Drift of weakly inertial plastic blocks under wave action of finite-water-depth
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摘要: 塑料漂浮垃圾对海洋环境影响巨大，在近岸的传播过程主要受波浪作用。针对塑料漂浮垃圾在近岸的运动特征，以往研究尚不深入。本文采用物理模型实验，对塑料漂浮物在有限水深波浪作用下的漂移规律开展研究，探讨了弱惯性塑料块体水平漂移速度与漂浮物性状以及波陡之间的关系。实验结果表明，塑料块体的漂移量受斯托克斯漂移与欧拉回流的共同影响，与二阶拉格朗日漂移理论吻合良好。在漂浮物尺寸远小于波长的情况下，漂浮物尺寸以及密度的改变对漂移没有显著的影响；漂浮物的漂移量与波陡的平方成正比，根据本文的实验及以往公开发表的实验数据，修正了经验公式，为塑料漂浮物在近岸的传播与预测提供了有益借鉴。Abstract: Plastic floating objects have a profound impact on the marine environment. The nearshore process of the floating objects is mainly influenced by the action of waves. On the kinetic characteristics of plastic floating objects, previous studies were not thorough for the nearshore regime. In this paper, laboratory experiments were used to study the drift-law of plastic-floating objects under finite-water-depth waves. The relationship between the horizontal drift velocity of a weakly inertial plastic blocks and their characteristics, along with the wave steepness were discussed. The experimental results show that the drift of plastic blocks is affected by Stokes drift and Euler return flow, which is in good agreement with the second-order Lagrange drift theory. As the floating object’s size is much smaller than the wave length, size or density of the floating objects has no significant effect on drift. The drift of floating objects is proportional to the square of wave steepness. Based on the experiments conducted in this study and previously published experimental data, the empirical formula is revised to provide useful reference for the nearshore migration law of plastic floating objects and so for the relevant prediction.
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图 1 物理模型实验波浪水槽布局（a）、拍摄装置（b）和基于深度学习的目标检测方法（YoloX）（c）
Fig. 1 Layout of the physical model experiment wave flume (a), imaging device (b), and object detection method based on deep learning (YoloX) (c)
图 2 不同波况的波面过程（a）、M3波况下波面过程的小波分析（b）、M3波况下波面过程的波能谱分析（c）和M3波况下波浪沿程的波能谱分析（d）
Fig. 2 Wave surface processes under different wave conditions (a), wavelet analysis of the wave surface processes under M3 wave condition (b), wave energy spectrum analysis of the wave surface processes under M3 wave condition (c), and wave energy spectrum analysis along wave propagation under M3 wave condition (d)
图 3 3次重复性实验水平方向的ADV测速（a），实验所测流速与理论流速对比（b），拉格朗日漂移、斯托克斯漂移和欧拉回流的关系（c）
Fig. 3 Three repetitions of horizontal ADV velocity measurements in experiments (a), comparison between experimental and theoretical flow velocities (b), relationship between Lagrange drift and Stokes drift and Eulerian return flow (c)
图 4 部分工况下塑料漂浮块体的漂移轨迹（a）和M3工况下不同塑料漂浮块体的漂移量时间过程线（b）
Fig. 4 Trajectories of plastic floating blocksunder certain conditions (a) and time series of driftdistance for different plastic floating blocks under M3 condition (b)
图 5 M3工况（a）与M5工况（b）下，实验塑料漂浮块体漂移过程线与水质点漂移理论对比
Fig. 5 Comparison between experimentaldrifting time series of plastic floating blocks and theoretical drifting time series of water particles, under M3 condition (a) and M5 condition (b)
图 6 塑料漂浮块体无量纲化的水平漂移速度与波陡的关系
Fig. 6 Relationship between non-dimensional horizontal drift velocity of plastic floating blocks and wave steepness
图 7 塑料漂浮块体无量纲化的水平漂移速度与尺寸（a）、密度（b）的关系
Fig. 7 Relationship between non-dimensional horizontal drift velocity of plastic floating blocksand size (a) , as well as density (b)
表 1 物理模型实验设计的波浪要素
Tab. 1 Wave parameters in the design of the physical model experiment
波况 初始水深d0/m 初始波高H0/m 初始波周期T0/s 水深d/m 波高H/m 波周期T/s 波长L/m 波速c/(m·s−1) 波陡S* 相对水深kd M1 0.6 0.074 0.75 0.3 0.060 0.75 0.86 1.14 0.220 2.199 M2 0.6 0.069 1 0.3 0.063 1 1.37 1.37 0.144 1.374 M3 0.6 0.051 1.5 0.3 0.064 1.5 2.34 1.56 0.086 0.805 M4 0.6 0.039 2 0.3 0.056 2 3.26 1.63 0.054 0.579 M5 0.6 0.113 1.5 0.3 0.155 1.5 2.34 1.56 0.207 0.805 M6 0.5 0.064 1.5 0.2 0.095 1.5 1.98 1.32 0.151 0.636 注：*S = ak，a为振幅，k为波数，0.01 < S ≤ 0.1，属于二阶斯托克斯波理论；S > 0.1，属于三阶斯托克斯波理论。 
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表 2 实验塑料漂浮块体属性
Tab. 2 Properties of experimental plastic floating block
漂浮物材质 形状 尺寸*/m 相对密度（ρ/ρw）** 斯托克斯数St*** PP 球体 0.012 0.9 0.055～0.147 PLA 正方体 0.02 0.8 0.086 PLA 正方体 0.03 0.8 0.107 PLA 正方体 0.04 0.8 0.096～0.255 PLA 正方体 0.04 0.6 0.17 PLA 正方体 0.04 0.4 0.199 PLA 正方体 0.04 0.2 0.245 注：*球体尺寸为直径（D），正方体尺寸为边长（l）。**水槽内为清水，取密度ρw=1 g/cm3。***St的范围与该属性漂浮物参与的波况相关，波周期较小，St较大。
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A1 字符说明及单位
A1 Symbol illustration and dimension
字符 说明 单位 d 设计静水深 m H 设计波高 m T 设计波周期 s d0 造波机所在位置处静水深 m H0 造波机所在位置处波高 m T0 造波机所在位置处波周期 s a 波振幅 m k 波数 m−1 L 波长 m S 波陡 − c 波速 m/s ρ 塑料漂浮物密度 g/cm3 ρw 实验水槽内水密度 g/cm3 l 塑料漂浮块体边长 m D 塑料漂浮球体直径 m St 斯托克斯数，与漂浮物属性相关，St $\ll $ 1，代表漂浮物弱惯性 − t 时间 s x 水平方向距离，且向岸为正 m z 距离静水面的距离，且向上为正 m x0 漂浮物/水质点水平方向初始位置 m z0 漂浮物/水质点垂直方向初始位置 m θ 相位，θ = kx − wt rad θ0 初始相位，θ0 = kx0 − wt rad ω 角频率 rad/s uw.exp 实验测量流速 m/s uw 水质点二阶斯托克斯理论水平方向流速 m/s ww 水质点二阶斯托克斯理论垂直方向流速 m/s uS, 2nd 二阶斯托克斯波理论下的水质点水平漂移速度 m/s uE 欧拉流速 m/s uL, 2nd 二阶拉格朗日理论下的水质点水平漂移速度 m/s udrift.exp 实验观测到的水平漂移速度 m/s χ1 待定系数 − f 频率 Hz Sf 能量谱密度（能量谱） m2·s τp 漂浮物的反应时间 s wp 漂浮物沉降速度 m/s g 重力加速度 m/s2 注：“−”表示无单位。
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