Transport in an idealized three-gyre system with application to the Adriatic Sea

Journal of Physical Oceanography

Volumn 39, Issue 3, 2009, Pages 675-690

  Rypina, Irina I ^a   Brown, Michael G ^b   Koçak, Huseyin ^c  

^a WOODS HOLE OCEANOGRAPHIC INSTITUTION   (United States)

^b UNIVERSITY OF MIAMI   (United States)

^c University of Miami   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADRIATIC; ADRIATIC SEA; ANALYTIC MODELS; BACKGROUND FLOW; PERTURBATION STRENGTH; SMALL PERTURBATIONS; SURFACE CIRCULATION; SURFACE DRIFTER; TIME-DEPENDENT; TIME-DEPENDENT PERTURBATION; VELOCITY FIELD;

DYNAMICAL SYSTEMS;

TWO DIMENSIONAL;

ALTIMETRY; CIRCULATION MODELING; DRIFT BEHAVIOR; GYRE; INCOMPRESSIBLE FLOW; OBSERVATIONAL METHOD; PERTURBATION; STEADY FLOW; TWO-DIMENSIONAL FLOW;

ADRIATIC SEA; MEDITERRANEAN SEA;

EID: 67649939218     PISSN: 00223670     EISSN: None     Source Type: Journal    
DOI: 10.1175/2008JPO3975.1     Document Type: Article

References (56)

