0 引言
1 控制方程和数值方法
1.1 控制方程
1.2 数值方法
2 数值模型验证
2.1 孤立波在斜坡式海堤上的越浪量验证
图2 不同测点处的波高时程曲线Fig.2 The temporal evolution of wave height for different wave gauges |
图3 不同时刻的沿程水位高程空间分布Fig.3 Spatial distributions of wave elevation at different times |
2.2 风影响下规则波传播变形的验证
3 工况设置与结果分析
表1 数值模拟工况和波浪破碎类型Tab.1 Parameter setup of numerical simulation and wave breaking types |
工况 | H/m | AC/m | cotα | cotβ | 破碎类型 | 工况 | H/m | AC/m | cotα | cotβ | 破碎类型 | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0 | 0.10 | 0.117 | 20 | 2 | 卷破波 | 23 | 4 | 0.10 | 0.067 | 20 | 2 | 卷破波 |
2 | 1 | 0.10 | 0.117 | 20 | 2 | 卷破波 | 24 | 0 | 0.10 | 0.117 | 10 | 2 | 激破波 |
3 | 2 | 0.10 | 0.117 | 20 | 2 | 卷破波 | 25 | 4 | 0.10 | 0.117 | 10 | 2 | 激破波 |
4 | 3 | 0.10 | 0.117 | 20 | 2 | 卷破波 | 26 | 0 | 0.10 | 0.117 | 15 | 2 | 卷破波 |
5 | 4 | 0.10 | 0.117 | 20 | 2 | 卷破波 | 27 | 4 | 0.10 | 0.117 | 15 | 2 | 卷破波 |
6 | 5 | 0.10 | 0.117 | 20 | 2 | 卷破波 | 28 | 0 | 0.10 | 0.117 | 20 | 2 | 卷破波 |
7 | 6 | 0.10 | 0.117 | 20 | 2 | 卷破波 | 29 | 4 | 0.10 | 0.117 | 20 | 2 | 卷破波 |
8 | 0 | 0.05 | 0.117 | 20 | 2 | 卷破波 | 30 | 0 | 0.10 | 0.117 | 25 | 2 | 卷破波 |
9 | 4 | 0.05 | 0.117 | 20 | 2 | 卷破波 | 31 | 4 | 0.10 | 0.117 | 25 | 2 | 卷破波 |
10 | 0 | 0.10 | 0.117 | 20 | 2 | 卷破波 | 32 | 0 | 0.10 | 0.117 | 30 | 2 | 卷破波 |
11 | 4 | 0.10 | 0.117 | 20 | 2 | 卷破波 | 33 | 4 | 0.10 | 0.117 | 30 | 2 | 卷破波 |
12 | 0 | 0.15 | 0.117 | 20 | 2 | 卷破波 | 34 | 0 | 0.10 | 0.117 | 20 | 0 | 卷破波 |
13 | 4 | 0.15 | 0.117 | 20 | 2 | 卷破波 | 35 | 4 | 0.10 | 0.117 | 20 | 0 | 卷破波 |
14 | 0 | 0.20 | 0.117 | 20 | 2 | 卷破波 | 36 | 0 | 0.10 | 0.117 | 20 | 1 | 卷破波 |
15 | 4 | 0.20 | 0.117 | 20 | 2 | 卷破波 | 37 | 4 | 0.10 | 0.117 | 20 | 1 | 卷破波 |
16 | 0 | 0.10 | 0.217 | 20 | 2 | 卷破波 | 38 | 0 | 0.10 | 0.117 | 20 | 2 | 卷破波 |
17 | 4 | 0.10 | 0.217 | 20 | 2 | 卷破波 | 39 | 4 | 0.10 | 0.117 | 20 | 2 | 卷破波 |
18 | 0 | 0.10 | 0.167 | 20 | 2 | 卷破波 | 40 | 0 | 0.10 | 0.117 | 20 | 3 | 卷破波 |
19 | 4 | 0.10 | 0.167 | 20 | 2 | 卷破波 | 41 | 4 | 0.10 | 0.117 | 20 | 3 | 卷破波 |
20 | 0 | 0.10 | 0.117 | 20 | 2 | 卷破波 | 42 | 0 | 0.10 | 0.117 | 20 | 4 | 卷破波 |
21 | 4 | 0.10 | 0.117 | 20 | 2 | 卷破波 | 43 | 4 | 0.10 | 0.117 | 20 | 4 | 卷破波 |
22 | 0 | 0.10 | 0.067 | 20 | 2 | 卷破波 |
3.1 水动力特性分析
图8 有风和无风时不同时刻水体的速度云图Fig.8 Velocity contours of water body at different time moments in windy and windless conditions |
图9 有风和无风时孤立波爬高(a)和越浪量(b)时程曲线对比Fig.9 Comparison of the time series of solitary wave runup height (a) and volume of overtopping water (b) in windy and windless conditions |
图10 有风和无风时海堤所受的水动力荷载Fig.10 Hydrodynamic forces exerted at the seawall in windy and windless conditions |
图11 有风和无风时沿程最大水位高程空间分布Fig.11 Spatial distributions of the maximum water elevation in windy and windless conditions |
3.2 风速的影响
图13 不同风速下孤立波的最大爬高(a)和最大越浪量(b)Fig.13 Maximum runup height (a) and maximum overtopping volume (b) of solitary wave under different onshore wind speeds |
图14 不同风速下不同测点处相对波高的比较Fig.14 Comparison of relative wave height for different wave gauges under different onshore wind speeds |
3.3 入射波高的影响
图16 不同入射波高下有风和无风时孤立波的最大爬高(a)和最大越浪量(b)Fig.16 Maximum value of runup height (a) and maximum overtopping volume (b) of solitary wave in windy and windless conditions under different incident wave heights |
图17 不同入射波高下有风和无风时不同测点处相对波高的比较Fig.17 Comparison of relative wave height for different wave gauges in windy and windless conditions under different incident wave heights |
3.4 堤顶超高的影响
图19 不同堤顶超高下有风和无风时孤立波的最大爬高(a)和最大越浪量(b)Fig.19 Maximum value of runup height (a) and maximum overtopping volume (b) of solitary wave in windy and windless conditions under different dimensionless crest freeboards |
图20 不同堤顶超高下有风和无风时不同测点处相对波高的比较Fig.20 Comparison of relative wave height for different wave gauges in windy and windless conditions under different dimensionless crest freeboards |
3.5 岸滩坡度的影响
图22 不同岸滩坡度下有风和无风时孤立波的最大爬高(a)和最大越浪量(b)Fig.22 Maximum value of runup height (a) and maximum overtopping volume (b) of solitary wave in windy and windless conditions under different beach slopes |
图23 不同岸滩坡度下有风和无风时不同测点处相对波高的比较Fig.23 Comparison of relative wave height for different wave gauges in windy and windless conditions under different beach slopes |
3.6 海堤坡度的影响
图25 不同海堤坡度下有风和无风时孤立波的最大爬高(a)和最大越浪量(b)Fig.25 Maximum value of runup height (a) and maximum overtopping volume (b) of solitary wave in windy and windless conditions under different seawall slopes |
图26 不同海堤坡度下有风和无风时不同测点处相对波高的比较Fig.26 Comparison of relative wave height for different wave gauges in windy and windless conditions under different seawall slopes |