A survey of the stability criteria of Thomson's vortex polygons outside a circular domain

DOI10.1007/s40590-016-0121-yzbMath1348.76041OpenAlexW2339332507MaRDI QIDQ334775

Leonid G. Kurakin, Andrey Melekhov, Irina V. Ostrovskaya

Publication date: 1 November 2016

Published in: Boletín de la Sociedad Matemática Mexicana. Third Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40590-016-0121-y

zbMATH Keywords

stabilityresonancestationary solutionHamiltonian equationspoint vortices

Mathematics Subject Classification ID

Vortex flows for incompressible inviscid fluids (76B47) Stability of solutions to ordinary differential equations (34D20) Nonlinear resonances for nonlinear problems in mechanics (70K30)

Related Items

On the stability of discrete tripole, quadrupole, Thomson' vortex triangle and square in a two-layer/homogeneous rotating fluid ⋮ On the Stability of the System of Thomson’s Vortex $n$-Gon and a Moving Circular Cylinder ⋮ On the influence of circulation on the linear stability of a system of a moving cylinder and two identical parallel vortex filaments ⋮ On the stability of a system of two identical point vortices and a cylinder ⋮ On stability of thomson's vortex \(N\)-gon in the geostrophic model of the point Bessel vortices ⋮ Stability of periodic solutions of the \(N\)-vortex problem in general domains ⋮ Three-dimensional quasi-geostrophic staggered vortex arrays ⋮ Resonances in the stability problem of a point vortex quadrupole on a plane ⋮ On stability of the Thomson's vortex \(N\)-gon in the geostrophic model of the point vortices in two-layer fluid

Cites Work

• The stability of the steady rotation of a system of three equidistant vortices outside a circle
• Stability of the Thomson vortex polygon with evenly many vortices outside a circular domain
• On stability at the Hamiltonian Hopf bifurcation
• On the stability of Thomson's vortex pentagon inside a circular domain
• Dynamics of vortex structures in a stratified rotating fluid. Translated from Russian by Gennady N. Krichivets and Olga I. Yakovenko
• Nonlinear stability analysis of a regular vortex pentagon outside a circle
• Geometry, mechanics, and dynamics. The legacy of Jerry Marsden. Selected papers presented at a focus program, Fields Institute for Research in Mathematical Sciences, Toronto, Canada, July 2012
• Vortices and polynomials
• Experiments on two-dimensional vortex patterns
• Stability of body-centered polygonal configurations of ideal vortices
• Spectral analysis of point-vortex dynamics: first application to vortex polygons in a circular domain
• Vortex Dynamics
• The stability of stationary rotation of a regular vortex polygon
• The \(N\)-vortex problem. Analytical techniques
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item