非周期波浪与直墙作用的非线性数值研究
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摘要
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,对非周期波浪与直墙的相互作用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.采用加速度式法求解直墙表面速度势的时间导数,对瞬时物体湿表面上的水动力压强积分,得到作用在物体上的瞬时波浪力.首先,将全非线性与Serre-Green-Naghdi(SGN)模型的结果进行了对比分析,发现对于大幅值双入射波问题,仅满足弱色散关系的SGN模型大大低估了最大波浪爬高;其次,研究了双入射波与直墙的非线性作用问题,发现线性预报对波浪最大爬高有较大低估,而波浪的非线性成分不只导致了自由面爬高的异常增大,也引起了局部自由面的高频振荡,该物理过程中,直墙所受的波浪载荷,也展示出了与波浪爬高相似的非线性特性;最后,对波浪爬升和波浪力的时间历程进行了频谱分析,发现入射主频波的部分能量传递给了更高频的波浪成分,反映出该问题具有典型的非线性特性.
In this study, a 2D fully-nonlinear numerical wave tank is developed based on the time-domain higher-order boundary element method. Non-periodic waves acting on a vertical cliff are investigated. 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 particle 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. Then the acceleration potential technique is adopted to calculate the temporal derivative of the potential on the vertical wall surface, and transient wave loads are obtained by integrating the Bernoulli equation along the wetted wall surface. The obtained nonlinear results are firstly compared with solutions of the Serre-Green-Naghdi(SGN) theory. It is observed that, for the highly nonlinear case of double-incidentwaves, the SGN model which only satisfies the weak dispersion relationship greatly underestimates the maximum wave run-up(MWR). Then, the nonlinear interaction between double-incident-waves and a vertical cliff is further studied. It is found that the linear prediction also underestimates the MWR. The nonlinearity not only leads to an evident increase of the MWR, but also results in a high-frequency oscillation of the free surface. During this process, nonlinear properties of wave loads are similar to those of the wave run-up. Finally, spectral analysis is performed on histories of wave run-up and wave loads. The dominant frequency wave component is found to transfer its energy to higher frequency components, as a typical nonlinear wave-wave interaction phenomenon.
In this study, a 2D fully-nonlinear numerical wave tank is developed based on the time-domain higher-order boundary element method. Non-periodic waves acting on a vertical cliff are investigated. 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 particle 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. Then the acceleration potential technique is adopted to calculate the temporal derivative of the potential on the vertical wall surface, and transient wave loads are obtained by integrating the Bernoulli equation along the wetted wall surface. The obtained nonlinear results are firstly compared with solutions of the Serre-Green-Naghdi(SGN) theory. It is observed that, for the highly nonlinear case of double-incidentwaves, the SGN model which only satisfies the weak dispersion relationship greatly underestimates the maximum wave run-up(MWR). Then, the nonlinear interaction between double-incident-waves and a vertical cliff is further studied. It is found that the linear prediction also underestimates the MWR. The nonlinearity not only leads to an evident increase of the MWR, but also results in a high-frequency oscillation of the free surface. During this process, nonlinear properties of wave loads are similar to those of the wave run-up. Finally, spectral analysis is performed on histories of wave run-up and wave loads. The dominant frequency wave component is found to transfer its energy to higher frequency components, as a typical nonlinear wave-wave interaction phenomenon.
引文
1张新曙,胡晓峰,尤云祥等.深海多立柱浮式平台涡激运动特性研究.力学学报,2016,48(3):593-598(Zhang Xinshu,Hu Xiaofeng,You Yunxiang,et al.Investigation on the characteristics of vortex induced motion of a deep sea muti-column floating platform.Chinese Journal of Theoretical and Applied Mechanics,2016,48(3):593-598(in Chinese))
2赵海峰,石俊,王斌斌.海上浮油定位浮标的力学分析与尺寸优化.力学学报,2016,48(1):235-242(Zhao Haifeng,Shi Jun,Wang Binbin.Mechanical analysis and sizing optimization of offshore oil slick tracking buoy.Chinese Journal of Theoretical and Applied Mechanics,2016,48(1):235-242(in Chinese))
