气泡线性振动时近海面气泡群的声散射
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摘要
海洋中的不同成因的气泡群是常见的水下声学目标及声呐混响源,因此对水下气泡群进行声学建模意义重大。利用有效媒质理论描述气泡群内部的相速度及声衰减变化,并考虑到海洋中气泡群往往产生于不同界面附近,进一步利用球面波叠加原理描述海面对气泡群散射声波的再辐射,导出了平海面作用下气泡群声散射截面的一般表达式,建立了其声散射模型,研究了单一尺寸及混合尺寸气泡群的声学特性。数值分析表明,气泡群的谐振频率会随其半径或孔隙率增加而降低;由于海面的存在,气泡群声散射截面会随频率进行周期性变化,且随气泡群远离海面,这一变化逐渐加剧。此外,若气泡的黏滞阻尼项在全部阻尼项中占比较高,气泡群声散射强度会在谐振频率附近存在起伏振荡。该模型可为近海面鱼群、气泡羽流及海底泄漏的甲烷气体的声学建模提供一定的理论基础。
Modeling acoustic field scattered by an underwater assembly of gas bubbles or similar resonant monopole scatterers is of considerable theoretical and practical interest. Using effective medium theory to describe the phase speed and attenuation in bubble clouds and using the addition theorem for the spherical wave functions to relate the scattered sound fields of both the bubble cloud and sea surface to a common origin, we obtain a modified scattering cross-section of the cloud near the boundary. Numerical simulations reveal that, with increasing void fraction or increasing cloud radius,the natural frequencies of the cloud can extend to smaller frequencies. Periodic oscillatory perturbations exists in the modified scattering cross-section that is due to the effect of sea surface and such oscillation becomes more considerable with increasing depth. Besides, if the viscous damping dominate the damping term, another oscillation will exists near the resonance frequencies. The approach may serve to model acoustic scattering by fish schools near the sea surface,bubble plumes and methane leaks near the seafloor.
Modeling acoustic field scattered by an underwater assembly of gas bubbles or similar resonant monopole scatterers is of considerable theoretical and practical interest. Using effective medium theory to describe the phase speed and attenuation in bubble clouds and using the addition theorem for the spherical wave functions to relate the scattered sound fields of both the bubble cloud and sea surface to a common origin, we obtain a modified scattering cross-section of the cloud near the boundary. Numerical simulations reveal that, with increasing void fraction or increasing cloud radius,the natural frequencies of the cloud can extend to smaller frequencies. Periodic oscillatory perturbations exists in the modified scattering cross-section that is due to the effect of sea surface and such oscillation becomes more considerable with increasing depth. Besides, if the viscous damping dominate the damping term, another oscillation will exists near the resonance frequencies. The approach may serve to model acoustic scattering by fish schools near the sea surface,bubble plumes and methane leaks near the seafloor.
引文
1安斯利M A著.声呐性能建模原理.张静远,颜冰译.北京:国防工业出版社,2015:232
2 Van Vossen R, Ainslie M A. The effect of wind-generated bubbles on sea-surface backscattering at 940 Hz. J. Acoust.Soc. Am., 2011; 130(5):3413-3420
3范雨喆,李海森,徐超,陈宝伟,杜伟东.基于声散射的水下气泡群空间关联性研究.物理学报,2017; 66(1):014305
4 Lovik A, Hovem J M. An experimental investigation of swimbladder resonance in fishes. J. Acoust. Soc. Am.,1979; 66(3):850-854
5李灿苹,刘学伟,赵罗臣.天然气水合物冷泉和气泡羽状流研究进展.地球物理学进展,2013; 28(2):1048-1056
6 Kargl S G. Effective medium approach to linear acoustics in bubbly liquids. J. Acoust. Soc. Am., 2002; 111(1):168-173
7 Foldy L L. The multiple scattering of waves. I. General theory of isotropic scattering by randomly distributed scatterers. Physical Review, 1945; 67(3-4):107-119
8 Ye Z, Ding L. Acoustic dispersion and attenuation relations in bubbly mixture. J. Acoust.Soc. Am., 1995; 98(3):1629-1636
9 Henyey F S. Corrections to Foldy's effective medium theoryfor propagation in bubble clouds and other collections of very small scatterers. J. Acoust. Soc. Am., 1999; 105(4):2149-2154
10 Commander K W, Prosperetti A. Linear pressure waves in bubbly liquids:Comparison between theory and experiments. J. Acoust. Soc. Am., 1989; 85(2):732-746
11苗博雅,安宇.两种气泡混合的声空化.物理学报,2014; 64(20):204301
12王勇,林书玉,张小丽.声波在含气泡液体中的线性传播.物理学报,2014; 63(3):034301
13 d'Agostino L, Brennen C E. Acoustical absorption and scattering cross sections of spherical bubble clouds. J.Acoust. Soc. Am., 1988; 84(6):2126-2134
14 Prosperetti A, Lu N Q, Kim H S. Active and passive acoustic behavior of bubble clouds at the ocean's surface. J.Acoust. Soc. Am., 1993; 93(6):3117-3127
15 Nicholas M, Roy R A, Crum L A et al. Sound emissions by a laboratory bubble cloud. J. Acoust. Soc. Am., 1994;95(6):3171-3182
16 Sarkar K, Prosperetti A. Coherent and incoherent scattering by oceanic bubbles. J. Acoust. Soc. Am., 1994; 96(1):332-341
17 Gaunaurd G C, Huang H. Acoustic scattering by an airbubble near the sea surface. IEEE J. Oceanic Eng., 1995;20(4):285-292
18 Gaunaurd G C, Huang H. Sound scattering by bubble clouds near the sea surface. J. Acoust. Soc. Am., 2000;107(1):95-102
19 Hahn T R. Low frequency sound scattering from spherical assemblages of bubbles using effective medium theory. J.Acoust. Soc. Am., 2007; 122(6):3252-3267
20钱祖文.颗粒介质中的声传播及其应用.北京:科学出版社,2012:17-34
21 Leighton T. The acoustic bubble. Massachusetts:Academic Press, 2012:172-191
22陈九生,朱哲民.粘弹包膜气泡的声散射特性.声学学报,2005;30(5):385-392
23范雨喆,陈宝伟,李海森,徐超.丛聚的含气泡水对线性声传播的影响.物理学报,2018; 67(17):174301
24 Fan Y, Li H,Xu C et al. Influence of bubble distributions on the propagation of linear waves in polydisperse bubbly liquids. J. Acoust. Soc. Am., 2019; 145(1):16-25
25王成会,林书玉.超声场中气泡的耦合运动.声学学报,2011;36(3):325-331
26杨德森,时洁,时胜国,张昊阳,江薇,靳仕源.声波作用下的气泡非线性动力学特性影响因素及功率谱变化规律研究.声学学报,2013; 38(2):113-127
27 Li K M, Lui W K, Frommer G H. The diffraction of sound by an impedance sphere in the vicinity of a ground surface.J. Acoust. Soc. Am.,2004; 115(1):42-56
2 Van Vossen R, Ainslie M A. The effect of wind-generated bubbles on sea-surface backscattering at 940 Hz. J. Acoust.Soc. Am., 2011; 130(5):3413-3420
3范雨喆,李海森,徐超,陈宝伟,杜伟东.基于声散射的水下气泡群空间关联性研究.物理学报,2017; 66(1):014305
4 Lovik A, Hovem J M. An experimental investigation of swimbladder resonance in fishes. J. Acoust. Soc. Am.,1979; 66(3):850-854
5李灿苹,刘学伟,赵罗臣.天然气水合物冷泉和气泡羽状流研究进展.地球物理学进展,2013; 28(2):1048-1056
6 Kargl S G. Effective medium approach to linear acoustics in bubbly liquids. J. Acoust. Soc. Am., 2002; 111(1):168-173
7 Foldy L L. The multiple scattering of waves. I. General theory of isotropic scattering by randomly distributed scatterers. Physical Review, 1945; 67(3-4):107-119
8 Ye Z, Ding L. Acoustic dispersion and attenuation relations in bubbly mixture. J. Acoust.Soc. Am., 1995; 98(3):1629-1636
9 Henyey F S. Corrections to Foldy's effective medium theoryfor propagation in bubble clouds and other collections of very small scatterers. J. Acoust. Soc. Am., 1999; 105(4):2149-2154
10 Commander K W, Prosperetti A. Linear pressure waves in bubbly liquids:Comparison between theory and experiments. J. Acoust. Soc. Am., 1989; 85(2):732-746
11苗博雅,安宇.两种气泡混合的声空化.物理学报,2014; 64(20):204301
12王勇,林书玉,张小丽.声波在含气泡液体中的线性传播.物理学报,2014; 63(3):034301
13 d'Agostino L, Brennen C E. Acoustical absorption and scattering cross sections of spherical bubble clouds. J.Acoust. Soc. Am., 1988; 84(6):2126-2134
14 Prosperetti A, Lu N Q, Kim H S. Active and passive acoustic behavior of bubble clouds at the ocean's surface. J.Acoust. Soc. Am., 1993; 93(6):3117-3127
15 Nicholas M, Roy R A, Crum L A et al. Sound emissions by a laboratory bubble cloud. J. Acoust. Soc. Am., 1994;95(6):3171-3182
16 Sarkar K, Prosperetti A. Coherent and incoherent scattering by oceanic bubbles. J. Acoust. Soc. Am., 1994; 96(1):332-341
17 Gaunaurd G C, Huang H. Acoustic scattering by an airbubble near the sea surface. IEEE J. Oceanic Eng., 1995;20(4):285-292
18 Gaunaurd G C, Huang H. Sound scattering by bubble clouds near the sea surface. J. Acoust. Soc. Am., 2000;107(1):95-102
19 Hahn T R. Low frequency sound scattering from spherical assemblages of bubbles using effective medium theory. J.Acoust. Soc. Am., 2007; 122(6):3252-3267
20钱祖文.颗粒介质中的声传播及其应用.北京:科学出版社,2012:17-34
21 Leighton T. The acoustic bubble. Massachusetts:Academic Press, 2012:172-191
22陈九生,朱哲民.粘弹包膜气泡的声散射特性.声学学报,2005;30(5):385-392
23范雨喆,陈宝伟,李海森,徐超.丛聚的含气泡水对线性声传播的影响.物理学报,2018; 67(17):174301
24 Fan Y, Li H,Xu C et al. Influence of bubble distributions on the propagation of linear waves in polydisperse bubbly liquids. J. Acoust. Soc. Am., 2019; 145(1):16-25
25王成会,林书玉.超声场中气泡的耦合运动.声学学报,2011;36(3):325-331
26杨德森,时洁,时胜国,张昊阳,江薇,靳仕源.声波作用下的气泡非线性动力学特性影响因素及功率谱变化规律研究.声学学报,2013; 38(2):113-127
27 Li K M, Lui W K, Frommer G H. The diffraction of sound by an impedance sphere in the vicinity of a ground surface.J. Acoust. Soc. Am.,2004; 115(1):42-56