Dynamics and bifurcation of passive tracers advected by a ring of point vortices on a sphere
We consider the dynamics of a passive tracer, advected by the presence of a latitudinal ring of identical point vortices. The corresponding instantaneous motion is modeled by a one degree of freedom Hamiltonian system. Such a dynamics presents a rich variety of behaviors with respect to the number o...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/530701 |
| Acceso en línea: | http://hdl.handle.net/2072/530701 |
| Access Level: | acceso abierto |
| Palabra clave: | Matemàtiques Física 51 |
| Sumario: | We consider the dynamics of a passive tracer, advected by the presence of a latitudinal ring of identical point vortices. The corresponding instantaneous motion is modeled by a one degree of freedom Hamiltonian system. Such a dynamics presents a rich variety of behaviors with respect to the number of vortices, N, and the ring’s co-latitude, θo—or, equivalently, its vertical position qo = cos θo. We carry out a complete description of the global phase portrait for the cases N = 2, 3, 4 by determining equilibrium points, their stability, and bifurcations with respect to the parameter θo, and by characterizing the separatrix skeleton. Moreover, for N ≥ 5, we prove the existence of a value of bifurcation θoN such that when θo = θoN (θo = π − θoN, respectively) the south (north, respectively) pole becomes a N-bifurcation point, i.e., a symmetric web of N centers and N saddles bifurcates from the corresponding pole. |
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