摘要
由于Skjelbreia导出的确定五阶斯托克斯波的二个方程不易求解,本文将其简化为确定d/L的一个方程:f(H,T,d,d/L)=0。根据这一简化解法,发现Skjelbreia方程组的解有3种情况:存在唯一的精确解;精确解不止一个;不存在精确解(但存在满足Skjelbreia方程组方面的最佳近似解)。当精确解不止一个时,可应用变分原理的方法判别出合理的解。应用变分原理的方法还可将Skjeilbria方程组的解改进为满足无旋运动非线性波浪理论的原始数学提法方面的最佳近似解,亦即给出最优化五阶斯托克斯波。
As the solution of the two equations for determining the existing fifth order Stokes wave derived from Skjelbreia was rather complex and tedious,this paper simplifies the two equations into one equation for determining d/L,i. e. ,f(H,T,d/L) = 0. According to this simplified method, three cases of the solution for Skjelbreia equations were found: one accurate solution ; more than one accurate solution; no accurate solution (but there exists the optimum approximate solution in the area of satisfying Skjelbreia equations). As to the case of more than one accurate solutions, the reasonable solution can be judged from the method of variational principle, using which an optimum solution improved from the solution of Skjelbreia equations in the area of satisfying the original mathematical equations of non-vortex and nonlinear wave theory,i, e. , the optimum fifth order Stokes wave,was given.
出处
《海洋通报》
CAS
CSCD
北大核心
1994年第3期53-61,共9页
Marine Science Bulletin
关键词
五阶
斯托克斯波
简化解
波浪理论
fifth order Stokes wave
simplified method
variational principle
improved solution
