Steep gravity waves in water of arbitrary uniform depth
Steep gravity waves in water of arbitrary uniform depth
复制标题
DOI：
10.1098/rsta.1977.0113
复制
发表时间：
1977-07
期刊：
影响因子：
--
通讯作者：
E. Cokelet
中科院分区：
文献类型：
--
作者：
E. Cokelet
水波研究的现代应用，以及一些最近的理论发展，已经表明，需要一个系统的和精确的计算的特点，稳定的，渐进的重力波的有限振幅在任意均匀深度的水。在本文中，速度，动量，能量和其他积分性质的精确计算通过级数展开的摄动参数的范围是已知的，精确地包括从最低到最高可能的波。级数被推广到高阶，并与Padé逼近求和。对于任何给定的波长和深度，发现最高的波不是最快的。此外，能量，动量和它们的通量被发现是最大的波低于最高。这证实并扩展了以前发现的孤立波和深水波的结果。通过计算深水波的轮廓，我们表明，轮廓的几乎最陡的波，它有一个尖锐的曲率在波峰，相交的波峰附近的一个稍微不太陡的波，因此在大部分的波长较低。沿波剖面的积分沿着交叉检查Padé近似结果，并确认中间能量最大值。附录中列出了从深水到极浅水的波陡完整范围和各种深度与波长比的速度、能量和其他积分性质的值。
Modern applications of water-wave studies, as well as some recent theoretical developments, have shown the need for a systematic and accurate calculation of the characteristics of steady, progressive gravity waves of finite amplitude in water of arbitrary uniform depth. In this paper the speed, momentum, energy and other integral properties are calculated accurately by means of series expansions in terms of a perturbation parameter whose range is known precisely and encompasses waves from the lowest to the highest possible. The series are extended to high order and summed with Padé approximants. For any given wavelength and depth it is found that the highest wave is not the fastest. Moreover the energy, momentum and their fluxes are found to be greatest for waves lower than the highest. This confirms and extends the results found previously for solitary and deep-water waves. By calculating the profile of deep-water waves we show that the profile of the almost-steepest wave, which has a sharp curvature at the crest, intersects that of a slightly less-steep wave near the crest and hence is lower over most of the wavelength. An integration along the wave profile cross-checks the Padé-approximant results and confirms the intermediate energy maximum. Values of the speed, energy and other integral properties are tabulated in the appendix for the complete range of wave steepnesses and for various ratios of depth to wavelength, from deep to very shallow water.