it\\delta}$. A bubble above a rigid wall is found to be subject to contraction from the lateral part leading to bubble splitting. New criteria are established based on experimental results for neutral collapses where there is no dominant jetting along one direction, which correlate well with the criteria of Blake et al. (J. Fluid Mech., vol. 170, 1986, pp. 479–497; J. Fluid Mech., vol. 181, 1987, pp. 197–212) but agree better with the experimental and computational results.

DIDENKO Y T , SUSLICK K S . The energy efficiency of formation of photons, radicals and ions during single-bubble cavitation [J ] . Nature , 2002 , 418 ( 6896 ): 394 - 397 . DOI: 10.1038/nature00895 http://doi.org/10.1038/nature00895 https://www.nature.com/articles/nature00895 https://www.nature.com/articles/nature00895

KLASEBOER E , HUNG K C , WANG C , et al. Experimental and numerical investigation of the dynamics of an underwater explosion bubble near a resilient/rigid structure [J ] . Journal of Fluid Mechanics , 2005 , 537 : 387 - 413 . DOI: 10.1017/S0022112005005306 http://doi.org/10.1017/S0022112005005306 http://www.journals.cambridge.org/abstract_S0022112005005306 http://www.journals.cambridge.org/abstract_S0022112005005306

汪斌 , 谭多望 . 水中爆炸形成水射流现象的实验研究 [J ] . 哈尔滨工程大学学报 , 2010 , 31 ( 1 ): 42 - 46 .

WANG B , TAN D W . Water jet phenomena caused by underwater explosions [J ] . Journal of Harbin Engineering University , 2010 , 31 ( 1 ): 42 - 46 . (in Chinese)

汪斌 , 张远平 , 王彦平 . 水中爆炸气泡与水底边界相互作用的水射流现象 [J ] . 爆炸与冲击 , 2011 , 31 ( 3 ): 250 - 255 .

WANG B , ZHANG Y P , WANG Y P . Water jet phenomena induced by the interaction between underwater explosion bubbles and water bottom boundaries [J ] . Explosion and Shock Waves , 2011 , 31 ( 3 ): 250 - 255 . (in Chinese)

ZHANGA M , WANG S P , HUANG C , et al. Influences of initial and boundary conditions on underwater explosion bubble dynamics [J ] . European Journal of Mechanics: B Fluids , 2013 , 42 : 69 - 91 . DOI: 10.1016/j.euromechflu.2013.06.008 http://doi.org/10.1016/j.euromechflu.2013.06.008 https://linkinghub.elsevier.com/retrieve/pii/S0997754613000708 https://linkinghub.elsevier.com/retrieve/pii/S0997754613000708

CUI P , ZHANG A M , WANG S P . Small-charge underwater explosion bubble experiments under various boundary conditions [J ] . Physics of Fluids , 2016 , 28 ( 11 ): 117103 . DOI: 10.1063/1.4967700 http://doi.org/10.1063/1.4967700 https://pubs.aip.org/pof/article/28/11/117103/315066/Small-charge-underwater-explosion-bubble https://pubs.aip.org/pof/article/28/11/117103/315066/Small-charge-underwater-explosion-bubble Small-charge underwater explosion experiments were performed to investigate bubbles subjected to gravity and various boundary conditions, including single boundary (free surface and rigid wall boundary), combined boundaries of free surface and solid wall, solid wall boundaries with a circular opening, and resilient wall boundaries. With high speed camera and pressure sensors, the behavior of explosion bubbles was studied and features of associated pressure pulses were analyzed. Detailed image analysis on the final stages of bubble collapse was carried out and revealed a possible explanation for the weakening of pressure waves at bubble rebound as the bubble approaches a wall boundary. Certain features also indicate that the magnitude of the pressure peaks induced by bubble rebound is related to the shape of the bubble shape during collapse. Pressure pulses arising from the two types of bubble behavior, specifically the collision of an annular jet and the impact of a jet with the wall boundary, were measured. Other curious types of bubble behavior were found, including jetting induced by suction when a bubble collapses covering a circular opening on a solid wall, and bubble splitting in interaction with a resilient wall boundary.

ZHAO X H , WANG G H , LU W B , et al. Damage features of RC slabs subjected to air and underwater contact explosions [J ] . Ocean Engineering , 2017 , 147 : 531 - 545 . DOI: 10.1016/j.oceaneng.2017.11.007 http://doi.org/10.1016/j.oceaneng.2017.11.007 https://linkinghub.elsevier.com/retrieve/pii/S0029801817306741 https://linkinghub.elsevier.com/retrieve/pii/S0029801817306741

YANG G D , WANG G H , LU W B , et al. Experimental and numerical study of damage characteristics of RC slabs subjected to air and underwater contact explosions [J ] . Marine Structures , 2019 , 66 : 242 - 257 . DOI: 10.1016/j.marstruc.2019.04.009 http://doi.org/10.1016/j.marstruc.2019.04.009 https://linkinghub.elsevier.com/retrieve/pii/S0951833918305008 https://linkinghub.elsevier.com/retrieve/pii/S0951833918305008

HAI L , REN X D . Computational investigation on damage of reinforced concrete slab subjected to underwater explosion [J ] . Ocean Engineering , 2019 , 195 : 106671 . DOI: 10.1016/j.oceaneng.2019.106671 http://doi.org/10.1016/j.oceaneng.2019.106671 https://linkinghub.elsevier.com/retrieve/pii/S0029801819307899 https://linkinghub.elsevier.com/retrieve/pii/S0029801819307899

CHEN Z , ZONG Z H , LU G , et al. Numerical investigation on dynamic response of air-backed RC slabs subjected to close-in underwater explosion [J ] . OceanEngineering , 2023 , 273 : 113962 .

BEST J P . The effect of non-spherical collapse on determination of explosion bubble parameters,AD-A407861 [R ] . 2002 .

张阿漫 , 姚熊亮 . 近自由面水下爆炸气泡的运动规律研究 [J ] . 物理学报 , 2008 , 57 ( 1 ): 339 - 354 .

ZHANG A M , YAO X L . The law of the underwater explosion bubble motion near free surface [J ] . Acta Physica Sinica , 2008 , 57 ( 1 ): 339 - 354 . (in Chinese) DOI: 10.7498/aps http://doi.org/10.7498/aps https://wulixb.iphy.ac.cn/ https://wulixb.iphy.ac.cn/

阿漫 , 姚熊亮 . 近壁面气泡的运动规律研究 [J ] . 物理学报 , 2008 , 57 ( 3 ): 1662 - 1671 .

ZHANG A M , YAO X L . The law of the bubble motion near the wall [J ] . Acta Physica Sinica , 2008 , 57 ( 3 ): 1662 - 1671 . (in Chinese) DOI: 10.7498/aps http://doi.org/10.7498/aps https://wulixb.iphy.ac.cn/ https://wulixb.iphy.ac.cn/