拖曳体激发内波时空特性实验及其理论模型

陈科; 王宏伟; 盛立; 尤云祥

doi:10.7498/aps.67.20170920

摘要

在具有密度跃层的分层流体中，采用沿水槽中纵剖面对称布置电导率探头阵列的方法，对1个球体和2个不同长径比细长体在拖曳运动下激发内波的时空特性进行了系列实验.结果表明：存在一个与长径比近似为线性关系的临界Froude数Frc，当FrFrc时，内波相关速度均与物体运动速度一致，体积效应内波为主控内波，内波波高均随拖曳速度增大而先增大后减小，Lee波峰值对应速度随长径比增大而增大；当FrFrc时，内波相关速度均小于物体运动速度，其相关速度Froude数Friw均在0.431.18之间的一个条带内变化，尾迹效应内波为主控内波，内波波高均随拖曳速度增大而近似线性增大.此外，从波形结构上看，体积效应内波关于水槽中纵剖面是对称的，而尾迹效应内波关于水槽中纵剖面是不对称的.结合上述实验结果，在已有针对拖曳球产生内波的等效源理论模型基础上，针对体积效应内波，提出了不同长径比模型的等效源移动速度和体积的设置方法；针对尾迹效应内波正对称和反对称这一特性，提出了正对称组合源和反对称组合源理论模型及其参数设置方法.所得计算结果在波高、波形结构和波系分布上与实验结果符合良好，表明了所提出的理论模型及其参数设置方法的合理性和有效性.

关键词:

Abstract

In this paper, we perform experiments on the time-space characteristics of internal waves generated by horizontally towed bodies with three aspect ratios in a stratified fluid with a halocline. By the real-time measurements of conductivity probe arrays which are arranged symmetrically in the transverse section of the stratified fluid tank, it is shown that the transition between the body-generated internal wave and the wake-generated internal wave is related to a critical Froude number Frc, which is linearly dependent on the aspect ratio. For FrFrc, the correlation velocities of internal waves are consistent with the towing speeds of the towed bodies, indicating that such internal waves in this range are dominated by the body-forced effect. The heights of such body-generated internal waves first increase with the increase of Fr until Fr reaches a certain value of Frp, which is also linearly dependent on the aspect ratio, and then decrease. For FrFrc, the correlation velocities of internal waves are noticeably lower than the towing speeds, indicating that such internal waves in this range are dominated by the wake-forced effect, and that the Froude numbers with respect to the correlation velocities of such internal waves vary in a range from 0.43 to 1.18. The heights of such wake-generated internal waves nearly linearly increase with Fr increasing regardless of the aspect ratio. Moreover, the patterns of body-generated waves are symmetric, while the patterns of wake-generated waves are not symmetric. Based on the experimental results and the equivalent source method which has been proposed to simulate the internal waves generated by a towed sphere, a new equivalent source method is developed to calculate the internal waves generated by towed slender bodies. For the body-generated waves, the method of designing the speed, length and diameter of the equivalent source is proposed. The symmetrical and anti-symmetrical equivalent source and their speed and size are also proposed for the wake-generated waves. The numerical results are in good accordance with the experimental results in the heights and patterns of waves, indicating that such a theoretical method and its parameter settings are reasonable and effective.

Keywords:

作者及机构信息

1.
上海交通大学, 海洋工程国家重点实验室, 上海 200240;

2.
高新船舶与深海开发装备协同创新中心, 上海 200240;

3.
中国舰船研究设计中心上海分部, 上海 201108;

4.
中国人民解放军 92537部队, 北京 100161

通信作者: 陈科, raulphan@sjtu.edu.cn

基金项目: 国家自然科学基金（批准号：11072153，11372184）资助的课题.

Authors and contacts

1.
State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;

2.
Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China;

3.
China Ship Development and Design Center(Shanghai), Shanghai 201108, China;

4.
No. 92537 Unit of PLA, Beijing 100161, China

Corresponding author: Chen Ke, raulphan@sjtu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11072153, 11372184).

参考文献

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[26]	Druzhinin O A, Papko V V, Sergeev D A, Troitskaya Y I 2006 Izv. Atmos. Ocean. Phys. 42 615
[27]	Druzhinin O A 2009 Fluid Dyn. 44 213
[28]	Vasholz D P 2011 Theoretical and Computational Fluid Dynamics 25 357
[29]	Diamessis P J, Gurka R, Liberzon A 2010 Phys. Fluids 22 086601
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[31]	Yao Z C, Zhao F, Liang C, Hong F W, Zhang J 2017 J. Ship Mech. 21 8 (in Chinese) [姚志崇, 赵峰, 梁川, 洪方文, 张军 2017 船舶力学 21 8]
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[34]	Cai S, Xie J, Xu J, Wang D, Chen Z, Deng X, Long X 2014 Deep Sea Res. Part I 84 73

