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Stability of Vortical Ensembles: The Tripole Eddy in Fluid Dynamics (1992)

This paper explores the stability of vortical structures in fluids, particularly focusing on the tripole vortex observed in the Bay of Biscay through laboratory experiments. A semi-analytical solution is provided to describe the flow patterns and vorticity cross-sections of the tripole, consisting of a core vortex and two satellite vortices (n=2). The study also examines quadrupole and pentapole configurations and utilizes concepts like the point-vortex model, Stock’s theorem, and Hamiltonian dynamics to analyze the dynamical behavior and stability of these vortex formations.

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Stability of Vortical Ensembles: The Tripole Eddy in Fluid Dynamics (1992)

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  1. 2D vortices in fluids:Stability of vortical ensembles Ziv Kizner

  2. Pingree & Le Cann, 1992 Tripole eddy observed in the Bay of Biscay

  3. Lab experiment Semi-analytical solution Flow pattern Vorticity cross sections Tripole:A core vortex & two (n = 2) satellites core satellite

  4. Quadrupole, n = 3 Vorticity cross section core satellite

  5. Pentapole, n = 4

  6. L r = R Point-vortex concept Stock’s theorem: v D L Point vortex: r

  7. y B b rA,B rB,C A a rA,C c C x Tripole: -1 2 -1 Point-vortex ensemble: Autonomic dynamical system

  8. -1 y B B l A A +2 l C C tripole troika -1 x Stability of a point-vortex tripole • Invariants of a troika • Impulse: • Hamiltonian: 2.Tripole 3.Tripole stability On the iso-Hamiltonian sheet Impulse: troika = tripole Hamiltonian: the tripole supplies a minimum to P2 monotonic function of l

  9. Tripole oscillator y y y y y y y y

  10. The end פרופ' זיו קיזנר: ziv.kizner@gmail.com 03-531 8790 משרד:

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