﻿ 分层流体孤立子模型的实验重现及流场分析
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 哈尔滨工程大学学报  2020, Vol. 41 Issue (2): 263-270  DOI: 10.11990/jheu.201905113 0

### 引用本文

ZOU Li, MA Xinyu, LI Zhenhao, et al. Experimental reconstruction and flow-field analysis of stratified fluid soliton model[J]. Journal of Harbin Engineering University, 2020, 41(2): 263-270. DOI: 10.11990/jheu.201905113.

### 文章历史

1. 大连理工大学 船舶工程学院, 辽宁 大连 116024;
2. 高技术船舶与深海开发装备协同创新中心, 上海 200240

Experimental reconstruction and flow-field analysis of stratified fluid soliton model
ZOU Li 1,2, MA Xinyu 1, LI Zhenhao 1, SUN Tiezhi 1, YU Zongbing 1
1. School of Naval Architecture, Dalian University of Technology, Dalian 116024, China;
2. Collaborative Innovation Center for Advanced Ship and Deep-Exploration, Shanghai 200240, China
Abstract: In view of the characteristics of the inner solitary wave, the isolator model can be used as its mathematical expression. To reproduce and further study the soliton model, we used an insoluble two-layer fluid to establish a small flume for the generation and evolution of solitary waves combined with particle image velocimetry technology to realize the capture and analysis of their flow characteristics. In the experimental conditions, the velocity field presents a clockwise vortex, with the velocity of the fluid particles in the upper layer being higher than that in the lower layer, and the vorticity near the trough being the largest. The internal wave generated in this experiment is in good agreement with the soliton traveling wave solution of the equation and satisfies the condition of an isolated wave. These results provide an experimental basis and characteristic supplement to the associated flow field of the theoretical isolated wave.
Keywords: internal wave flume    stratified fluid    soliton    internal solitary wave    PIV technology    MCC equation    velocity field    vortex field

1 实验设置

PIV实验选用能够发出纯绿色片状光源(光源夹角60°)的激光器，激光器布置在水槽上方，垂直向下照射，如图 1所示。分别在两层流体中混入密度为1.03×103 kg/m3，表面积为24 μm、体积为31 μm的聚苯乙烯来作为示踪粒子，即使粒子的比重相对于硅油偏大，但会在硅油粘度的作用下长时间保持悬浮状态，并可以清晰刻画流场特征，此时相机的帧速率为42 Hz，分辨率为1 368×1 096像素。PIV实验在暗室中进行，通过在相机镜头前安装偏振镜并采用黑色背景色，最大程度的降低了反射光与折射光对实验测量的影响，在得到高质量的流场时间序列图片后，使用互相关法对图像进行分析处理[19]。对于本实验搭建的水槽可完成造波及内孤立波波形和流场特征的提取，最终染色剂和PIV效果如图 2所示。

2 实验结果与分析 2.1 实验造波波形评价

 $\begin{array}{c} \alpha_{j 1} \eta_{1}^{\prime \prime}+\alpha_{j 2} \eta_{2}^{\prime \prime}+\alpha_{j 3} \eta_{1}^{\prime 2}+\alpha_{j 4} \eta_{3}^{\prime 2}+\alpha_{j s} \eta_{1}^{\prime} \eta_{2}^{\prime}=\alpha_{j 6} \\ j=1, 2 \end{array}$ (1)

 \begin{aligned} &\eta_{2}=h_{2}+\zeta_{2};\\ &\alpha_{11}=\frac{1}{3} \frac{c^{2} h_{1}^{2}}{\eta_{1}}, \alpha_{12}=\frac{1}{2} \frac{c^{2} h_{1}^{2}}{\eta_{1}}, \\ &\alpha_{13}=-\frac{1}{6} \frac{c^{2} h_{1}^{2}}{\eta_{1}}, \alpha_{14}=\frac{1}{2} \frac{c^{2} h_{1}^{2}}{\eta_{1}^{2}}, \alpha_{15}=0, \\ &\alpha_{16}=-g\left[\left(\eta_{1}-h_{1}\right)+\left(\eta_{2}-h_{2}\right)\right]+\\ &\frac{1}{2} c^{2}\left[1-\left(\frac{h_{1}}{\eta_{1}}\right)^{2}\right]\\ &\alpha_{21}=\frac{1}{2} \frac{\rho c^{2} h_{1}^{2}}{\eta_{1}}, \alpha_{22}=\frac{\rho c^{2} h_{1}^{2}}{\eta_{1}}+\frac{1}{3} \frac{c^{2} h_{2}^{2}}{\eta_{2}}, \\ &\alpha_{23}=-\frac{1}{2} \frac{\rho c^{2} h_{1}^{2}}{\eta_{1}^{2}}, \alpha_{24}=-\frac{1}{6} \frac{c^{2} h_{2}^{2}}{\eta_{2}^{2}}, \alpha_{25}=-\frac{\rho c^{2} h_{1}^{2}}{\eta_{1}^{2}}, \\ &\alpha_{26}=-g\left[\rho\left(\eta_{1}-h_{1}\right)+\left(\eta_{2}-h_{2}\right)\right]+\\ &\frac{1}{2} c^{2}\left[1-\left(\frac{h_{2}}{\eta_{2}}\right)^{2}\right]。\end{aligned}

 Download: 图 3 实验波形与理论波形对比 Fig. 3 The comparison between experimental waveform and theoretical solutions

2.2 速度场演变特性分析

 Download: 图 4 内孤立波速度场分布 Fig. 4 Internal solitary wave velocity field distribution

 Download: 图 5 内孤立波速度场时间序列 Fig. 5 Time series of internal solitary wave velocity field

 Download: 图 7 4种不同深度水平流速时历曲线 Fig. 7 Time series of four difference depth horizontal velocity

 Download: 图 8 波谷位置水平流速沿垂直方向分布曲线 Fig. 8 Trough position horizontal velocity distribution curve along the vertical direction
2.3 涡量场特性分析

 Download: 图 11 波谷位置涡量垂向分布 Fig. 11 The vertical distribution of vorticity at the trough position
3 结论

1) 实验波形与多组理论解进行比较，与现存最为准确的MCC理论解吻合最佳，能够生成稳定传播的内孤立波，并可准确测量其流场数据，实验结果可为理论孤立波的伴生流场提供依据并且可为实际海洋内孤立波流场特征提供一定参考。

2) 内孤立波在传播过程中速度场有较好的稳定性与对称性，波面线以上流体质点速度与内孤立波传播方向相同，波面线以下流体速度与内孤立波传播方向相反。上层流体的水平速度分量占据整个速度的主要部分，且在波面附近流体质点的速度变化最为剧烈。

3) 围绕内孤立波波面涡呈顺时针方向，随内波波幅增大涡量场表现形式相似，且涡量峰值随时间变化趋势与内孤立波波形基本趋于一致，涡量最大值出现在波谷附近，波谷垂向位置涡量从增大到减小的过程所对应流体深度的变化并未随波幅的增大而显著增加。

