发表机构
Ohio State University; Imperial College London（俄亥俄州立大学; 伦敦帝国学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究将无表面张力涡流与无旋毛细流动之间的数学类比扩展到剪切流中的空腔涡与应变流中的毛细气泡，构造了精确解与数值解，并发现了共形映射恒等式。
AI 中文摘要
在最近的一篇论文中，发现了无粘流体力学中两类物理上不同的二维自由边界问题之间的数学类比。一类涉及体积内具有恒定涡量但边界无表面张力的自由表面流动，另一类包括体积内无涡量但边界具有非零表面张力（毛细作用）的自由表面流动。文中给出了若干对物理上不同的自由边界问题的例子，这些问题归结为求解相同的数学问题，尽管毛细流动可能出现单一约束。本研究证明，该类比扩展到另一对物理上不同的问题：具有三阶无旋应变的剪切流中的空腔涡平衡，以及简单应变流中具有表面张力的稳态气泡。对于这两个问题，当参数$\gamma=0$时，我们构造了一个孤立的精确解，并为非零$\gamma$提供了数值解。一个有趣的特征是，从具有毛细作用的问题类别中涌现出非平凡的共形映射恒等式，这些恒等式在参数适当约束时同样适用于空腔涡问题。
英文摘要
In a recent paper, a mathematical analogy was found between two physically distinct classes of two-dimensional free boundary problems in inviscid fluid mechanics. One class involves free surface flows with constant vorticity in the bulk but without boundary surface tension, the other comprises free surface flows without vorticity in the bulk but with non-zero boundary surface tension (capillarity). Several examples were given of pairs of physically-distinct free boundary problems that amount to solving the same mathematical problem, albeit with the possibility of a single constraint arising for the capillary flows. The present work shows that this analogy extends to another pair of physically-distinct problems: a hollow vortex equilibrium in a shear flow with a third order irrotational strain and a steady bubble with surface tension in a simple straining flow. For both problems, we construct an isolated exact solution when a parameter $γ=0$ and provide numerical solutions for non-zero $γ$. An interesting feature is that non-trivial conformal mapping identities emerge from the class of problems with capillarity that apply equally for the hollow vortex problems when the parameters are appropriately constrained.
