Study on development characteristics of gas-liquid mixture zones and kinematics of breaking wave with different breaking type
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摘要: 了解波浪破碎速度场的分布特性对于波浪破碎物理机制的研究极为重要，同时，对比研究不同类型破碎产生的气液混合区的演化特征有利于波浪白冠覆盖率模型的完善。在实验室水槽，生成了深水临界波、单次崩破波和单次卷破波，采用图像测速技术获取了波浪破碎图像、波面下水体和气液混合区速度场。结果表明，崩破波的水平向速度u和垂直向速度v在波峰前和波峰后的分布极为不对称，其水平向最大速度umax并不位于峰顶，而是在主导波峰前0.7
$\eta_{\max} $ 处；卷破波的umax出现在波峰峰顶前端极小的区域内，且该区域与周围区域的速度梯度极大。崩破波和卷破波生成的气液混合区发展特征也存在差异：崩破波的umax值大、影响区域长、混合区厚度较小、各区域影响时间短；而卷破波的各项特征参数与崩破波形成对比。Abstract: To understand the internal physical mechanism of wave breaking, it is important to study the distribution characteristics of the particle velocity field under breaking wave. In addition, a comparative study of the evolution characteristics of the gas-liquid mixing zone caused by different types of breaking is beneficial to the improvement of the whitecap coverage model. In the laboratory wave flume, a critical wave, a single spilling wave, and a single plunging wave are generated in deep water based on the linear phase focusing theory. The velocity fields below the wave surface and the velocity fields in the gas-liquid mixing zone are measured using particle image velocimetry (PIV) and bubble image velocimetry (BIV), respectively. The distribution characteristics of the velocity field at the extreme state of different breaking types are compared and discussed. The results show that the horizontal velocity u and vertical velocity v of the spilling wave are extremely asymmetrical in the front part and back part of the wave crest. In addition, the maximum horizontal velocity umax is not at the top of the wave peak, but at the pre-peak position about 0.7$\eta_{\max} $ front part and back part of the wave crest. In addition, the maximum horizontal velocity of the peak. For plunging wave, the maximum horizontal velocity umax appears at the top and very front of the wave peak with a very small region, and the velocity gradient between this area and the surrounding area is very large. The development characteristics of the gas-liquid mixing zone produced by different wave breaking also have differences. For spilling wave, the gas-liquid mixing zone generated by breaking has high horizontal movement speed, long influencing area, short influence time at each location, and small thickness. For plunging wave, the gas-liquid mixing zone has relatively slow horizontal movement speed and larger vertical input, shorter affected area, longer affected time at each location, and greater thickness.small thickness. However, for plunging wave, these characteristic parameters are in contrast with those of the spilling wave. -
图 3 粒子图像测速技术分析的临界波波峰区间速度场
a. 水平向速度；b. 垂向速度，黑色矢量为合速度
Fig. 3 Particle image velocimetry velocity field in wave crest area of critical wave
a. Horizontal velocity; b. vertical velocity. The black vector is the absolute velocity
图 4 临界波波峰区间，速度矢量平面图
Fig. 4
$ \hat{u} $ vs$ \hat {v}$ for wave crest area of critical wave
图 5 崩破波形成过程波峰区间速度场
左列为水平向速度；右列为垂向速度，黑色矢量为合速度
Fig. 5 Particle image velocimetry velocity field in wave crest area of spilling wave
Left column represents horizontal velocity; right column represents vertical velocity. The black vector is the absolute velocity
图 6 图 5b时刻波峰区间速度矢量平面图
Fig. 6
$ \hat{u} $ vs$\hat{v} $ for wave crest area of spilling wave in Fig. 5b
图 7 卷破波水舌入水前波峰区间速度场
左列为水平向速度；右列为垂向速度。黑色矢量为合速度
Fig. 7 Particle image velocimetry velocity field in wave crest area of plunging wave
Left column represents horizontal velocity, right column represents vertical velocity. The black vector is the absolute velocity
图 8 图 7b时刻，波峰区间速度矢量平面图
Fig. 8
$ \hat{u} $ vs$ \hat{v}$ for wave crest area of plunging wave in Fig. 7b
图 11 崩破导致混合区影响深度随时间的变化（左列）和混合区最大水平向速度与水体最大水平向速度的比较（右列）
混合区最大水平向速度由BIV测量获得，水体最大水平向速度由PIV测量获得
Fig. 11 Spilling wave, the thickness of mixed zone varies with time (left column) and the comparison of the maximum horizontal velocity
$ \hat{u}_{\max}$ in mixed zone and the maximum horizontal velocity$ \hat{u}_{\max}$ in water body (right column)Maximum horizontal velocity $ \hat{u}_{\max}$ of the mixed zone is measured by BIV, maximum horizontal velocity $ \hat{u}_{\max}$ of the water body is measured by PIV
图 12 卷破导致混合区影响深度随时间的变化（左列）和混合区最大水平向速度与水体最大水平向速度的比较（右列）
混合区最大水平向速度由BIV测量获得，水体最大水平向速度由PIV测量获得
Fig. 12 Plunging wave, the thickness of mixed zone varies with time (left column) and the comparison of the maximum horizontal velocity
$ u_{ \max } $ in mixed zone and the maximum horizontal velocity$ u_{ \max } $ in water body (right column)Maximum horizontal velocity $ u_{ \max } $ of the mixed zone is measured by BIV, maximum horizontal velocity $ u_{ \max } $ of the water body is measured by PIV
表 1 试验工况参数
Tab. 1 Experimental conditions
工况 fp Sinput $ \Delta f $ γ 破碎类型 1 0.8 0.33 0.56 6.0 临界波 2 0.75 0.38 0.64 3.3 崩破波 3 0.75 0.35 1.46 3.3 卷破波 
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表 2 不同破碎类型特征参数的对比
Tab. 2 Comparison of characteristic parameters of different breaking types
破碎
类型极限状态运动
特征参数气液混合区特征参数 速度场分布 $ u_{ \max } $ 总长度Lm 总时长Tm Dmax tmax $ u_{ \max } ^m$ 临界波 对称 0.66Cd 崩破波 极不对称 0.84Cd 1.15Ld 1.86T 0.75$ \eta_{\max}$ 0.6T 1.5Cd 卷破波 不对称 0.83Cd 0.5Ld 2.0T 1.55$ \eta_{\max}$ 1.0T 1.0Cd
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