3徐道临,卢超,张海成.海上浮动机场动力学建模及非线性动力响应特性.力学学报,2015,47(2):289-300(Xu Daolin,Lu Chao,Zhang Haicheng.Dynamic modeling and nonlinear characteristics of floating airport.Chinese Journal of Theoretical and Applied Mechanics,2015,47(2):289-300(in Chinese))
4 Isaacson M,Cheung KF,Second order wave diffraction around twodimensional bodies by time-domain method.Applied Ocean Research,1991,13(4):175-186
5 Grilli ST,Guyenne P,Dias F.A fully non-linear model for threedimensional overturning waves over an arbitrary bottom.International Journal for Numerical Methods in Fluids,2001,35(7):829-867
6 Jamois E,Fuhrman DR,Bingham HB,et al.A numerical study of nonlinear wave run-up on a vertical plate.Coastal Engineering,2006,53(11):929-945
7 Fuhrman DR,Madsen PA.Simulation of nonlinear wave run-up with a high-order Boussinesq model.Coastal Engineering,2008,55(2):139-154
8 Pelinovsky E,Kharif C,Talipova T.Large-amplitude long wave interaction with a vertical wall.European Journal of MechanicsB/Fluids,2008,27(4):409-418
9孙英伟.直立堤前的破碎波流场特征及波浪力研究.[博士论文].大连:大连理工大学,2012(Sun Yingwei.A study of breaking wave flow field in front of the vertical breakwater and wave force.[PhD Thesis].Dalian:Dalian University of Technology,2012(inChinese))
10 Chatjigeorgiou IK,Molin B.Third-order interactions,wave run-up and hydrodynamic loading on a vertical plate in an infinite wave field.Applied Ocean Research,2013,41:57-64
11 Su CH,Mirie RM.On head-on collision between two solitary waves.Journal of Fluid Mechanics,1980,98:509-525
12 Fenton JD,Rienecker MM.A Fourier method for solving nonlinear water-wave problems:Application to solitary-wave interactions.Journal of Fluid Mechanics,1982,118:411-443
13 Kim SK,Liu PLF,Liggett JA.Boundary integral equation solutions for solitary wave generation,propagation and run-up.Coastal Engineering,1983,7(4):299-317
14 Power H,Chwang AT.On reflection of a planar solitary wave at a vertical wall.Wave Motion,1984,6(2):183-195
15 Cooker MJ,Weidman PD,Bale DS.Reflection of a high-amplitude solitary wave at a vertical wall.Journal of Fluid Mechanics,1997,342(1):141-158
16 Maiti S,Sen D.Computation of solitary waves during propagation and runup on a slope.Ocean Engineering,1999,26(11):1063-1083
17 Liu PLF,AI-Banaa K.Solitary wave runup and force on a vertical barrier.Journal of Fluid Mechanics,2004,505:225-233
18 Jian W,Sim SY,Huang Z,et al.Modelling of solitary wave runup on an onshore coastal cliff by smoothed particle hydrodynamics method.Procedia Engineering,2015,16:88-96
19 Park H,Cox DT.Empirical wave run-up formula for wave,storm surge and berm width.Coastal Engineering,2015,115:67-78
20 Chambarel J,Kharif C,Touboul J.Head-on collision of two solitary waves and residual falling jet formation.Nonlinear Processes in Geophysics,2009,16:111-122
21宣瑞韬,吴卫,刘桦等.双孤立波直墙爬高的实验研究.水动力学研究与进展A辑,2013,03:241-251(Xuan Ruitao,Wu Wei,Liu Ye,et al.An experimental study on run-up of double solitary waves against a vertical wall.Chinese Journal of Hydrodynamics A,2013,03:241-251(in Chinese))
22 Carbone F,Dutykh D,Dudley JM,et al.Extreme wave runup on a vertical cliff.Geophysical Research Letters,2013,40(12):3138-3143
23 Green AE,Laws N,Naghdi PM.On the theory of water waves//Proceedings of the Royal Society of London A:Mathematical,Physical and Engineering Sciences.The Royal Society,1974,338:43-55
24 Green AE,Naghdi PM.A derivation of equations for wave propagation in water of variable depth.Journal of Fluid Mechanics,1976,78:237-246
25 Zhao BB,Ertekin RC,Duan WY.A comparative study of diffraction of shallow-water waves by high-level IGN and GN Equations.Journal of Computational Physics,2015,283:129-147
26 Zhao BB,Duan WY,Ertekin RC.Application of higher-level GN theory to some wave transformation problems.Coastal Engineering,2014,83:177-189
27 Ning D,Teng B,Zhao H,et al.A comparison of two methods for calculating solid angle coefficients in a BIEM numerical wave tank.Engineering Analysis with Boundary Elements,2010,34(1):92-96
28 Ning D.Zhuo X,Teng B.Focused waves interaction with a vertical wall//Twenty-third(2013)International Offshore and Polar Engineering,Alaska,USA,June 30-July 5,2013
2赵海峰,石俊,王斌斌.海上浮油定位浮标的力学分析与尺寸优化.力学学报,2016,48(1):235-242(Zhao Haifeng,Shi Jun,Wang Binbin.Mechanical analysis and sizing optimization of offshore oil slick tracking buoy.Chinese Journal of Theoretical and Applied Mechanics,2016,48(1):235-242(in Chinese))
