Lagrangian coherent structures in n-dimensional systems

Journal of Mathematical Physics

Volumn 48, Issue 6, 2007, Pages

  Lekien, Francois ^a   Shadden, Shawn C ^b   Marsden, Jerrold E ^c  

^a Princeton University   (United States)

^b Stanford University   (United States)

^c CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34250616203     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2740025     Document Type: Article

References (42)

1. Arratia, P. E., Voth, G. A., and Gollub, J. P., " Stretching and mixing of non-Newtonian fluids in time-periodic flows., " Phys. Fluids 17, 053102 (2005).
2. Beigie, D., " Multiple separatrix crossing in multi-degree-of- freedom Hamiltonian flows., " J. Nonlinear Sci. 5, 57-103 (1995).
3. Beigie, D., Leonard, A., and Wiggins, S., " A global study of enhanced stretching and diffusion in chaotic tangles., " Phys. Fluids A 3, 1039-1050 (1991).
4. Coulliette, C., Lekien, F., Haller, G., Paduan, J., and Marsden, J. E., " Optimal pollution mitigation in Monterey Bay based on coastal radar data and nonlinear dynamics., " Environ. Eng. Sci. (to be published).
5. Coulliette, C. and Wiggins, S., " Intergyre transport in a wind-driven, quasigeostrophic double gyre: An application of lobe dynamics., " Nonlinear Processes Geophys. 7, 59-85 (2000).
6. Dieci, L. and Eirola, T., " On smooth decompositions of matrices., " SIAM J. Matrix Anal. Appl. 20, 800-819 (1999).
7. Green, M. A., Rowley, C. W., and Haller, G., " Detection of Lagrangian coherent structures in three-dimensional turbulence., " J. Fluid Mech. 572, 111-120 (2007).
8. Guckenheimer, J. and Holmes, P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York, 1986).
9. Haller, G., " Distinguished material surfaces and coherent structures in three-dimensional fluid flows., " Physica D 149, 248-277 (2001).
10. Haller, G., " Finding finite-time invariant manifolds in two-dimensional velocity fields., " Chaos 10, 99-108 (2000).
11. Haller, G., " Lagrangian coherent structures from approximate velocity data., " Phys. Fluids 14, 1851-1861 (2002).
12. Haller, G. and Poje, A. C., " Finite time transport in aperiodic flows., " Physica D 119, 352-380 (1998).
13. Hirsch, M. W. and Smale, S., Differential Equations, Dynamical Systems and Linear Algebra (Academic, New York, 1974).
14. Homburg, A. J., De Vilder, R., and Sands, D., " Computing invariant sets., " Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, 497-504 (2003).
15. Inanc, T., Shadden, S. C., and Marsden, J., Proceedings of the 2005 American Control Conference, Portland, OR, 2005, pp. 674-679 (http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1470035).
16. Jones, C. K. R. T. and Winkler, S., Handbook of Dynamical Systems, edited by, B. Fiedler, (Elsevier, Amsterdam, 2002), Vol. 2, pp. 55-92.
17. Joseph, B. and Legras, B., " Relation between kinematic boundaries, stirring, and barriers for the Antarctic polar vortex., " J. Atmos. Sci. 59, 1198-1212 (2002).
18. Kato, T., Perturbation Theory for Linear Operators (Classics in Mathematics) (Springer-Verlag, Berlin, 1995).
19. Koh, T. Y. and Legras, B., " Hyperbolic lines and the stratospheric polar vortex., " Chaos 12, 382-394 (2002).
20. Krauskopf, B., Osinga, H. M., Doedel, E. J., Henderson, M. E., Guckenheimer, J. M., Vladimirsky, A., Dellnitz, M., and Junge, O., " A survey of methods for computing (un)stable manifolds of vector fields., " Int. J. Bifurcation Chaos Appl. Sci. Eng. 15, 763-791 (2005).
21. Lekien, F., Berman, S., and Fiorelli, E., Multivariate Gaussian noise generator, 2005a (http://www.lekien.com/~francois/software/rndfieldgen).
22. Lekien, F., Coulliette, C., Bank, R., and Marsden, J., " Open-boundary modal analysis: Interpolation, extrapolation, and filtering., " J. Geophys. Res., [Oceans] 109, C12004 (2004).
23. Lekien, F., Coulliette, C., Mariano, A. J., Ryan, E. H., Shay, L. K., