Computer extension and analytic continuation of Stokes’ expansion for gravity waves
Computer extension and analytic continuation of Stokes’ expansion for gravity waves
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DOI：
10.1017/s0022112074000802
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发表时间：
1974-02
影响因子：
3.7
通讯作者：
L. Schwartz
中科院分区：
文献类型：
--
作者：
L. Schwartz
利用计算机进行系数计算，将Stokes的无限小波展开式推广到高阶。斯托克斯展开式已被发现不能产生任何水深的最高波，因为收敛受到距离最大值短一段距离的平方根分支点的限制。通过使用不同的独立参数对问题进行重新描述，正确地获得了最高波。级数求和和解析延拓通过使用Padé逼近而变得容易。该方法原则上适用于波长的任意有限值，对大部分波高和水深都能得到高精度的解。哈夫洛克提出的另一种用于计算短于最高点的波的展开方法已经被重新考虑，并被发现是有缺陷的。
Stokes’ infinitesimal-wave expansion for steady progressive free-surface waves has been extended to high order using a computer to perform the coefficient arithmetic. Stokes’ expansion has been found to be incapable of yielding the highest wave for any value of the water depth since convergence is limited by a square-root branch-point some distance short of the maximum. By reformulating the problem using a different independent parameter, the highest waves are obtained correctly. Series summation and analytic continuation are facilitated by the use of Padé approximants. The method is valid in principle for any finite value of the wavelength and solutions of high accuracy can be obtained for most values of the wave height and water depth. An alternative expansion procedure proposed by Havelock for the computation of waves short of the highest has been reconsidered and found to be defective.