2019
DOI: 10.1111/sapm.12273
|View full text |Cite
|
Sign up to set email alerts
|

On the existence of leapfrogging pair of circular vortex filaments

Abstract: We propose and analyze a system of nonlinear partial differential equations describing the motion of a pair of vortex filaments. As a preliminary analysis, we first consider the case when the filaments are arranged as straight and parallel lines, and explicitly solve the system to show that the motion of the lines resemble that of point vortices moving in a plane. Then, we consider the motion of a pair of coaxial circular vortex filaments. We show that in this case, the system can be reduced to a two‐dimension… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1

Citation Types

1
9
0

Year Published

2020
2020
2024
2024

Publication Types

Select...
3
1

Relationship

1
3

Authors

Journals

citations
Cited by 4 publications
(10 citation statements)
references
References 51 publications
(97 reference statements)
1
9
0
Order By: Relevance
“…The criteria we have presented can be expected to be in only qualitative accord with those presented in Borisov, Kilin, and Mamaev [13] and in Aiki [4].…”
Section: Discussionsupporting
confidence: 81%
See 1 more Smart Citation
“…The criteria we have presented can be expected to be in only qualitative accord with those presented in Borisov, Kilin, and Mamaev [13] and in Aiki [4].…”
Section: Discussionsupporting
confidence: 81%
“…The rear ring then passes through the leading ring, with this process of 'leapfrogging' then repeating again and again [23]. We note that interactions of such vortex rings -primarily with filament cores -have been considered in Hicks [20] and more recently in Borisov, Kilin, and Mamaev [13], in Caplan, Talley, Carretero-González, and Kevrekidis [14], in Cheng, Lou, and Lim [15] and in Aiki [4].…”
Section: Introductionmentioning
confidence: 89%
“…Since the model system is derived by assuming that the vortex filaments are nearly straight and parallel, it is not suitable for describing motions of circular vortex filaments. In [22], the author proposed a system of nonlinear partial differential equations describing the interaction of vortex filaments. The paper [22] focused on deriving a new system describing the interaction of vortex filaments with general shape and proving the existence of solutions corresponding to leapfrogging in the case of coaxial circular vortex filaments.…”
Section: Introductionmentioning
confidence: 99%
“…In [22], the author proposed a system of nonlinear partial differential equations describing the interaction of vortex filaments. The paper [22] focused on deriving a new system describing the interaction of vortex filaments with general shape and proving the existence of solutions corresponding to leapfrogging in the case of coaxial circular vortex filaments. The aim of this paper is to prove the existence of solutions to the model system proposed in [22] which correspond to head-on collision of coaxial circular vortex filaments.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation