2005.28: Stability of Relative Equilibria of Point Vortices on the Sphere
2005.28: Frederic Laurent-Polz, James Montaldi and Mark Roberts (2005) Stability of Relative Equilibria of Point Vortices on the Sphere.
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We describe the linear and nonlinear stability and instability of certain configurations of point vortices on the sphere forming relative equilibria. These configurations consist of up to two rings, with and without polar vortices. Such configurations have dihedral symmetry, and the symmetry is used both to block diagonalize the relevant matrices and to distinguish the subspaces on which their eigenvalues need to be calculated.
|Item Type:||MIMS Preprint|
|Uncontrolled Keywords:||Hamiltonian systems, symmetry methods, momentum map|
|Subjects:||MSC 2000 > 37 Dynamical systems and ergodic theory|
MSC 2000 > 76 Fluid mechanics
|Deposited By:||Dr James Montaldi|
|Deposited On:||02 December 2005|
Available Versions of this Item
- Point Vortices on the Sphere: Stability of Symmetric Relative Equilibria (deposited 29 March 2011)
- Stability of Relative Equilibria of Point Vortices on the Sphere (deposited 02 December 2005) [Currently Displayed]