发表机构
University of Birmingham; University of East Anglia（伯明翰大学; 东英吉利大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对稳态受迫水波问题，通过分析fKdV模型精确解与不同地形上的欧拉系统数值解，揭示了超临界流下含同宿脱落现象的非平凡分岔结构，解答了流速进入超临界区及地形衰减率对解结构的影响问题。
AI 中文摘要
近期，针对局部地形凹陷上方的无粘无旋流，研究人员发现了无穷多组稳态孤立波解分支，这些解仅存在于弗劳德数为1的临界流状态。研究人员提出了两个关键问题：一是当流速持续进入超临界区时，解结构会发生怎样的变化？二是地形的衰减率如何影响解结构？本文通过研究fKdV模型的精确稳态解，以及在沟槽、高斯地形、广义阿格尼地形上的完全非线性欧拉系统数值解，对上述问题进行了回答。研究揭示了由螺旋和闭合回路构成的高度非平凡分岔结构，其特征是“同宿脱落”现象：当振幅变化时，会向上游和下游发射成对的孤立波。
英文摘要
Recently, an infinite set of steady solitary-wave solution branches was discovered for inviscid and irrotational flow over a localised topographic depression. These solutions were restricted to critical flow, when the Froude number is unity. Several questions were raised, including i) what happens to the solution structure as the flow speed is continued into the supercritical regime? and ii) how does the decay rate of the topography affect the solution structure? In this article, we answer these questions by examining exact steady solutions of the fKdV model and numerical solutions of the fully nonlinear Euler system over i) trench, ii) Gaussian and iii) generalised Agnesi topographies. We uncover a highly non-trivial bifurcation structure consisting of spirals and closed loops, characterised by the phenomenon of `homoclinic shedding', where pairs of solitary waves are emitted up- and downstream as the amplitude is varied.
Comments26 pages
