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

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

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

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

5. Pentapole, n = 4

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

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

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

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: