Numerical simulation of regular wave propagation and deformation on steep slope submerged breakwater

doi:10.16411/j.cnki.issn1006-7736.2021.01.006

PDF(820 KB)

Journal of Dalian Maritime University ›› 2021, Vol. 47 ›› Issue (1) : 45-51. DOI: 10.16411/j.cnki.issn1006-7736.2021.01.006

TONG Shi-qi, LI Zhen, ZHANG Ting-yu, LIU Zhong-bo^*

Author information +

History +

Abstract

In order to investigate the applicability of the water wave equation under the assumption of gentle slope on steep submerged breakwater, a finite difference calculation model was established for a group of double-layer Boussinesq water wave equations to numerically simulate the wave propagation process on the trapezoidal submerged breakwater with the slope of 1∶2 on both sides, and compared the calculated wave surface displacement and harmonic wave amplitude with the experimental data of trapezoidal submerged breakwater in literature, the results show higher coincidence. At the same time, the coincidence degree between the simulated wave surface displacement and the experimental data is more than 0.99,which indicates excellent linear and nonlinear performance of calculation model. The above results show that the model can be used to accurately simulate the propagation and deformation of non-linear waves on submerged breakwaters with slope less than 1∶2.

Key words

Boussinesq numerical model / steep slope / wave propagation deformation

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

TONG Shi-qi, LI Zhen, ZHANG Ting-yu, LIU Zhong-bo. Numerical simulation of regular wave propagation and deformation on steep slope submerged breakwater[J]. Journal of Dalian Maritime University. 2021, 47(1): 45-51 https://doi.org/10.16411/j.cnki.issn1006-7736.2021.01.006

References

[1].参考文献 [2]KIRBY J T, WEI G, CHEN Q, et al.FUNWAVE 1.0. Fully nonlinear Boussinesq wave model. Documentation and user' s manual[J]. University of Delaware, 1998. [3]SHI F Y, KIRBY J T, HARRIS J C, et al.A high-order adaptive time-stepping TVD solver for Boussinesq modeling of breaking waves and coastal inundation[J], Ocean Modelling, 2012, 43-44(2):36-51. [4]WEI G, KIRBY J T, GRILLI S T, et al.A fully nonlinear Boussinesq model for surface wavesI. Highly nonlinear,unsteady waves[J].Journal of Fluid Mechanics, 1995, 294(-1):71-92 [5]MADSEN P A, S?RENSEN O R.A new form of the Boussinesq equations with improved linear dispersion characteristicsPart 2: A slowly-varying bathymetry[J].Coast Engrg, 1992, 18(3-4):183-204 [6]LYNETT P, LIU L F.A two-layer approach to wave modeling[J].Proc R Soc Lond A, 2004, 460(2049):2637-2669 [7]孙家文，朱桐，房克照，等.基于加速的类波浪传播变形数值模型[J].海洋工程, 2020, 38(02):111-119 [8]SUN J W, ZHU T, FANG K Z, et al.A GPU accelerated Boussinesq wave propagation model[J].The Ocean Engineering, 2020, 38(02):111-119 [9]YUAN Y, SHI F Y, KIRBY J T, et al.FUNWAVE‐GPU: Multiple‐GPU Acceleration of a Boussinesq-Type Wave Model[J].Journal of Advances in Modeling Earth Systems, 2020, 12(5):1-19 [10]孙家文，房克照，刘忠波，等.关于型水波方程理论和应用研究的综述[J].海洋学报, 2020, 42(5):1-11 [11]SUN J W, FANG K Z, LIU Z B, et al.A review on the theory and application of Boussinesq-type equations for water waves[J].Haiyang Xuebao, 2020, 42(5):1-11 [12]LIU Z B, FANG K Z, CHENG Y Z.A new multi-layer irrotational Boussinesq-type model for highly nonlinear and dispersive surface waves over a mildly sloping seabed[J]. Journal of Fluid Mechanics, 2018, 842:323-353. [13]MADSEN P A, FUHRMAN D R.High-order Boussinesq-type modeling of nonlinear wave phenomena in deep and shallow water. In Advances in Numerical Simulation of Nonlinear Water Waves [M]. (ed. Q. W. Ma). World Scientific Publishing, 2010. [14]OHYAMA T, KIOKA W, TADA A.Applicability of numerical models to nonlinear dispersive waves[J].Coastal Engineering, 1995, 24(3-4):297-313 [15]NWOGU O.Alternative Form of Boussinesq Equations for Nearshore Wave Propagation[J].Journal of Waterway Port Coastal & Ocean Engineering, 1993, 119(6):618-638 [16]GOBBI M F, KIRBY J T.Wave evolution over submerged sills: tests of a high-order Boussinesq model[J].Coastal Engineering, 1999, 37(1):57-96 [17]郑永红，沈永明，吴修广，等.用改进的Boussinesq方程模拟潜堤上的波浪变形[J]. 中国工程科学，2004，(04): 34-40. [18]ZHENG Y H, SHEN Y M, WU X G, et al.Simulation of Wave Propagation Over a Submerged Bar Using a Modified Boussinesq Equation[J]. Strategic Study of CAE, 2004, (04): 34-40. (in Chinese) [19]BEJI S, NADAOKA K.A formal derivation and numerical modelling of the improved Boussinesq equations for varying depth[J].Ocean Engineering, 1996, 23(8):691-704 [20]MADSEN P A, SCH?FFER H A.Higher-Order Boussinesq-Type Equations for Surface Gravity Waves: Derivation and Analysis[J].Philosophical Transactions Mathematical Physical & Engineering Sciences, 1998, 356(1749):3123-3184 [21]ZOU Z L, FANG K Z.Alternative forms of the higher-order Boussinesq equations: Derivations and validations[J].Coastal Engineering, 2008, 55(6):506-521 [22]LIU Z B, FANG K Z.Two-layer Boussinesq models for coastal water waves[J]. Wave Motion, 2015, 57:88-111. [23]刘忠波，邹志利，王诺.四阶Boussinesq模型验证及非线性精度对数值结果的影响[J]. 海洋通报, ，2008，(05): 1-7. [24]LIU Z B, ZOU Z L, WANG N.Validation of a Fourth Order Boussinesq Model and the Effect of Nonlinearity Accuracy on Numerical Results[J]. Marine Science Bulletin, 2008, (05): 1-7. (in Chinese) [25]LIU Z B, FANG K Z, SUN J W.A multi-layer Boussinesq-type model with second-order spatial derivatives:Theoretical analysis and numerical implementation[J]. Ocean Engineering, 2019, 191 :106545. [26]邹志利，张晓莉.高阶水波方程数值模型及其与实验结果的对比[J].水动力学研究与进展辑, 2002, 17(5):592-603 [27]ZOU Z L, ZHANG X L.Numerical model of higher-order Boussinesq equations and comparisons with laboratory measurements[J].Chinese Journal of Hydrodynamics, 2002, 17(5):592-603 [28]ZOU Z L, LIU Z B, FANG K Z.Further improvements to the higher-order Boussinesq equations: Bragg reflection[J].Coastal Engineering, 2009, 56(5-6):672-687 [29]HSIAO S C, LYNETT P, HWUNG H H, et al.Numerical Simulations of Nonlinear Short Waves Using a Multilayer Model[J].Journal of Engineering Mechanics, 2005, 131(3):231-243 [30]WILMOTT C J.On the validation of models[J].Physical Geography, 1981, 2(2):219-232