Dynamic generation of capillary waves
Dynamic generation of capillary waves
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DOI：
10.1063/1.869975
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发表时间：
1999-05-01
影响因子：
4.6
通讯作者：
Hou, TY
中科院分区：
文献类型：
--
作者：
Ceniceros, HD;Hou, TY
我们研究了具有表面张力的二维、无粘性和无旋转水波中毛细波的动态产生。众所周知，短毛细波出现在陡峭水波的前缘。尽管各种实验和分析研究有助于理解这一物理现象，但毛细波动态形成的确切机制仍未得到很好的理解。采用数值稳定、光谱精确的边界积分方法，系统地研究了表面张力作用下破碎波的时间演化。我们发现毛细波起源于附近的波峰附近，在那里曲率及其导数都是极大的。当表面张力较小时，曲率最大值随时间增加，界面在波峰前形成一列振荡的毛细波。我们的数值实验还表明，随着时间的增加，界面倾向于通过自相交形成困泡。另一方面，在一定时间内，随着表面张力系数的减小，毛细波长及其幅值均呈非线性减小。界面解接近于tau=0轮廓。在毛细血管开始时，其导数与动态边界条件下重力项的导数相当，并且相对于这两项，表面张力变得明显。我们发现，基于tau=0波，有可能估计一个阈值tau(0)，这样，如果tau小于或等于tau(0)，则没有毛细波产生。另一方面，当tau足够大时，断裂被抑制，并观察到purl毛细管运动。极限行为与经典KdV方程非常相似。我们还研究了粘度对毛细波产生的影响。我们发现，只要粘度不明显大于表面张力，毛细波仍然存在。(C) 1999年美国物理研究所。[s1070 - 6631(99) 03005 - 6]。
We investigate the dynamic generation of capillary waves in two-dimensional, inviscid, and irrotational water waves with surface tension. It is well known that short capillary waves appear in the forward front of steep water waves. Although various experimental and analytical studies have contributed to the understanding of this physical phenomenon, the precise mechanism that generates the dynamic formation of capillary waves is still not well understood. Using a numerically stable and spectrally accurate boundary integral method, we perform a systematic study of the time evolution of breaking waves in the presence of surface tension. We find that the capillary waves originate near the crest in a neighborhood, where both the curvature and its derivative an maximum. For tired but small surface tension, the maximum of curvature increases in time and the interface develops an oscillatory train of capillary waves in the forward front of the crest. Our numerical experiments also show that, as time increases, the interface tends to a possible formation of trapped bubbles through self-intersection. On the other hand, for a fixed time, as the surface tension coefficient tau is reduced, both the capillary wavelength and its amplitude decrease nonlinearly. The interface solutions approach the tau=0 profile. At the onset of the capillar ies, the derivative of the conviction is comparable to that of the gravity term in the dynamic boundary condition and the surface tension becomes appreciable with respect to these two terms. We find that, based on the tau=0 wave, it is possible to estimate a threshold value tau(0) such that if tau less than or equal to tau(0) then no capillary waves arise. On the other hand, for tau sufficiently large, breaking is inhibited and purl capillary motion is observed. The limiting behavior is very similar to that in the classical KdV equation. We also investigate the effect of viscosity on the generation of capillary waves. We find that the capillary waves still persist as long as the viscosity is not significantly greater than surface tension. (C) 1999 American Institute of Physics. [S1070-6631(99)03005-6].