On the stability of Thomson's vortex configurations inside a circular domain

DOI10.1134/S1560354710010028zbMath1229.37055MaRDI QIDQ653272

Leonid G. Kurakin

Publication date: 9 January 2012

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

zbMATH Keywords

stabilityresonancepoint vorticesstationary motion

Mathematics Subject Classification ID

Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Vortex flows for incompressible inviscid fluids (76B47) Stability of solutions to ordinary differential equations (34D20) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25) Nonlinear resonances for nonlinear problems in mechanics (70K30)

Related Items (7)

On the stability of discrete tripole, quadrupole, Thomson' vortex triangle and square in a two-layer/homogeneous rotating fluid ⋮ The stability of the steady rotation of a system of three equidistant vortices outside a circle ⋮ Dynamics of two vortex rings in a Bose-Einstein condensate ⋮ On the stability of Thomson's vortex pentagon inside a circular domain ⋮ Nonlinear stability analysis of a regular vortex pentagon outside a circle ⋮ Influence of annular boundaries on Thomson's vortex polygon stability ⋮ Three-dimensional quasi-geostrophic staggered vortex arrays

Cites Work

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• On stability of a regular vortex polygon in the circular domain
• Experiments on two-dimensional vortex patterns
• Point vortices on a sphere: Stability of relative equilibria
• On nonlinear stability of the regular vortex systems on a sphere
• The stability of stationary rotation of a regular vortex polygon
• Stability of Thomson's configurations of vortices on a sphere
• The \(N\)-vortex problem. Analytical techniques

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