二阶挠曲重力波对直墙作用及其奇异解

The second-order flexural-gravity wave loads on vertical wall and singularity in solution

利用特征函数展开法,对有限水深下二阶挠曲重力波在直墙前的反射问题做了求解.计算了直墙上二阶挠曲重力波作用力随入射波浪频率的变化关系.数值结果显示在某一特殊频率下二阶挠曲重力波作用力会趋向无穷.进一步研究表明,在该频率下挠曲重力波的相速度与倍频下的相速度相等,使得挠曲重力波的二阶分量分母为零而出现奇异性.这一奇异解的出现,使得入射波浪存在不确定性,对非线性挠曲重力波与结构物作用问题的求解造成困难.这是一个非常有意义但尚未解决的问题,需进一步探索.

The problem of the second-order flexural-gravity wave reflection from a vertical wall in the finite water depth is investigated by the eigenfunction expansion method.The variation of the force of the second-order flexural-gravity wave on a vertical wall with the incident wave frequency is calculated.Numerical results show that the second-order flexural-gravity wave loads on a vertical wall will approach to infinity at a special frequency.Further studies show that at the special frequency the phase velocity of the flexural-gravity waves is equal to that of the waves with the double frequency,and the second-order component of the flexural-gravity waves is singular with the denominator of it being zero.The existence of this singular solution will induce uncertainty of the incident waves,and limit the application of solutions for nonlinear flexural-gravity wave loads on structures.This is a very meaningful but unresolved problem and deserves further exploration.