Leapfrogging vortex rings for the three-dimensional incompressible Euler equations

被引：7

作者：

Davila, Juan ^{[1
]}

Pino, Manuel del ^{[1
]}

Musso, Monica ^{[1
,3
]}

Wei, Juncheng ^{[2
]}

机构：

[1] Univ Bath, Dept Math Sci, Bath, England

[2] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China

[3] Univ Bath, Dept Math Sci, Bath BA2 7AY, England

来源：

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | 2024年 / 77卷 / 10期

基金：

英国工程与自然科学研究理事会;

关键词：

STEADY VORTEX; SINGULARITY FORMATION; IDEAL; STABILITY; CONJECTURE; EXISTENCE; VORTICES; MOTION; FLOWS; PAIR;

D O I：

10.1002/cpa.22199

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A classical problem in fluid dynamics concerns the interaction of multiple vortex rings sharing a common axis of symmetry in an incompressible, inviscid three-dimensional fluid. In 1858, Helmholtz observed that a pair of similar thin, coaxial vortex rings may pass through each other repeatedly due to the induced flow of the rings acting on each other. This celebrated configuration, known as leapfrogging, has not yet been rigorously established. We provide a mathematical justification for this phenomenon by constructing a smooth solution of the 3D Euler equations exhibiting this motion pattern.

引用

页码：3843 / 3957

页数：115

共 65 条

[1] On the existence of leapfrogging pair of circular vortex filaments [J].