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On the dynamics of leapfrogging vortex rings

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arxiv 2503.21604 v2 pith:BM3D2YRC submitted 2025-03-27 math.AP math-phmath.MP

Martin Donati , Lars Eric Hientzsch , Christophe Lacave , Evelyne Miot This is my paper · ORCID
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keywords ringsdynamicsleapfroggingregimeargumentaroundaxisymmetricclass
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The evolution of highly concentrated vorticity around rings in the three-dimensional axisymmetric Euler equations is studied in a regime for which the leapfrogging dynamics predicted by Helmholtz is expected to occur. We provide in this paper the first result deriving this phenomenon for a general class of initial data in the suitable regime. The singular interaction of rings requires significant improvements of weak and strong localization estimates obtained in prior works. Our method is based on the combination of a new variational argument and a recently introduced double iterative procedure.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Linear Growth of the Vorticity Maximum for Axisymmetric Euler Flows Without Swirl

    math.AP 2025-11 conditional novelty 8.0 of 10

    For axisymmetric Euler flows without swirl with anti-parallel, one-signed vorticity, the radial moment satisfies P(t)[log t]^{5/2}/t^{3/2} -> infinity and the vorticity maximum reaches a fixed fraction of t on (1-eta)...

  2. Stability for multiple Lamb dipoles

    math.AP 2025-07 conditional novelty 7.0 of 10

    Finite sums of Lamb dipoles in the half-plane, with ordered speeds and well-separated initial positions, are Lyapunov stable under the 2D Euler equations.

  3. Stability of oppositely-propagating pair of Hill's spherical vortices

    math.AP 2025-07 conditional novelty 6.0 of 10

    An odd-symmetric pair of Hill's spherical vortices is globally stable in 3D axisymmetric Euler flow, with propagation speed close to the single-vortex speed and a sharp linear error estimate.

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