3徐道临,卢超,张海成.海上浮动机场动力学建模及非线性动力响应特性.力学学报,2015,47(2):289-300(Xu Daolin,Lu Chao,Zhang Haicheng.Dynamic modeling and nonlinear characteristics of floating airport.Chinese Journal of Theoretical and Applied Mechanics,2015,47(2):289-300(in Chinese))
4 Isaacson M,Cheung KF,Second order wave diffraction around twodimensional bodies by time-domain method.Applied Ocean Research,1991,13(4):175-186
5 Grilli ST,Guyenne P,Dias F.A fully non-linear model for threedimensional overturning waves over an arbitrary bottom.International Journal for Numerical Methods in Fluids,2001,35(7):829-867
6 Jamois E,Fuhrman DR,Bingham HB,et al.A numerical study of nonlinear wave run-up on a vertical plate.Coastal Engineering,2006,53(11):929-945
7 Fuhrman DR,Madsen PA.Simulation of nonlinear wave run-up with a high-order Boussinesq model.Coastal Engineering,2008,55(2):139-154
8 Pelinovsky E,Kharif C,Talipova T.Large-amplitude long wave interaction with a vertical wall.European Journal of MechanicsB/Fluids,2008,27(4):409-418
9孙英伟.直立堤前的破碎波流场特征及波浪力研究.[博士论文].大连:大连理工大学,2012(Sun Yingwei.A study of breaking wave flow field in front of the vertical breakwater and wave force.[PhD Thesis].Dalian:Dalian University of Technology,2012(inChinese))
10 Chatjigeorgiou IK,Molin B.Third-order interactions,wave run-up and hydrodynamic loading on a vertical plate in an infinite wave field.Applied Ocean Research,2013,41:57-64
11 Su CH,Mirie RM.On head-on collision between two solitary waves.Journal of Fluid Mechanics,1980,98:509-525
12 Fenton JD,Rienecker MM.A Fourier method for solving nonlinear water-wave problems:Application to solitary-wave interactions.Journal of Fluid Mechanics,1982,118:411-443
13 Kim SK,Liu PLF,Liggett JA.Boundary integral equation solutions for solitary wave generation,propagation and run-up.Coastal Engineering,1983,7(4):299-317
14 Power H,Chwang AT.On reflection of a planar solitary wave at a vertical wall.Wave Motion,1984,6(2):183-195
15 Cooker MJ,Weidman PD,Bale DS.Reflection of a high-amplitude solitary wave at a vertical wall.Journal of Fluid Mechanics,1997,342(1):141-158
16 Maiti S,Sen D.Computation of solitary waves during propagation and runup on a slope.Ocean Engineering,1999,26(11):1063-1083
17 Liu PLF,AI-Banaa K.Solitary wave runup and force on a vertical barrier.Journal of Fluid Mechanics,2004,505:225-233
18 Jian W,Sim SY,Huang Z,et al.Modelling of solitary wave runup on an onshore coastal cliff by smoothed particle hydrodynamics method.Procedia Engineering,2015,16:88-96
19 Park H,Cox DT.Empirical wave run-up formula for wave,storm surge and berm width.Coastal Engineering,2015,115:67-78
20 Chambarel J,Kharif C,Touboul J.Head-on collision of two solitary waves and residual falling jet formation.Nonlinear Processes in Geophysics,2009,16:111-122
21宣瑞韬,吴卫,刘桦等.双孤立波直墙爬高的实验研究.水动力学研究与进展A辑,2013,03:241-251(Xuan Ruitao,Wu Wei,Liu Ye,et al.An experimental study on run-up of double solitary waves against a vertical wall.Chinese Journal of Hydrodynamics A,2013,03:241-251(in Chinese))
22 Carbone F,Dutykh D,Dudley JM,et al.Extreme wave runup on a vertical cliff.Geophysical Research Letters,2013,40(12):3138-3143
23 Green AE,Laws N,Naghdi PM.On the theory of water waves//Proceedings of the Royal Society of London A:Mathematical,Physical and Engineering Sciences.The Royal Society,1974,338:43-55
24 Green AE,Naghdi PM.A derivation of equations for wave propagation in water of variable depth.Journal of Fluid Mechanics,1976,78:237-246
25 Zhao BB,Ertekin RC,Duan WY.A comparative study of diffraction of shallow-water waves by high-level IGN and GN Equations.Journal of Computational Physics,2015,283:129-147
26 Zhao BB,Duan WY,Ertekin RC.Application of higher-level GN theory to some wave transformation problems.Coastal Engineering,2014,83:177-189
27 Ning D,Teng B,Zhao H,et al.A comparison of two methods for calculating solid angle coefficients in a BIEM numerical wave tank.Engineering Analysis with Boundary Elements,2010,34(1):92-96
28 Ning D.Zhuo X,Teng B.Focused waves interaction with a vertical wall//Twenty-third(2013)International Offshore and Polar Engineering,Alaska,USA,June 30-July 5,2013