长波波列传播特性的模拟研究
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摘要
长波波列在结构上会产生很大的波浪爬高和荷载。这种波列在长距离的传播中无法维持稳定,导致其波面形态发生改变,并对其之后与结构的相互作用产生很大影响,该现象亦出现在对海啸波波列的观测中。该文基于时域高阶边界元方法,建立了完全非线性二维数值波浪水槽,对长波波列传播过程中的变形和各阶波浪间能量交换问题进行了模拟和研究。自由表面满足完全非线性自由水面运动学和动力学边界条件,采用混合欧拉-拉格朗日方法追踪瞬时自由面流体质点,采用四阶Runge-Kutta法对下一时间步的波面和自由面速度势进行更新。研究发现,在长波传播过程中,波面会产生振荡变形,能量会由低阶传递到高阶成分,使得波高显著增大,这会导致在结构上产生极大的瞬时荷载和波浪爬高。
Long wave can produce large wave run-up and wave loads on the structures. This type of wave is not stable in long-distance propagation. The profile of the free surface will deform during the propagation, which has a great influence on the process of wave-structure interaction. The deformation phenomenon also appears in the observation of tsunami wave trains. In this study, a 2 D fully-nonlinear numerical wave tank is developed based on the time-domain higher-order boundary element method. The deformation phenomenon and the energy exchange between waves of different orders during the propagation of long wave are studied. The fully nonlinear kinematic and dynamic boundary conditions are satisfied on the instantaneous free surface. The mixed Eulerian-Lagrangian method is adopted to track the transient water particles on the free surface and the fourth order Runge-Kutta method is used to predict the velocity potential and wave elevation on the free surface. It is found that the free surface deforms and oscillates violently during the propagation. The energy is transferred to the higher order component waves, which lead to the amplification of the surface elevation. This will create enormous transient loads and extreme run-up on the structures.
Long wave can produce large wave run-up and wave loads on the structures. This type of wave is not stable in long-distance propagation. The profile of the free surface will deform during the propagation, which has a great influence on the process of wave-structure interaction. The deformation phenomenon also appears in the observation of tsunami wave trains. In this study, a 2 D fully-nonlinear numerical wave tank is developed based on the time-domain higher-order boundary element method. The deformation phenomenon and the energy exchange between waves of different orders during the propagation of long wave are studied. The fully nonlinear kinematic and dynamic boundary conditions are satisfied on the instantaneous free surface. The mixed Eulerian-Lagrangian method is adopted to track the transient water particles on the free surface and the fourth order Runge-Kutta method is used to predict the velocity potential and wave elevation on the free surface. It is found that the free surface deforms and oscillates violently during the propagation. The energy is transferred to the higher order component waves, which lead to the amplification of the surface elevation. This will create enormous transient loads and extreme run-up on the structures.
引文
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[2]CARTWRIGHT D E,LONGUET-HIGGINS M S.The statistical distribution of the maxima of a random function[J].Proceedings of the Royal Society of London,1956,237(1209):212-232.
[3]GODA Y.Random seas and design of maritime structures[M].Singapore,Singapore:World Scientific Publishing Company,2010.
[4]DAVIS M C,ZARNICK E E.Testing ship models in transient waves[R].Washiongton D C,USA:David Taylor Model Basin Washington DC Hydromechanics Lab,1966.
[5]BAI W,TAYLOR R E.Numerical simulation of fully nonlinear regular and focused wave diffraction around a vertical cylinder using domain decomposition[J].Applied Ocean Research,2007,29(1-2):55-71.
[6]XIAO X,TENG B,GOU Y,et al.Transient response of TLP under freak waves[J].Port and Waterway Engineering,2009,5:9-14.
[7]WESTPHALEN J,GREAVES D M,WILLIAMS C J K,et al.Focused waves and wave-structure interaction in a numerical wave tank.[J].Ocean Engineering,2012,45:9-21.
[8]李翔,张崇伟,宁德志,等.非周期波浪与直墙作用的非线性数值研究[J].力学学报,2017,49(5):1042-1049.LI Xiang,ZHANG Chong-wei,NING De-zhi,et al.Nonlinear numerical study of non-periodic waves acting on a vertical cliff.[J].Chinese Journal of Theoretical and Applied Mechanics,2017,49(5):1042-1049.
[9]GRUE J,PELINOVSKY E N,FRUCTUS D,et al.Formation of undular bores and solitary waves in the Strait of Malacca caused by the 26 December 2004Indian Ocean tsunami.[J].Journal of Geophysical Research:Oceans,2008,113(C5).
[10]CONSTANTIN A,JOHNSON R S.Propagation of very long water waves,with vorticity,over variable depth,with applications to tsunamis.[J].Fluid Dynamics Research,2008,40(3):175-211.
[11]MADSEN P A,FUHRMAN D R,SCH?FFER H A.On the solitary wave paradigm for tsunamis[J].Journal of Geophysical Research:Oceans,2008,113(C12).
[12]AKRISH G,RABINOVITCH O,AGNON Y.Extreme run-up events on a vertical wall due to nonlinear evolution of incident wave groups[J].Journal of Fluid Mechanics,2016,797:644-664.
[13]NING D,TENG B,ZHAO H,et al.A comparison of two methods for calculating solid angle coefficients in a BIEM numerical wave tank[J].Engineering Analysis with Boundary Elements,2010,34(1):92-96.
[14]NING D Z,TENG B.Numerical simulation of fully nonlinear irregular wave tank in three dimension[J].International Journal for Numerical Methods in Fluids,2007,53(12):1847-1862.
[15]王大国.港口非线性波浪耦合计算模型[D].大连理工大学,大连,中国:2005.Wang Da-guo.The coupled numerical model of non-linear wave in harbor[D].Dalian University of Technology,Dalian,China:2005.