论文标题
在小表面张力极限中的寄生重力毛皮波的结构上
On the structure of parasitic gravity-capillary waves in the small surface tension limit
论文作者
论文摘要
在本文中，我们研究了陡峭的稳定旅行重力波表面上的小毛细管波（寄生波纹）的形成。以前，作者已经开发了临时分析程序，以描述潜在流中这种寄生波纹的形成。但是，尚不清楚小表面张力限量是否适合 - 也就是说，是否有可能在消失的表面张力的极限下连续变形到经典的Stokes波。 Chen＆Saffman（1980）的作品表明，不可能保持平稳的延续。在本文中，我们从数值探索陡峭的重力毛细管旅行波问题的低表面张力极限。我们的结果允许对出现的分叉结构进行分类，并有助于统一许多先前的数值研究。至关重要的是，我们证明了溶液振幅的不同选择可以导致对持续程序的细微限制。将波能作为振幅条件的使用允许将溶液分支连续变形至零表面张力极限。
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.
