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With using the effective medium theory to describe acoustic scattering from bubble clouds, one of the underlying assumptions shows that the probability of an individual bubble located at some position in space is independent of the locations of other bubbles. However, bubbles within the clouds that naturally occur are usually influenced by the motion of the fluid, which makes them preferentially concentrated or clustered. According to Weber's method, it is a useful way of introducing the spatial correlation function to describe this phenomenon in bubble cloud. The spatial correlation function is involved in acoustic scattering and it is important to notice that the spatial correlation should be dependent on the position and radius of each bubble due to the “hole correction” or the effect of the dynamics of the fluid. Because of these reasons, it is hard to invert the spatial distribution of bubble clouds by using the spatial correlation function in acoustic scattering. A method is described here in which bubble clouds are separated into many small subareas and the conception, called effective spatial correlation function which is the statistic of spatial correlation function, is used to describe the correlation between subareas of bubble clouds. Since the effective spatial correlation function is independent of bubble radius and positions, the bubble clouddistribution and the trend of clustering can be inverted by using this function. The simulation indicates that the effective spatial correlation function can precisely trace the position of the clustering center, even the clustering center covered by other bubble clouds can be detected. With using the multi-bean sonar for measuring the bubbly ship wake generated by a small trial vessel, the method is used to invert the spatial distribution and clustering centers of bubble field in the ship wake. The results show that the effective spatial correlation function accurately inverts the distribution and clustering centers of bubbles in ship wake. Furthermore, the method presented in this paper could distinguish between the bubble clouds caused by different reasons and detect upper ocean bubble clouds covered by other bubbles generated by wave breaking as well.
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Keywords:
- acoustic scattering /
- bubble clouds /
- spatial correlation /
- wake
[1] Kargl S G 2002 J. Acoust. Soc. Am. 111 1
[2] Foldy L L 1945 Phys. Rev. 67 107
[3] Ye Z, Ding L 1995 J. Acoust. Soc. Am. 98 3
[4] Henyey F S 1999 J. Acoust. Soc. Am. 105 4
[5] Commander K W, Prosperetti A 1989 J. Acoust. Soc. Am. 85 732
[6] Wang Y 2014 Ph. D. Dissertation（Xi'an:Shanxi Normal University)（in Chinese)[王勇2014博士学位论文(西安:陕西师范大学)]
[7] Wang Y, Lin S Y, Zhang X L 2013 Acta Phys. Sin. 62 064304 （in Chinese)[王勇, 林书玉, 张小丽2013物理学报62 064304]
[8] Eaton J, Fessler J 1994 Int. J. Multiphase Flow 20 94
[9] Weber T C, Lyons A P, Bradley D L 2007 IEEE J. Ocean Eng. 32 2
[10] Shaw R A, Kostinski A B, Larsen M L 2002 Qu. J. R. Meteorol Soc. 128 582
[11] Weber T C 2008 J. Acoust. Soc. Am. 124 5