施引文献

[1]	Liang J J, Du T, Huang W G, Zeng K, He M X 2016 J. Ship Mech. 20 635 (in Chinese) [梁建军, 杜涛, 黄韦艮, 曾侃, 贺明霞 2016 船舶力学 20 635]
[2]	Robey H F 1997 Phys. Fluids 9 3353
[3]	Hopfinger E J, Flor J B, Chomaz J M, Bonneton P 1991 Exp. Fluids 11 255
[4]	Lin Q, Boyer D L, Fernando H J S 1993 Exp. Fluids 15 147
[5]	Chomaz J M, Bonneton P, Hopfinger E J 1993 J. Fluid Mech. 254 1
[6]	Bonneton P, Chomaz J M, Hopfinger E J 1993 J. Fluid Mech. 254 23
[7]	Wei G, Zhao X Q, Su X B, You Y X 2009 Sci. China: Series G 39 1338 (in Chinese) [魏岗, 赵先奇, 苏晓冰, 尤云祥 2009 中国科学G 39 1338]
[8]	Zhao X Q, You Y X, Chen K, Hu T Q, Wei G 2009 J. Shanghai Jiao Tong Univ. 43 1298 (in Chinese) [赵先奇, 尤云祥, 陈科, 胡天群, 魏岗 2009 上海交通大学学报 43 1298]
[9]	Wang J, You Y X, Hu T Q, Wang X Q, Zhu M H 2012 Acta Phys. Sin. 61 074701 (in Chinese) [王进, 尤云祥, 胡天群, 王小青, 朱敏慧 2012 61 074701]
[10]	Wang J, You Y X, Hu T Q, Zhu M H, Wang X Q, Wei G 2012 Chin. Sci. Bull. 57 606 (in Chinese) [王进, 尤云祥, 胡天群, 朱敏慧, 王小青, 魏岗 2012 科学通报 57 606]
[11]	Wang H W, Chen K, You Y X, Zhang X S 2017 Chin. Sci. Bull. 62 2132 (in Chinese) [王宏伟, 陈科, 尤云祥, 张新曙 2017 科学通报 62 2132]
[12]	Lighthill J 1978 Waves in Fluid (Cambridge: Cambridge University Press) pp23-30
[13]	Keller J B, Munk W H 1970 Phys. Fluids 13 1425
[14]	Miles J W 1971 Geo. Fluid Dynamics 2 63
[15]	Gray E P 1983 Phys. Fluids 26 2919
[16]	Voisin B 1994 J. Fluid Mech. 261 333
[17]	Yeung R W, Nguyen T C 1999 J. Eng. Math. 35 85
[18]	Broutman D, Rottman J, Eckermann S D 2004 Annu. Rev. Fluid Mech. 36 233
[19]	Milder M 1974 Internal Waves Radiated by a Moving Source Technical Report (Vol. 1) (Santa Monica: Defense Advanced Research Projects Agency) pp19-25
[20]	You Y X, Zhao X Q, Chen K, Wei G 2009 Acta Phys. Sin. 58 6750 (in Chinese) [尤云祥, 赵先奇, 陈科, 魏岗 2009 58 6750]
[21]	Brandt A, Rottier J R 2015 J. Fluid Mech. 769 103
[22]	Lin J T, Pao Y H 1979 Annu. Rev. Fluid Mech. 11 317
[23]	Gilreath H E, Brandt A 1985 AIAA J. 23 693
[24]	Wei G, Wu N, Xu X H, Su X B, You Y X 2011 Acta Phys. Sin. 60 044704 (in Chinese) [魏岗, 吴宁, 徐小辉, 苏晓冰, 尤云祥 2011 60 044704]
[25]	Dupont P, Kadri Y, Chomaz J M 2001 Phys. Fluids 13 3223
[26]	Druzhinin O A, Papko V V, Sergeev D A, Troitskaya Y I 2006 Izv. Atmos. Ocean. Phys. 42 615
[27]	Druzhinin O A 2009 Fluid Dyn. 44 213
[28]	Vasholz D P 2011 Theoretical and Computational Fluid Dynamics 25 357
[29]	Diamessis P J, Gurka R, Liberzon A 2010 Phys. Fluids 22 086601
[30]	Abdilghanie A M, Diamessis P J 2013 J. Fluid Mech. 720 104
[31]	Yao Z C, Zhao F, Liang C, Hong F W, Zhang J 2017 J. Ship Mech. 21 8 (in Chinese) [姚志崇, 赵峰, 梁川, 洪方文, 张军 2017 船舶力学 21 8]
[32]	Dupont P, Voisin B 1996 Dynamics Atmo. Oceans 23 289
[33]	Liang C, Hong F W, Yao Z C 2015 J. Hydrodynamics Ser. A 30 9 (in Chinese) [梁川, 洪方文, 姚志崇 2015 水动力学研究与进展 30 9]
[34]	Cai S, Xie J, Xu J, Wang D, Chen Z, Deng X, Long X 2014 Deep Sea Res. Part I 84 73

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