A semi-analytic solution for nonlinear standing waves in deep water
A semi-analytic solution for nonlinear standing waves in deep water
复制标题
深水中非线性驻波的半解析解
DOI：
10.1017/s0022112081001717
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发表时间：
1981
影响因子：
3.7
通讯作者：
A. Whitney
中科院分区：
文献类型：
--
作者：
L. Schwartz;A. Whitney
本文提出了一种含时保角变换的方法来简化求解深水中时间和空间周期驻波的幂级数过程。已发现一个解决方案，以25阶波的振幅。某些系数的值由必须抑制长期项的要求决定。由于波剖面的级数并不总是一致收敛的，所以Padé近似用于求和。对于非常高的波浪，表面的斜率至少有两个相对最大值。讨论了解的奇异性结构。
A method of time-dependent conformal mapping is introduced to simplify the power-series solution procedure for time- and space-periodic standing waves in deep water. A solution has been found to 25th order in the wave amplitude. The values of certain coefficients are determined by the requirement that secular terms must be suppressed. Because the series for the wave profile is not always uniformly convergent, Padé approximants are used for summation. For very high waves, the slope of the surface has at least two relative maxima. The singularity structure of the solution is also discussed.