How reliable are finite-size Lyapunov exponents for the assessment of ocean dynamics?

Ocean Modelling

Volumn 36, Issue 3-4, 2011, Pages 208-218

  Hernández Carrasco, Ismael ^a   López, Cristóbal ^a   Hernández García, Emilio ^a   Turiel, Antonio ^b  

^a INSTITUTO DE FÍSICA INTERDISCIPLINAR Y SISTEMAS COMPLEJOS IFISC CSIC UIB   (Spain)

^b INSTITUT DE CIÈNCIES DEL MAR   (Spain)

Author keywords

Finite size Lyapunov exponents; Lagrangian methods

Indexed keywords

BENCHMARK DATA; COHERENT STRUCTURE; FINITE-SIZE LYAPUNOV EXPONENTS; LAGRANGIAN METHODS; LAGRANGIAN TECHNIQUES; MEDITERRANEAN SEA; NUMERICAL MODELS; OCEAN DYNAMICS;

ATMOSPHERIC MOVEMENTS; DIFFERENTIAL EQUATIONS; DYNAMICS; LAGRANGE MULTIPLIERS; LYAPUNOV FUNCTIONS; TRANSPORT PROPERTIES;

LYAPUNOV METHODS;

LAGRANGIAN ANALYSIS; NUMERICAL MODEL; OCEANOGRAPHY; RELIABILITY ANALYSIS;

MEDITERRANEAN SEA;

EID: 79951675529     PISSN: 14635003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ocemod.2010.12.006     Document Type: Article

References (34)

