On nonlinear stability of the regular vortex systems on a sphere
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Publication:5705423
DOI10.1063/1.1764432zbMath1080.76031OpenAlexW1990847619WikidataQ80784739 ScholiaQ80784739MaRDI QIDQ5705423
Publication date: 8 November 2005
Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/0d14fa1f8969fef98c3bc5f5e7f321991f7d8e8c
Vortex flows for incompressible inviscid fluids (76B47) Nonlinear effects in hydrodynamic stability (76E30)
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Platonic solids and symmetric solutions of the \(N\)-vortex problem on the sphere ⋮ Shape dynamics of N point vortices on the sphere ⋮ 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 ⋮ The N -vortex problem on a rotating sphere. II. Heterogeneous Platonic solid equilibria ⋮ TheN-vortex problem on a rotating sphere. I Multi-frequency configurations ⋮ On the stability of Thomson's vortex configurations inside a circular domain ⋮ Latitudinal point vortex rings on the spheroid ⋮ On the stability of Thomson's vortex pentagon inside a circular domain ⋮ Invariant dynamical systems embedded in the \(N\)-vortex problem on a sphere with pole vortices ⋮ Energy-momentum stability of icosahedral configurations of point vortices on a sphere ⋮ Lyapunov orbits in the \(n\)-vortex problem ⋮ The spatial problem of 2 bodies on a sphere. Reduction and stochasticity ⋮ Chaotic motion of the \(N\)-vortex problem on a sphere. I. Saddle-centers in two-degree-of-freedom Hamiltonians ⋮ Influence of annular boundaries on Thomson's vortex polygon stability ⋮ Three-dimensional quasi-geostrophic staggered vortex arrays
Cites Work
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- Stability and bifurcations for the \(N+1\) vortex problem on the sphere
- Motion of three point vortices on a sphere
- Point vortices on a rotating sphere
- Point vortices on the sphere: a case with opposite vorticities
- Experiments on two-dimensional vortex patterns
- Stability of streets of vortices on surfaces of revolution with a reflection symmetry
- Quasi-steady flow of a rotating stratified fluid in a sphere
- Wave and vortex dynamics on the surface of a sphere
- Barotropic vortex pairs on a rotating sphere
- Point vortices on a sphere: Stability of relative equilibria
- The stability of stationary rotation of a regular vortex polygon
- Point-vortex cluster formation in the plane and on the sphere: An energy bifurcation condition
- Stability of Thomson's configurations of vortices on a sphere
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