Deterministic simulation of multidirectional irregular waves
-
摘要: 波浪波动时间过程及波列的模拟，对于开展实际波浪对于工程建筑物的作用具有重要的意义。本文采用线性叠加的单叠加模型，建立了多向不规则波浪的确定性模拟方法。基于理论模拟的规则波、单向不规则波和多向不规则波，验证了波浪确定性模拟方法的有效性。定性地对比分析了模拟波列和已知波列的一致性；定量地研究了模拟波浪在空间范围rr/Ls的误差分布情况(rr表示指定位置与给定位置的空间距离，Ls为有效波长)。并且建议，采用本文方法进行波浪确定性模拟时，最佳的浪高仪间距应小于0.12Ls。Abstract: The simulation of wave time series or wave elevation histories is of great significance for the accurate study of real wave-action on marine structures. In this paper, a method of simulating multi-directional irregular wave elevations is proposed based on a linear single-summation model. To evaluate the effectiveness of the proposed method, theoretical simulated regular waves, unidirectional and multidirectional irregular waves are deterministically simulated. The consistence between the simulated wave time series and the original ones is verified. The simulated accuracy range is further evaluated based on the quantitative error analysis along the spatial dimension represented by the ratio of rr/Ls (in which, rr denotes the separations of the two wave gauges, and Ls dotes the significant wave length). It is suggested that the optimum relative separations of the wave gauges should be less than 0.12Ls when the proposed method is used to reconstruct multidirectional irregular waves.
-
图 2 2号（a）和5号（b）浪高仪在T0=250/256 s，H0=0.04 m，θ=π/6时的波浪过程线
Fig. 2 Comparison of the wave surface elevation histories for T0= 250/256 s, H0=0.04 m, θ=π/6 of No.2 (a) and No.5 (b) gauges
图 3 理论波浪频谱(Ts=1.5 s，Hs=0.04 m)
Fig. 3 Theoretical wave frequency spectrum (Ts=1.5 s，Hs=0.04 m)
图 4 R/Ls为0.06和0.12时，average-θi和max-Energy-θi的θEr沿fi的分布（Ts=1.5 s, Hs=0.04 m）
Fig. 4 Variation of the θEr for average-θi and max-Energy-θi with fi for R/Ls=0.06 and R/Ls=0.12 (Ts=1.5 s, Hs=0.04 m)
图 5 单向不规则波已知波列和模拟波列在不同rr/Ls时的对比（Ts=1.5 s，Hs=0.04 m）
Fig. 5 Comparison of the original and simulated uni-directional irregular wave surface elevation histories (Ts=1.5 s，Hs=0.04 m)
图 6 采用average-θi和max-Energy-θi模拟所得波浪的Ermax随rr/Ls的变化（Ts=1.5 s，Hs=0.04 m）
Fig. 6 Variation of Ermax for simulated waves with rr/Ls using average-θi and max-Energy-θi respectively (Ts=1.5 s, Hs=0.04 m)
图 7 R/Ls不同时，采用average-θi方法计算的θEr沿fi的分布（Ts=1.5 s，Hs=0.04 m，s=25）
Fig. 7 Variation of θEr with fi for average-θi method with different R/Ls (Ts=1.5 s, Hs=0.04 m, s=25)
图 8 rr/Ls=0.35，R/Ls不同时，3号浪高仪位置理论波列和确定性模拟波列的对比（Ts=1.5 s，Hs=0.04 m，s=25)
Fig. 8 Comparison of theoretical and simulated wave surface elevation histories for different R/Ls with rr/Ls=0.35 at No.3 gauge (Ts=1.5 s, Hs=0.04 m, s=25)
图 9 R/Ls=0.06，rr/Ls不同时，3号浪高仪位置处理论波列和确定性模拟波列的对比（Ts=1.5 s，Hs=0.04 m，s=25）
Fig. 9 Comparison of theoretical and simulated wave surface elevation histories for different rr/Ls with R/Ls=0.06 at No.3 gauge (Ts=1.5 s, Hs=0.04 m, s=25)
图 10 R/Ls=0.06时采用计算的average-θi和max-Energy-θi模拟所得波浪的Ermax随rr/Ls的变化（Ts=1.5 s, Hs=0.04 m, s=25）
Fig. 10 Variation of Ermax for simulated waves with rr/Ls using average-θi and max-Energy-θi of R/Ls=0.06 (Ts=1.5 s, Hs=0.04 m, s=25)
-
[1] Baldock T E, Swan C. Numerical calculations of large transient water waves[J]. Applied Ocean Research, 1994, 16(2): 101−112. doi: 10.1016/0141-1187(94)90006-X [2] 裴玉国, 张宁川, 张运秋. 畸形波数值模拟和定点生成[J]. 海洋工程, 2006, 24(4): 20−26. doi: 10.3969/j.issn.1005-9865.2006.04.004Pei Yuguo, Zhang Ningchuan, Zhang Yunqiu. Numerical simulation of freak waves and its generation at a certain location[J]. The Ocean Engineering, 2006, 24(4): 20−26. doi: 10.3969/j.issn.1005-9865.2006.04.004 [3] Liang Xiufeng, Yang JianMin, Li Jun, et al. Numerical simulation of irregular wave-simulating irregular wave train[J]. Journal of Hydrodynamics, 2010, 22(4): 537−545. doi: 10.1016/S1001-6058(09)60086-X [4] 崔成, 张宁川, 裴玉国. 