Lagrangian Flow Geometry of Tripolar Vortex

  • Lorena A. Barba
  • Oscar U. Velasco Fuentes
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 6)


Tripolar vortices have been observed to emerge in two-dimensional flows from the evolution of unstable shielded monopoles. They have also been obtained from a stable Gaussian vortex with a large quadrupolar perturbation. In this case, if the amplitude of the perturbation is small, the flow evolves into a circular monopolar vortex, but if it is large enough a stable tripolar vortex emerges. This change in final state has been previously explained by invoking a change of topology in the co-rotating stream function. We find that this explanation is insufficient, since for all perturbation amplitudes, large or small, the co-rotating stream function has the same topology; namely, three stagnation points of centre type and two stagnation points of saddle type. In fact, this topology lasts until late in the flow evolution. However, the time-dependent Lagrangian description can distinguish between the two evolutions, as only when a stable tripole arises the hyperbolic character of the saddle points manifests persistently in the particle dynamics (i.e. a hyperbolic trajectory exists for the whole flow evolution).


Lagrangian flow tripolar vortex scatter plot 


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Copyright information

© Springer Science + Business Media B.V 2008

Authors and Affiliations

  • Lorena A. Barba
    • 1
  • Oscar U. Velasco Fuentes
    • 2
  1. 1.Department of MathematicsUniversity of BristolUK
  2. 2.Depto. de Oceanografía FísicaCICESEEnsenadaMéxico

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