Rotating \(n\)-gon/\(kn\)-gon vortex configurations

DOI10.1007/BF02440160zbMath0869.76012MaRDI QIDQ2563688

Tudor S. Ratiu, Debra Lewis

Publication date: 4 September 1997

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

zbMATH Keywords

existencelinear stability analysisnecessary conditions for stabilitystationary point-vortex configurations

Mathematics Subject Classification ID

Vortex flows for incompressible inviscid fluids (76B47) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Hydrodynamic stability (76E99)

Related Items

Von Kármán vortex streets on the sphere ⋮ Vortices on Closed Surfaces ⋮ Periodic orbits of Gross-Pitaevskii in the disc with vortices following point vortex flow ⋮ Global continua of periodic solutions of singular first-order Hamiltonian systems of \(N\)-vortex type ⋮ Dynamics of two vortex rings in a Bose-Einstein condensate ⋮ Fixed equilibria of point vortices in symmetric multiply connected domains ⋮ Relative equilibria of the \((1+N)\)-vortex problem ⋮ Relative equilibria of point vortices on the sphere ⋮ The stability of stationary rotation of a regular vortex polygon ⋮ Energy-momentum stability of icosahedral configurations of point vortices on a sphere ⋮ Construction of point vortex equilibria via Brownian ratchets ⋮ Point vortices on a sphere: Stability of relative equilibria ⋮ Relative equilibria in the 3-dimensional curved n-body problem ⋮ Vortices and Polynomials ⋮ Relative equilibria of point vortices and the fundamental theorem of algebra ⋮ Hamiltonian systems near relative equilibria

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On Aref's vortex motions with a symmetry center
• The topology of reduced phase spaces of the motion of vortices on a sphere
• On the driving of a piston with a rigid collar into an elastic half-space
• Point vortex motions with a center of symmetry
• Integrable, Chaotic, and Turbulent Vortex Motion in Two-Dimensional Flows
• Nonexistence of Lyapunov functions and the instability of the von Kármán vortex streets
• On the equilibrium and stability of a row of point vortices

This page was built for publication: Rotating \(n\)-gon/\(kn\)-gon vortex configurations