畸形波生成、演化过程研究——波面时间过程随位置的变化[J]. 海洋通报, 2011, 30(4): 387−396. doi: 10.3969/j.issn.1001-6392.2011.04.005Cui Cheng, Zhang Ningchuan, Pei Yuguo. Research on the generation and evolution of freak wave−time-process of the water surface elevations’ variation with positions[J]. Marine Science Bulletin, 2011, 30(4): 387−396. doi: 10.3969/j.issn.1001-6392.2011.04.005 [5] Finnegan W, Goggins J. Linear irregular wave generation in a numerical wave tank[J]. Applied Ocean Research, 2015, 52: 188−200. doi: 10.1016/j.apor.2015.06.006 [6] 沈王刚. 基于FMBEM的数值波浪水池及非线性波浪重构方法[D]. 上海: 上海交通大学, 2018.Shen Wanggang. Fmbem-based numerical wave tank and nonlinear wave refactoring method[D]. Shanghai: Shanghai Jiao Tong University, 2018. [7] Naaijen P, Blondel-Couprie E. Reconstruction and prediction of short-crested seas based on the application of a 3d-FFT on synthetic waves: Part 1-Reconstruction[C]//ASME 2012 31st International Conference on Ocean, Offshore and Arctic Engineering. Rio de Janeiro, Brazil: American Society of Mechanical Engineers (ASME), 2012. [8] Blondel-Couprie E, Naaijen P. Reconstruction and prediction of short-crested seas based on the application of a 3D-FFT on synthetic waves: Part 2-Prediction[C]//ASME 2012 31st International Conference on Ocean, Offshore and Arctic Engineering. Rio de Janeiro, Brazil: American Society of Mechanical Engineers (ASME), 2012. [9] 刘思. 多向不规则波群的模拟研究[D]. 大连: 大连理工大学, 2012.Liu Si. The research on simulation of multidirectional irregular wave groups[D]. Dalian: Dalian University of Technology, 2012. [10] 俞聿修, 柳淑学. 随机波浪及其工程应用[M]. 4版. 大连: 大连理工大学出版社, 2011.Yu Yuxiu, Liu Shuxue. Random Wave and its Applications to Engineering[M]. 4th ed. Dalian: Dalian University of Technology Press, 2011. [11] Draycott S, Davey T, Ingram D M, et al. The SPAIR method: Isolating incident and reflected directional wave spectra in multidirectional wave basins[J]. Coastal Engineering, 2016, 114: 265−283. doi: 10.1016/j.coastaleng.2016.04.012 [12] Luo L, Liu S, Li J, et al. The deterministic reconstruction of multi-directional irregular waves[C]//Proceedings of the Twenty-ninth (2019) International Ocean and Polar Engineering Conference. Honolulu, Hawaii, USA: ISOPE, 2019 (3): 3546–3552. [13] Borgman L E. Statistical reliability of computations based on wave spectral relations[C]// Proceedings of the International Symposium on Ocean Wave Measurement and Analysis. New York: ASCE, 1974: 362–378. [14] Esteva D. Wave direction computations with three gage arrays[J]. Coastal Engineering Proceedings, 1976, 1(15): 19. doi: 10.9753/icce.v15.19 [15] Fernandes A A, Gouveia A D, Nagarajan R. Determination of wave direction from linear and polygonal arrays[J]. Ocean Engineering, 1988, 15(4): 345−357. doi: 10.1016/0029-8018(88)90050-9 [16] Fernandes A A, Sarma Y V B, Menon H B. Directional spectrum of ocean waves from array measurements using phase/time/path difference methods[J]. Ocean Engineering, 2000, 27(4): 345−363. doi: 10.1016/S0029-8018(99)00024-4 [17] Goda Y. A comparative review on the functional forms of directional wave spectrum[J]. Coastal Engineering Journal, 1999, 41(1): 1−20. doi: 10.1142/S0578563499000024 [18] 孙忠滨, 柳淑学, 李金宣. 基于改进Boussinesq方程三角形网格有限元模型[J]. 海洋工程, 2010, 28(3): 50−58, 67. doi: 10.3969/j.issn.1005-9865.2010.03.008Sun Zhongbin, Liu Shuxue, Li Jinxuan. Triangular element FEM model based on modified Boussinesq equations[J]. The Ocean Engineering, 2010, 28(3): 50−58, 67. doi: 10.3969/j.issn.1005-9865.2010.03.008 -
下载:
计量
- 文章访问数: 158
- HTML全文浏览量: 50
- PDF下载量: 11
- 被引次数: 0