 [1] JACKSON C. Internal wave detection using the moderate resolution Imaging spectroradiometer (MODIS)[J]. Journal of geophysical research:oceans, 2007, 112(C11): C11012. DOI:10.1029/2007JC004220 (0) [2] DUDA T F, LYNCH J F, IRISH J D, et al. Internal tide and nonlinear internal wave behavior at the continental slope in the northern South China Sea[J]. IEEE journal of oceanic engineering, 2004, 29(4): 1105-1130. DOI:10.1109/JOE.2004.836998 (0) [3] KLYMAK J M, PINKEL R, LIU C, et al. Prototypical solitons in the South China Sea[J]. Geophysical research letters, 2006, 33(L1160711). (0) [4] CHAKRABARTI S. Handbook of offshore engineering (2-volume set)[M]. Amsterdam: Elsevier Ltd, 2005. (0) [5] DE VRIES G. XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves[J]. The London, Edinburgh, and Dublin philosophical magazine and journal of science, 1895, 39(240): 422-443. DOI:10.1080/14786449508620739 (0) [6] FUNAKOSHI M, OIKAWA M. Long internal waves of large amplitude in a two-layer fluid[J]. Journal of the physical society of japan, 1986, 55(1): 128-144. DOI:10.1143/JPSJ.55.128 (0) [7] CHOI W, CAMASSA R. Fully nonlinear internal waves in a two-fluid system[J]. Journal of fluid mechanics, 1999, 396: 1-36. DOI:10.1017/S0022112099005820 (0) [8] CAMASSA R, CHOI W, MICHALLET H, et al. On the realm of validity of strongly nonlinear asymptotic approximations for internal waves[J]. Journal of fluid mechanics, 2006, 549: 1-23. DOI:10.1017/S0022112005007226 (0) [9] KODAIRA T, WASEDA T, MIYATA M, et al. Internal solitary waves in a two-fluid system with a free surface[J]. Journal of fluid mechanics, 2016, 804: 201-223. DOI:10.1017/jfm.2016.510 (0) [10] CHEN Chenyuan, HSU J R C, CHENG M H, et al. An investigation on internal solitary waves in a two-layer fluid:propagation and reflection from steep slopes[J]. Ocean engineering, 2007, 34(1): 171-184. DOI:10.1016/j.oceaneng.2005.11.020 (0) [11] 黄文昊, 尤云祥, 王旭, 等. 有限深两层流体中内孤立波造波实验及其理论模型[J]. 物理学报, 2013, 62(8): 084705. HUANG Wenhao, YOU Yunxiang, WANG Xu, et al. Wave-making experiments and theoretical models for internal solitary waves in a two-layer fluid of finite depth[J]. Acta physica sinica, 2013, 62(8): 084705. (0) [12] 王旭, 林忠义, 尤云祥. 内孤立波与直立圆柱体相互作用特性数值模拟[J]. 哈尔滨工程大学学报, 2015, 36(1): 6-11. WANG Xu, LIN Zhongyi, YOU Yunxiang. Numerical simulation for the interaction characteristics of internal solitary waves with a vertical circular cylinder[J]. Journal of Harbin Engineering University, 2015, 36(1): 6-11. (0) [13] 盛立, 王怡然, 尤云祥, 等. 有限深两层流体中内孤立波传播演化理论模型研究[J]. 水动力学研究与进展(A辑), 2016, 31(6): 659-672. SHENG Li, WANG Yiran, YOU Yunxiang, et al. Investigation on propagation and evolution models for internal solitary waves in a two layer fluid system of finite depth[J]. Chinese journal of hydrodynamics, 2016, 31(6): 659-672. (0) [14] 许联锋, 陈刚, 李建中, 等. 粒子图像测速技术研究进展[J]. 力学进展, 2003(04): 533-540. XU Lianfeng, CHEN Gang, LI Jianzhong, et al. Reserch progress of particle image velocimetry[J]. Advances in mechanics, 2003(04): 533-540. DOI:10.3321/j.issn:1000-0992.2003.04.010 (0) [15] MOORE C D, KOSEFF J R, HULT E L. Characteristics of bolus formation and propagation from breaking internal waves on shelf slopes[J]. Journal of fluid mechanics, 2016, 791: 260-283. DOI:10.1017/jfm.2016.58 (0) [16] 孟静, 王树亚, 陈旭, 等. 内孤立波对小直径直立桩柱作用力的实验研究[J]. 海洋与湖沼, 2018, 49(3): 535-540. MENG Jing, WANG Shuya, CHEN Xu, et al. An experimental study on the force of internal solitary wave on a cylinder of small diameter[J]. Oceanologia et limnologia sinica, 2018, 49(3): 535-540. (0) [17] 殷文明, 郭海燕, 廖发林, 等. 内孤立波对不同水深竖直圆柱体水平作用力分析[J]. 中国海洋大学学报, 2018, 48(9): 125-131. YIN Wenming, GUO Haiyan, LIAO Falin, et al. Analysis of horizontal forces on vertical cylinders under internal solitary waves in different depths[J]. Periodical of Ocean University of China, 2018, 48(9): 125-131. (0) [18] 黄鹏起, 陈旭, 孟静, 等. 内孤立波破碎所致混合的实验研究[J]. 海洋与湖沼, 2016, 47(3): 533-539. HUANG Pengqi, CHEN Xu, MENG Jing, et al. An experimental study on mixing induced by internal solitary wave breaking[J]. Oceanologia et limnologia sinica, 2016, 47(3): 533-539. (0) [19] 段俐, 康琦, 申功炘. PIV技术的粒子图像处理方法[J]. 北京航空航天大学学报, 2000, 26(1): 79-82. DUAN Li, KANG Qi, SHEN Gongxin. Image processing method of PIV technique[J]. Journal of Beijing University of Aeronautics and Astronautics, 2000, 26(1): 79-82. DOI:10.3969/j.issn.1001-5965.2000.01.022 (0) [20] CHEN Min, CHEN Ke, YOU Yunxiang. Experimental investigation of internal solitary wave forces on a semi-submersible[J]. Ocean engineering, 2017, 141: 205-214. DOI:10.1016/j.oceaneng.2017.06.027 (0) [21] BOEGMAN L, STASTNA M. Sediment resuspension and transport by internal solitary waves[J]. Annual review of fluid mechanics, 2019, 51: 129-154. DOI:10.1146/annurev-fluid-122316-045049 (0)