1. Artale V., Boffetta G., Celani A., Cencini M., Vulpiani A. Dispersion of passive tracers in closed basins: beyond the diffusion coefficient. Physics of Fluids 1997, 9:3162-3171.
2. Aurell E., Boffetta G., Crisanti A., Palading G., Vulpiani A. Predictability in the large: an extension of the concept of Lyapunov exponent. Journal of Physics A 1997, 30:1-26.
3. Beron-Vera F., Olascoaga M., Goni G. Oceanic mesoscale eddies as revealed by lagrangian coherent structures. Geophysical Research Letters 2008, 35:L12603.
4. Boffetta G., Lacorata G., Redaelli G., Vulpiani A. Detecting barriers to transport: a review of different techniques. Physica D 2001, 159:58-70.
5. Buffoni G., Falco P., Griffa A., Zambianchi E. Dispersion processes and residence times in a semi-enclosed basin with recirculating gyres: an application to the Tyrrhenian sea. Journal of Geophysical Research - Oceans 1997, 102:18699-18713.
6. d'Ovidio F., Fernández V., Hernández-García E., López C. Mixing structures in the mediterranean sea from finite-size Lyapunov exponents. Geophysical Research Letters 2004, 10.1029/2004GL020328.
7. d'Ovidio F., Isern-Fontanet J., López C., Hernández-García E., García-Ladona E. Comparison between Eulerian diagnostics and finite-size Lyapunov exponents computed from altimetry in the Algerian basin. Deep-Sea Research I 2009, 56:15-31.
8. Falconer K. Fractal Geometry: Mathematical Foundations and Applications 1990, John Wiley and Sons, Chichester.
9. Fernández V., Dietrich D., Haney R., Tintoré J. Mesoscale, seasonal and interannual variability in the Mediterranean sea using a numerical ocean model. Progress in Oceanography 2005, 66:321-340.
10. Frisch U. Turbulence: The Legacy of A.N. Kolmogorov 1995, Cambridge University Press, Cambridge, MA.
11. Garcia-Olivares A., Isern-Fontanet J., Garcia-Ladona E. Dispersion of passive tracers and finite-scale Lyapunov exponents in the Western Mediterranean Sea. Deep Sea Research I 2007, 54:253-268.
12. Griffa A. Applications of stochastic particle models to oceanographic problems. Stochastic modelling in physical oceanography 1996, Birkhauser. R. Adler, P. Muller, B. Rozovskii (Eds.).
13. Haller G. Finding finite-time invariant manifolds in two-dimensional velocity fields. Chaos 2000, 10(1):99-108.
14. Haller G. Lagrangian coherent structures from approximate velocity data. Physics of Fluids 2002, 14:1851-1861.
15. Haller G., Poje A. Finite time transport in aperiodic flows. Physica D 1998, 119:352-380.
16. Haller G., Yuan G. Lagrangian coherent structures and mixing in two-dimensional turbulence. Physica D 2000, 147:352-370.
17. Haza A.C., Poje A.C., Özgökmena T.M., Martin P. Relative dispersion from a high-resolution coastal model of the Adriatic Sea. Ocean Modelling 2008, 22:48-65.
18. Isern-Fontanet J., Turiel A., Garcia-Ladona E., Font J. Microcanonical multifractal formalism: application to the estimation of ocean surface velocities. Journal of Geophysical Research 2007, 112:C05024.
19. Iudicone D., Lacorata G., Rupolo V., Santoreli R., Vulpiani A. Sensitivity of numerical tracer trajectories to uncertainties in ogcm velocity fields. Ocean Modelling 2002, 313-325.
20. Joseph B., Legras B. Relation between kinematic boundaries, stirring, and barriers for the antartic polar vortex. Journal of Atmospheric Sciences 2002, 59:1198-1212.
21. Kai E.T., Rossi V., Sudre J., Weimerskirch H., López C., Hernández-García E., Marsac F., Garcon V. Top marine predators track lagrangian coherent structures. Proceedings of the National Academy of Sciences of the USA 2009, 106:8245-8250.
22. Koh T.-Y., Legras B. Hyperbolic lines and the stratospheric polar vortex. Chaos 2002, 12(2):382-394.
23. Lapeyre G. Characterization of finite-time Lyapunov exponents and vectors in two-dimensional turbulence. Chaos 2002, 12(2):688-698.
24. Mancho A., Hernández-García E., Small D., Wiggins S., Fernández V. Lagrangian transport through an ocean front in the North-Western Mediterranean Sea. Journal of Physical Oceanography 2008, 38:1222-1237.
25. Mancho A., Small D., Wiggins S. A tutorial on dynamical systems concepts applied to lagrangian transport in oceanic flows defined as finite time data sets: theoretical and computational studies. Physics Reports 2006, 437:55-124.
26. Molcard A., Poje A., Ozgokmen T. Directed drifter launch strategies for lagrangian data assimilation using hyperbolic trajectories. Ocean Modelling 2006, 12:268-289.
27. Okubo A. Ocean diffusion diagramas. Deep Sea Research 1971, 18:789-802.
28. Ott E. Chaos in Dynamical Systems 1993, Cambridge University Press, Cambridge, UK.
29. Peacock T., Dabiri J. Introduction to focus issue: Lagrangian coherent structures. Chaos 2010, 20:017501.
30. Poje A., Haza A., Ozgokme T., Magaldi M., Garraffo Z. Resolution dependent relative dispersion statistics in a hierarchy of ocean models. Ocean Modelling 2010, 31:36-50.
31. Schneider J., Fernández V., Hernández-García E. Leaking method approach to surface transport in the Mediterranean Sea from a numerical ocean model. Journal of Marine Systems 2005, 57:111-126.
32. Turiel A., del Pozo A. Reconstructing images from their most singular fractal manifold. IEEE Transactions on Image Processing 2002, 11:345-350.
33. Turiel A., Pérez-Vicente C., Grazzini J. Numerical methods for the estimation of multifractal singularity spectra on sampled data: a comparative study. Journal of Computational Physics 2006, 216(1):362-390.
34. Turiel A., Yahia H., Pérez-Vicente C. Microcanonical multifractal formalism: a geometrical approach to multifractal systems. Part I: Singularity analysis. Journal of Physics A 2008, 41:015501.