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2D vortices in fluids: Stability of vortical ensembles

2D vortices in fluids: Stability of vortical ensembles. Ziv Kizner. Pingree & Le Cann, 1992. Tripole eddy observed in the Bay of Biscay. Lab experiment. Semi-analytical solution. Flow pattern. Vorticity cross sections. Tripole: A core vortex & two ( n = 2) satellites. core. satellite.

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2D vortices in fluids: Stability of vortical ensembles

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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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