非周期波浪与直墙作用的非线性数值研究

NONLINEAR NUMERICAL STUDY OF NON-PERIODIC WAVES ACTING ON A VERTICAL CLIFF

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,a2D fully-nonlinear numerical wave tank is developed based on the time-domain higher-orderboundary element method.Non-periodic waves acting on a vertical cliff are investigated.The fully nonlinear kinematicand dynamic boundary conditions are satisfied on the instantaneous free surface.The mixed Eulerian-Lagrangian methodis adopted to track the transient water particle on the free surface and the fourth order Runge-Kutta method is used topredict the velocity potential and wave elevation on the free surface.Then the acceleration potential technique is adoptedto calculate the temporal derivative of the potential on the vertical wall surface,and transient wave loads are obtained byintegrating the Bernoulli equation along the wetted wall surface.The obtained nonlinear results are firstly compared withsolutions 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 waverun-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 ofthe MWR,but also results in a high-frequency oscillation of the free surface.During this process,nonlinear properties ofwave loads are similar to those of the wave run-up.Finally,spectral analysis is performed on histories of wave run-up andwave loads.The dominant frequency wave component is found to transfer its energy to higher frequency components,asa typical nonlinear wave-wave interaction phenomenon.