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Numerical analysis of wave run-up characteristics on dual non-submerged vertical cylinders system
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摘要: 波浪爬升是近海构筑物和海洋平台结构设计中的重要参数。全面掌握波浪的爬升特性有利于结构的安全保证和优化。采用有限元方法建立了求解Berkhoff缓坡方程的数值模型，并计算了非淹没单个直立圆柱周围的波高分布，计算结果与解析解吻合很好。以非淹没双直立圆柱为研究对象，探讨了圆柱间距对波浪爬升的影响。结果表明：上游圆柱周围的波高分布曲线波动较大，但最大相对波高和最小相对波高的发生位置基本与单个圆柱的情况相同；当圆柱间距为1/4波长的奇数倍时，最小相对波高明显减小，圆柱肩部出现第二峰值；而当圆柱间距为1/4波长的偶数倍时，最小相对波高则明显增加，圆柱肩部出现第二谷值。下游圆柱周围的波高分布曲线与单个圆柱的情况相似，但波高相对较小。Abstract: Wave run-up is an important parameter in offshore structures and ocean platforms design. A comprehensive understanding of its characteristics benefits the structural safety and design optimization. In this study, a numerical model is set up to solve the mild slope equation proposed by Berkhoff using the finite element method. The computational results of wave height distribution around the single non-submerged vertical cylinder match with the analytical solutions very well, verifying the validity of the numerical model. Subsequently, the effect of the spacing between two cylinders on wave run-up is investigated by observing the dual non-submerged vertical cylinders system. The numerical results show that the curve of wave height distribution around the upstream cylinder has a big fluctuation. However, the positions of maximum and minimum wave heights are the same as those in the single cylinder case. When the spacings are odd times of 1/4 incident wavelength, the minimum wave height decreases obviously and the secondary peak appears on the shoulder of the cylinder; when the spacings are even times of 1/4 incident wavelength, the minimum wave height obviously increases and the secondary trough appears on the shoulder of the cylinder. The curve of wave height distribution around the downstream cylinder is similar but smaller than that in the single cylinder case.
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图 2 非淹没单个直立圆柱地形（单位：m）
Figure 2. Sketch of single non-submerged vertical circular cylinder (unit: m)
图 3 单个直立圆柱周围波高分布比较
Figure 3. Comparison of calculated wave run-up with analytical solutions along circumference
图 4 非淹没双直立圆柱地形（单位：m）
Figure 4. Sketch of dual non-submerged vertical circular cylinder (unit: m)
图 5 圆柱间距改变对上游圆柱波浪爬高的影响
Figure 5. Influence of spacing between two cylinders on wave run-up of upstream cylinder
图 6 圆柱间距改变对下游圆柱波浪爬升的影响
Figure 6. Influence of spacing between two cylinders on wave run-up of downstream cylinder
表 1 下游圆柱波浪爬高最大值和最小值
Table 1. The maximum and minimum values of wave run-up around downstream cylinder
工况 S/L 最大相对波高 最小相对波高 工况 S/L 最大相对波高 最小相对波高 单个圆柱 / 1.801 0.517 5 2.25 1.672 0.467 1 1.25 1.609 0.444 6 2.50 1.754 0.491 2 1.50 1.749 0.485 7 2.75 1.684 0.473 3 1.75 1.649 0.456 8 3.00 1.754 0.490 4 2.00 1.754 0.491 
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