Finite time transport in aperiodic flows

Physica D: Nonlinear Phenomena

Volumn 119, Issue 3-4, 1998, Pages 352-380

  Haller, G ^a   Poje, A C ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001229490     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(98)00091-8     Document Type: Article

References (35)

1. H.S. Balasuriya, C.K.R.T. Jones, B. Sandstede, Viscous perturbations of vorticity-conserving flows and splitting of separatrices, Nonlinearity 11 (1998) 47-77.
2. D. Beigie, Codimension-one partitioning in multi-degree-of-freedom Hamiltonian systems with non-toroidal invariant manifold intersections, Preprint, 1994.
3. D. Beigie, Multiple separatrix crossing in multi-degree-of-freedom Hamiltonian flows, Preprint, 1994.
4. D. Beigie, A. Leonard, S. Wiggins, Chaotic transport in the homoclinic and heteroclinic tangle regions of quasi-periodically forced two-dimensional dynamical systems, Nonlinearity 4 (1991) 775-819.
5. D. Beigie, A. Leonard, S. Wiggins, The dynamics associated with the chaotic tangles of two-dimensional quasiperiodic vector fields Theory and applications, in: F.G. Carnevale, R. Pierrehumbert (Eds.), Nonlinear Phenomena in Atmospheric Oceanic Sciences, IMA Volumes in Mathematics and Applications, vol. 40, Springer, New York, 1992, pp. 47-138.
6. A.S. Bower, A simple kinematic mechanism for mixing fluid parcels across a meandering jet, J. Phys. Oceanogr. 21 (1991) 173-180.
7. R. Camassa, S. Wiggins, Chaotic advection in a Rayleigh-Bénard flow, Phys. Rev. A 43 (1991) 774-797.
8. J.Q. Duan, S. Wiggins, Fluid exchange across a meandering jet with quasi-periodic variability, J. Phys. Oceanogr. 26 (1996) 1176-1188.
9. S. Dutkiewitz, N. Paldor, On the mixing enhancement in a meandering jet due to the interaction with an eddy, J. Phys. Oceanogr. 24 (1994) 2418-2423.
10. M. Feingold, L.P. Kadanoff, O. Piro, Passive scalars, three-dimensional volume preserving maps, and chaos, J. Stat. Phys. 50 (1988) 529-565.
11. N. Fenichel, Persistence and smoothness for invariant manifolds for flows, Indiana Univ. Math. 21 (1971) 193-225.
12. G. Haller, I. Mezić, Reduction of three-dimensional, volume-preserving flows with symmetry, Nonlinearity 11 (1998) 319-339.
13. G. Haller, A. Poje, Eddy growth and mixing in mesoscale oceanographic flows, Nonlin. Proc. Geophys., submitted.
14. P. Holmes, Some remarks on chaotic particle paths in time-periodic, three-dimensional swirling flows, Contemp. Math. 28 (1984) 393-404.
15. T.J. Kaper, G.A. Kovačič, A geometric criterion for adiabatic chaos, J. Math. Phys. 35 (3) (1994) 1202-1218.
16. T.J. Kaper, S. Wiggins, Lobe area in adiabatic Hamiltonian systems, Physica D 51 (1991) 205-212.
17. Y.T. Lau, J.M. Finn, Dynamics of a three-dimensional incompressible flow with a stagnation point, Physica D 5 (1992) 283-310.
18. R.S. MacKay, Transport in three-dimensional volume-preserving flows, J. Nonlinear Sci. 4 (1994) 329-354.
19. R.S. MacKay, J.D. Meiss, I.C. Percival, Transport in Hamiltonian systems, Physica D 13 (1984) 55-81.
20. K.R. Meyer, G.R. Sell, Melnikov bundles, and almost periodic perturbations, Trans. Am. Math. Soc. 314 (1991) 63-105.
21. I. Mezić, S. Wiggins, On the integrability and perturbation of three-dimensional fluid flows with symmetry, J. Nonlinear. Sci. 4 (1994) 157-194.
22. P.D. Miller, C.K.R.T. Jones, A.M. Rogerson, L.J. Pratt, Quantifying transport in numerically generated velocity fields, Physica D 110 (1997) 105-122.
23. Z. Neufeld, T. Tél, Advection in chaotically time-dependent open Flows, Preprint, 1997.
24. A. Poje, G. Haller, Lagrangian geometry of cross-stream mixing in a double gyre ocean model, J. Phys. Oceanogr., submitted.
25. A.M. Rogerson, L.J. Pratt, P.D. Miller, C.K.R.T. Jones, J. Biello, J. Chaotic mixing in a barotropic jet, J. Phys. Oceanogr., submitted.
26. V. Rom-Kedar, Homoclinic tangles-classification and applications, Nonlinearity 7 (1994) 441-473.
27. V. Rom-Kedar, Secondary homoclinic bifurcation theorems, Chaos 5 (1995) 385-401.
28. V. Rom-Kedar, A. Leonard, S. Wiggins, An analytical study of transport, mixing, and chaos in an unsteady vortical flow, J. Fluid. Mech. 214 (1990) 347-394.
29. V. Rom-Kedar, S. Wiggins, Transport in two-dimensional maps, Arch. Rat. Mech. Anal. 109 (1990) 239-298.
30. J. Scheurle, Chaotic solutions in systems with almost periodic forcing J. Appl. Math. Phys. (ZAMP) 37 (1986) 12-26.
31. S. Wiggins, Global Bifurcations and Chaos: Analytic Methods, Springer, New York, 1988.
32. S. Wiggins, On the geometry and transport in phase space-I: Transport in k-degree-of-freedom Hamiltonian systems, 2 ≤ k < ∞ Physica D 44 (1990) 471-501.
33. S. Wiggins, Chaotic Transport in Dynamical Systems, Springer, New York, 1992.
34. A.A. Wray, J.C.R. Hunt, Algorithms for classification of turbulent structures, in: H.K. Moffatt, A. Tsinober (Eds.), Topological Fluid Mechanics Cambridge University Press, Cambridge, 1990.
35. E.M. Ziemniak, C. Jung, T. Tél, Tracer dynamics in open hydrodynamical flows as chaotic scattering, Physica D 44 (1994) 123-146.