1. Arnold, V. I., 1963: Proof of a theorem of A. N. Kolmogorov on the invariance of quasi-periodic motions under small perturbations of the Hamiltonian. Russ. Math. Surv., 18, 9-36.
2. Artegiani, A., D. Bregant, E. Pashini, N. Pinardi, F. Raicich, and A. Russo, 1997a: The Adriatic Sea general circulation. Part I: Air-sea interactions and water mass structure. J. Phys. Oceanogr., 27, 1492-1514.
3. Artegiani, A., D. Bregant, E. Pashini, N. Pinardi, F. Raicich, and A. Russo, 1997b: The Adriatic Sea general circulation. Part II: Baroclinic circulation structure. J. Phys. Oceanogr., 27, 1515-1532.
4. Beron-Vera, F. J., M. J. Olasocaga, and G. J. Goni, 2008: Oceanic mesoscale eddies as revealed by Lagrangian coherent structures. Geophys. Res. Lett., 35, L12603, doi:10.1029/2008GL033957.
5. Brown, M. G., 1998: Phase space structure and fractal trajectories in 11/ 2 degree of freedom Hamiltonian systems whose time dependence is quasiperiodic. Nonlinear Processes Geophys., 5, 69-74.
6. Castellari, S., A. Griffa, T. M. Ozkomen, and P.-M. Poulain, 2001: Prediction of particle trajectories in the Adriatic Sea using Lagrangian data assimilation. J. Mar. Syst., 29, 33-50.
7. Chirikov, B. V., 1979: A universal instability of many-dimensional oscillator systems. Phys. Rep., 52, 265-379.
8. Coulliette, C., and S. Wiggins, 2001: Intergyre transport in a wind-driven, quasigeostrophic double gyre: An application of lobe dynamics. Nonlinear Processes Geophys., 8, 69-94.
9. Coulliette, C., F. Lekien, J. D. Paduan, G. Haller, and J. E. Marsden, 2007: Optimal pollution mitigation in Monterey Bay based on coastal radar data and nonlinear dynamics. Environ. Sci. Technol., 41, 6562-6572.
10. Cushman-Roisin, B., M. Gacic, P.-M. Poulain, and A. Artegiani, 2001: Physical Oceanography of the Adriatic Sea: Past, Present and Future. Kluwer Academic, 304 pp.
11. Falco, P., A. Griffa, P.-M. Poulain, and E. Zambianchi, 2000: Transport properties of the Adriatic Sea as deduced from drifter data. J. Phys. Oceanogr., 30, 2055-2071.
12. Haller, G., 2000: Finding finite-time invariant manifolds in two-dimensional velocity fields. Chaos, 10, 99-108.
13. Haller, G., 2001a: Distinguished material surfaces and coherent structures in 3D fluid flows. Physica D, 149, 248-277.
14. Haller, G., 2001b: Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence. Phys. Fluids, 13, 3365-3385.
15. Haller, G., 2002: Lagrangian coherent structures from approximate velocity data. Phys. Fluids, 14, 1851-1861.
16. Haller, G., and G. Yuan, 2000: Lagrangian coherent structures and mixing in two-dimensional turbulence. Physica D, 147, 352-370.
17. Haza, A. C., L. I. Piterbarg, P. Martin, T. M. Ozgokmen, and A. Griffa, 2007a: A Lagrangian subgridscale model for particle transport improvement and application in the Adriatic Sea using the Navy Ocean Model. Ocean Modell., 17, 68-91.
18. Haza, A. C., and Coauthors, 2007b: Model-based directed drifter launches in the Adriatic Sea: Results from DART experiment. Geophys. Res. Lett., 34, L10605, doi:10.1029/2007GL029634.
19. Jorba, Á., and C. Simó, 1996: On quasi-periodic perturbations of elliptic equilibrium points. SIAM J. Math. Anal., 27, 1704-1737.
20. Kolmogorov, A. N., 1954: On the persistence of conditionally periodic motions under a small change of the Hamilton function (in Russian). Dokl. Akad. Nauk SSSR, 98, 525-530.
21. Koshel, K. V., and S. V. Prants, 2006: Chaotic advection in the ocean. Phys.-Usp., 49, 1151-1178.
22. Lacorata, G., E. Aurell, and A. Vulpiani, 2001: Drifter dispersion in the Adriatic Sea: Lagrangian data and chaotic model. Ann. Geophys., 19, 121-129.
23. Landau, L. D., and E. M. Lifshitz, 1976: Mechanics. 3rd ed. Course of Theoretical Physics, Vol. 1, Pergamon, 169 pp.
24. Lekien, F., C. Coulliette, A. J. Mariano, E. H. Ryan, L. K. Shay, G. Haller, and J. E. Marsden, 2005: Pollution release tied to invariant manifolds: A case study for the coast of Florida. Physica D, 210, 1-20.
25. Lichtenberg, A. G., and M. A. Lieberman, 1983: Regular and Stochastic Motion. Springer-Verlag, 499 pp.
26. Malhotra, N., and S. Wiggins, 1998: Geometric structures, lobe dynamics, and Lagrangian transport in flows with aperiodic time-dependence, with applications to Rossby wave flow. J. Nonlinear Sci., 8, 401-456.
27. Mancho, A. M., D. Small, and S. Wiggins, 2006: A tutorial on dynamical systems concepts applied to Lagrangian transport in oceanic flows defined as finite time data sets: Theoretical and computational issues. Phys. Rep., 437, 55-124.
28. Mancho, A. M., E. Hernández-García, D. Small, S. Wiggins, and V. Fernández, 2008: Lagrangian transport through an ocean front in the northwestern Mediterranean Sea. J. Phys. Oceanogr., 38, 1222-1237.
