论文标题
涡旋毛细管水波的分叉分析涡流和漩涡
Bifurcation analysis for axisymmetric capillary water waves with vorticity and swirl
论文作者
论文摘要
我们研究稳定的轴对称水波，具有一般的涡度和漩涡，受表面张力的影响。就Stokes的流函数而言，这可以作为椭圆自由边界问题的配方。变量的变化使我们能够克服通用坐标诱导的奇异性，并以“身份加上紧凑型”形式抛弃问题，这对Rabinowitz的全局分叉定理很适合，而对流中缺少停滞点的缺乏限制。在这种新公式的范围内，构建了局部和全局溶液曲线，构建了从层流的层流层面的分叉。
We study steady axisymmetric water waves with general vorticity and swirl, subject to the influence of surface tension. This can be formulated as an elliptic free boundary problem in terms of Stokes' stream function. A change of variables allows us to overcome the generic coordinate-induced singularities and to cast the problem in the form "identity plus compact", which is amenable to Rabinowitz' global bifurcation theorem, while no restrictions regarding the absence of stagnation points in the flow have to be made. Within the scope of this new formulation, local and global solution curves, bifurcating from laminar flows with a flat surface, are constructed.