[12] Landau L D, Lifshitz E M（translated by Shu R G, Shu C) 2011 Statistical Physics （Beijing:Higher Education Press) p309(in Chinese)[朗道L D, 栗弗席兹(E M)著(束仁贵, 束莼译) 2014统计物理学I（北京:高等教育出版社)第309页]
[13] Ma Y, Lin S Y, Xian X J 2016 Acta Phys. Sin. 65 014301 （in Chinese)[马艳, 林书玉, 鲜小军2016物理学报65 014301]
[14] Caleap M, Drinkwater B W, Wilcox P D 2012 J. Acoust. Soc. Am. 131 3
[15] Gustavssion K, Mehlig B 2016 Adv. Phys. 65 1
[16] Sun C S 2008 Ph. D. Dissertation（Changsha:National University of Defense Technology University)（in Chinese)[孙春生2008博士学位论文(长沙:国防科学技术大学)]
[17] Peltzer R D, Garrett W D, Smith P M 1987 Int. J. Remote Sens. 85
[18] Trevorrow M V, Vagle S, Farmer D M 1994 J. Acoust. Soc. Am. 95 4
[19] Weber T C, Lyons A P, Bradley D L 2005 J. Geophys. Res. 110C 4
[20] Li S 2014 Ph. D. Dissertation（Harbin:Harbin Engineering University)（in Chinese)[李珊2014博士学位论文(哈尔滨:哈尔滨工程大学)]
[21] Li H, Li S, Chen B, Xu C, Zhu J, Du W 2014 Oceans'14 MTS/IEEE St. John's, Canada, September 14-19, 2014 pp1-5
[22] Vagle S, Burch H 2005 J. Acoust. Soc. Am. 117 1
[23] Leightion T G, Ginfer D C, Chua G H, White P R, Dix J K 2011 J. Acoust. Soc. Am. 130 5
[24] Chen W Z, 2014 Acoustic Cavitation Physics (Beijing:Science Press) p214(in Chinese)[陈伟中2014声空化物理(北京:科学出版社)第341页]
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[1] Kargl S G 2002 J. Acoust. Soc. Am. 111 1
[2] Foldy L L 1945 Phys. Rev. 67 107
[3] Ye Z, Ding L 1995 J. Acoust. Soc. Am. 98 3
[4] Henyey F S 1999 J. Acoust. Soc. Am. 105 4
[5] Commander K W, Prosperetti A 1989 J. Acoust. Soc. Am. 85 732
[6] Wang Y 2014 Ph. D. Dissertation（Xi'an:Shanxi Normal University)（in Chinese)[王勇2014博士学位论文(西安:陕西师范大学)]
[7] Wang Y, Lin S Y, Zhang X L 2013 Acta Phys. Sin. 62 064304 （in Chinese)[王勇, 林书玉, 张小丽2013物理学报62 064304]
[8] Eaton J, Fessler J 1994 Int. J. Multiphase Flow 20 94
[9] Weber T C, Lyons A P, Bradley D L 2007 IEEE J. Ocean Eng. 32 2
[10] Shaw R A, Kostinski A B, Larsen M L 2002 Qu. J. R. Meteorol Soc. 128 582
[11] Weber T C 2008 J. Acoust. Soc. Am. 124 5
[12] Landau L D, Lifshitz E M（translated by Shu R G, Shu C) 2011 Statistical Physics （Beijing:Higher Education Press) p309(in Chinese)[朗道L D, 栗弗席兹(E M)著(束仁贵, 束莼译) 2014统计物理学I（北京:高等教育出版社)第309页]
[13] Ma Y, Lin S Y, Xian X J 2016 Acta Phys. Sin. 65 014301 （in Chinese)[马艳, 林书玉, 鲜小军2016物理学报65 014301]
[14] Caleap M, Drinkwater B W, Wilcox P D 2012 J. Acoust. Soc. Am. 131 3
[15] Gustavssion K, Mehlig B 2016 Adv. Phys. 65 1
[16] Sun C S 2008 Ph. D. Dissertation（Changsha:National University of Defense Technology University)（in Chinese)[孙春生2008博士学位论文(长沙:国防科学技术大学)]
[17] Peltzer R D, Garrett W D, Smith P M 1987 Int. J. Remote Sens. 85
[18] Trevorrow M V, Vagle S, Farmer D M 1994 J. Acoust. Soc. Am. 95 4
[19] Weber T C, Lyons A P, Bradley D L 2005 J. Geophys. Res. 110C 4
[20] Li S 2014 Ph. D. Dissertation（Harbin:Harbin Engineering University)（in Chinese)[李珊2014博士学位论文(哈尔滨:哈尔滨工程大学)]
[21] Li H, Li S, Chen B, Xu C, Zhu J, Du W 2014 Oceans'14 MTS/IEEE St. John's, Canada, September 14-19, 2014 pp1-5
[22] Vagle S, Burch H 2005 J. Acoust. Soc. Am. 117 1
[23] Leightion T G, Ginfer D C, Chua G H, White P R, Dix J K 2011 J. Acoust. Soc. Am. 130 5
[24] Chen W Z, 2014 Acoustic Cavitation Physics (Beijing:Science Press) p214(in Chinese)[陈伟中2014声空化物理(北京:科学出版社)第341页]
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