29. Mathur, M., G. Haller, T. Peacock, J. E. Ruppert-Felsot, and H. L. Swinney, 2007: Uncovering the Lagrangian skeleton of turbulence. Phys. Rev. Lett., 98, Abstract 144502.
30. Maurizi, A., A. Griffa, P.-M. Poulain, and F. Tampieri, 2004: Lagrangian turbulence in the Adriatic Sea as computed from drifter data: Effects of inhomogeneity and nonstationarity. J. Geophys. Res., 109, C04010, doi:10.1029/2003JC002119.
31. Miller, P. D., C. K. R. T. Jones, A. M. Rogerson, and L. J. Pratt, 1997: Quantifying transport in numerically generated velocity fields. Physica D, 110, 105-122.
32. Miller, P. D., L. J. Pratt, K. R. Helrich, and C. K. R. T. Jones, 2002: Chaotic transport of mass and potential vorticity for an island recirculation. J. Phys. Oceanogr., 32, 80-102.
33. Olascoaga, M. J., I. I. Rypina, M. G. Brown, F. J. Beron-Vera, H. Koçak, L. E. Brand, G. R. Halliwell, and L. K. Shay, 2006: Persistent transport barrier on the West Florida Shelf. Geophys. Res. Lett., 33, L22603, doi:10.1029/2006GL027800.
34. Olascoaga, M. J., F. J. Beron-Vera, L. E. Brand, and H. Kocak, 2008: Tracking the early development of harmful algal blooms on the West Florida Shelf with the aid of Lagrangian coherent structures. J. Geophys. Res., 113, C12014, doi:10.1029/2007JC004533.
35. Orlic, M., M. Gacic, and P. E. La Violette, 1992: The currents and circulation of the Adriatic Sea. Oceanol. Acta, 15, 109-124.
36. Palmer, K., and D. Stoffer, 1989: Chaos in almost periodic systems. Z. Angew. Math. Phys., 40, 592-602.
37. Poje, A. C., and G. Haller, 1999: Geometry of cross-stream mixing in a double-gyre ocean model. J. Phys. Oceanogr., 29, 1649-1665.
38. Poulain, P.-M., 1999: Drifter observations of surface circulation in the Adriatic Sea between December 1994 and March 1996. J. Mar. Syst., 20, 231-253.
39. Poulain, P.-M., 2001: Adriatic Sea surface circulation as derived from drifter data between 1990 and 1999. J. Mar. Syst., 29, 3-32.
40. Rogerson, A., P. D. Miller, L. J. Pratt, and C. K. R. T. Jones, 1999: Lagrangian motion and fluid exchange in a barotropic meandering jet. J. Phys. Oceanogr., 29, 2635-2655.
41. Rom-Kedar, V., and S. Wiggins, 1990: Transport in two-dimensional maps. Arch. Ration. Mech. Anal., 109, 239-298.
42. Rom-Kedar, V., A. Leonard, and S. Wiggins, 1990: An analytical study of transport, mixing, and chaos in an unsteady vortical flow. J. Fluid Mech., 214, 347-394.
43. Rüssmann, H., 1989: Non-degeneracy in the perturbation theory of integrable dynamical systems. Number Theory and Dynamical Systems, M. M. Dodson and J. A. G. Vickers, Eds., London Mathematical Society Lecture Notes Series, Vol. 134, Cambridge University, 5-18.
44. Rypina, I. I., M. G. Brown, F. J. Beron-Vera, H. Koçak, M. J. Olascoaga, and I. A. Udovydchenkov, 2007a: On the Lagrangian dynamics of atmospheric zonal jets and the permeability of the Stratospheric Polar Vortex. J. Atmos. Sci., 64, 3595-3610.
45. Rypina, I. I., M. G. Brown, F. J. Beron-Vera, H. Koçak, M. J. Olascoaga, and I. A. Udovydchenkov, 2007b: Robust transport barriers resulting from strong Kolmogorov-Arnold-Moser stability. Phys. Rev. Lett., 98, Abstract 104102, doi:10.1103/PhysRevLett.98.104102.
46. Samelson, R. M., 1992: Fluid exchange across a meandering jet. J. Phys. Oceanogr., 22, 431-440.
47. Samelson, R. M., and S. Wiggins, 2006: Lagrangian Transport in Geophysical Jets and Waves: The Dynamical Systems Approach. Springer, 147 pp.
48. Sevryuk, M. B., 2007: Invariant tori in quasi-periodic non-autonomous dynamical systems via Herman's method. Discrete Contin. Dyn. Syst., 18, 569-595.
49. Shadden, S. C., F. Lekien, and J. E. Marsden, 2005: Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperidic flows. Physica D, 212, 271-304.
50. Ursella, L., P.-M. Poulain, and R. P. Signell, 2006: Surface drifter derived circulation in the northern and middle Adriatic Sea: Response to wind regime and season. J. Geophys. Res., 111, C03S04, doi:10.1029/2005JC003177.
51. Wiggins, S., 1992: Chaotic Transport in Dynamical Systems. Springer-Verlag, 301 pp.
52. Wiggins, S., 1999: Chaos in the dynamics generated by sequences of maps, with applications to chaotic advection in flows with aperiodic time dependence. Z. Angew. Math. Phys., 50, 585-616.
53. Wiggins, S., 2005: The dynamical systems approach to Lagrangian transport in oceanic flows. Annu. Rev. Fluid Mech., 37, 295-328.
54. Yi, Y., 1993: A generalized integral manifold theorem. J. Differ. Equations, 102, 153-187.
55. Yuan, G. C., L. J. Pratt, and C. K. R. T. Jones, 2004: Cross-jet Lagrangian transport and mixing in a 21/2-layer model. J. Phys. Oceanogr., 34, 1991-2005.
56. Zaslavskii, G. M., and B. V. Chirikov, 1972: Stochastic instability of non-linear oscillations. Sov. Phys.-Usp., 14, 549-568.