Almost extreme waves
Almost extreme waves
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DOI：
10.1017/jfm.2022.1047
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发表时间：
2023-01-13
影响因子：
3.7
通讯作者：
Silantyev, Denis A.
中科院分区：
文献类型：
--
作者：
Dyachenko, Sergey A.;Hur, Vera Mikyoung;Silantyev, Denis A.
高精度数值计算是在重力作用下、不受表面张力影响的不可压缩无粘性流体的二维、无限深且恒定涡旋流的自由表面上的周期性行波。特别令人感兴趣的是几乎极端波浪的流体表面与水平面形成的角度。发现的数值如下。 (i) 存在一个边界层，其中角度从波峰处的 0 急剧上升到局部最大值，收敛到 30.3787...，与涡度无关，随着振幅向极端波的方向增加，极端波在波峰处显示出一个角度为 30 的角。 (ii) 存在一个外部区域，在负涡度的波谷处，角度下降到 0，而在大正涡度的波谷处，角度上升到最大值，大于 30，然后急剧下降到 0。 (iii) 存在一个角度在 30° 左右振荡的过渡区域，类似于吉布斯现象。数值证据表明，当波廓接近极端形式时，振荡的幅度和频率变得与涡度无关。
Numerically computed with high accuracy are periodic travelling waves at the free surface of a two-dimensional, infinitely deep, and constant vorticity flow of an incompressible inviscid fluid, under gravity, without the effects of surface tension. Of particular interest is the angle the fluid surface of an almost extreme wave makes with the horizontal. Numerically found are the following. (i) There is a boundary layer where the angle rises sharply from 0 at the crest to a local maximum, which converges to 30.3787.. ., independently of the vorticity, as the amplitude increases towards that of the extreme wave, which displays a corner at the crest with a 30 angle. (ii) There is an outer region where the angle descends to 0 at the trough for negative vorticity, while it rises to a maximum, greater than 30, and then falls sharply to 0 at the trough for large positive vorticity. (iii) There is a transition region where the angle oscillates about 30, resembling the Gibbs phenomenon. Numerical evidence suggests that the amplitude and frequency of the oscillations become independent of the vorticity as the wave profile approaches the extreme form.