Lagrangian flow geometry of tripolar vortex

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Abstract

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). © 2008 Springer.

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Barba, L. A., & Fuentes, O. U. V. (2008). Lagrangian flow geometry of tripolar vortex. In Solid Mechanics and its Applications (Vol. 6, pp. 247–256). Springer Verlag. https://doi.org/10.1007/978-1-4020-6744-0_21

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