闭合涡旋薄膜内在演化的哈密顿结构
流体动力学
2025-05-27 v3 其他凝聚态物理
数学物理
math.MP
斑图形成与孤子
摘要
受前人关于涡旋薄膜及其应用的启发，本文研究闭合平面涡旋薄膜的内在无粘演化方程及其哈密顿形式。该模型可应用于两个不可混合流体界面动力学问题。获得包含曲线切向导数 的新型边界泊杆括号，与 KdV 泊杆括号相关。还推导了由其自激速度导致的薄膜运动中拉格朗日不变式——即双标逊积积分的柯西主值。
引用
@article{arxiv.2408.13462,
title = {On the Hamiltonian structure of the intrinsic evolution of a closed vortex sheet},
author = {Banavara N. Shashikanth},
journal= {arXiv preprint arXiv:2408.13462},
year = {2025}
}
备注
The previous version (v2) had some typos and omissions, which have been corrected. A new observation has been made: the vortex sheet bracket has the form of the KdV bracket. An appendix on Poisson brackets on infinite-dimensional manifolds has been added