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arXiv 2007.14337physics.flu-dyn
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小表面张力极限下寄生重力-毛细波的结构

On the structure of parasitic gravity-capillary waves in the small surface tension limit

Josh Shelton, Paul Milewski, Philippe H. Trinh

摘要:

在本文中,我们研究了小毛细波(寄生波纹)的表面上的陡峭的缓慢行进的重力波的形成。在此之前,作者已经开发了特设的分析程序来描述这种寄生波纹的形成,在潜在的流量,但是,它一直不清楚是否小的表面张力限制是适定的-也就是说,是否有可能为一个适当的旅行重力毛细波连续变形的经典斯托克斯波的极限消失的表面张力。Chen & Saffman(1980)的研究表明,平稳的延续是不可能的。本文用数值方法研究了陡重力毛细行波问题的低表面张力极限。我们的研究结果允许出现的分歧结构的分类,并统一了以前的数值研究。至关重要的是,我们证明了不同的选择的解决方案的振幅可以导致微妙的限制的延续过程中,使用波能量作为振幅条件允许解决方案分支连续变形到零表面张力限制。

英文摘要:

In this paper, we examine the formation of small capillary waves (parasitic ripples) on the surface of steep steadily-travelling gravity waves. Previously, authors have developed ad-hoc analytical procedures for describing the formation of such parasitic ripples in potential flows; however, it has not been clear whether the small-surface tension limit is well-posed -- that is, whether it is possible for an appropriate travelling gravity-capillary wave to be continuously deformed to the classic Stokes wave in the limit of vanishing surface tension. The work of Chen & Saffman (1980) had suggested smooth continuation was not possible. In this paper, we numerically explore the low surface tension limit of the steep gravity-capillary travelling-wave problem. Our results allow for a classification of the bifurcation structure that arises, and serve to unify a number of previous numerical studies. Crucially, we demonstrate that different choices of solution amplitude can lead to subtle restrictions on the continuation procedure; the use of wave energy as an amplitude condition allows solution branches to be continuously deformed to the zero surface tension limit.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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