Shear instability in spilling breakers
Shear instability in spilling breakers
复制标题
溢出破碎机的剪切不稳定性
DOI：
10.1098/rspa.1994.0111
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
M. Longuet
中科院分区：
文献类型：
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作者：
M. Longuet
高速摄影的一个轻轻破碎的水波已经显示出特定的不稳定性的波峰预测Longuet-Higgins等人。259，333 - 344（1994））和Longuet-Higgins & Cleaver（J. Fluid Mech.258，115 - 129（1994）），在波的前表面上具有“凸起”，并且在不稳定性之前产生寄生毛细管，从凸起的“趾部”发出。这些照片还显示了在隆起趾部以上意外出现的较长（2型）毛细波。在本文中，它表明，2型毛细管可能是剪切流不稳定性所产生的涡脱落的1型（寄生）毛细管。在大振幅时，初始线性剪切不稳定性必然分裂成离散涡。通过制定一个简单的模型的剪切不稳定性的涡旋波，它示出的2型毛细管的波长应该是约4倍的波长的1型毛细管，结果与观察一致。当流动在凸起的趾部处分离时，使用普朗特规则来估计旋涡的强度证实了上述关系。在较大的长度尺度时，表面张力可以忽略不计，参数导致一个简单的规则，用于预测的波长的初始表面粗糙度的溢出破碎机。
High-speed photographs of a gently breaking water wave have shown the particular instability of the wave crest predicted by Longuet-Higgins et al. (J. Fluid Mech. 259, 333 –344 (1994)) and Longuet-Higgins & Cleaver (J. Fluid Mech. 258, 115 –129 (1994)), with a ‘bulge’ on the forward face of the wave and the generation of parasitic capillaries ahead of the instability, emanating from the ‘toe’ of the bulge. The photographs also show the unexpected occurence of longer (type 2) capillary waves above the toe of the bulge. In this paper it is shown that the type 2 capillaries are probably shear-flow instabilities arising from the vorticity shed by type 1 (parasitic) capillaries. At large amplitudes the initially linear shear instabilities must break up into discrete vortices. By formulating a simple model of the shear instabilities as vortex waves it is shown that the wavelength of the type 2 capillaries should be about 4 times the wavelength of the type 1 capillaries, a result in agreement with observation. When the flow separates at the toe of the bulge, the use of Prandtl’s rule to estimate the strength of the vortices confirms the above relation. At larger length-scales when surface tension is negligible, the argument leads to a simple rule for predicting the wavelength of the initial surface roughness of a spilling breaker.