Lagrangian Flow Geometry of Tripolar Vortex
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).
KeywordsLagrangian flow tripolar vortex scatter plot
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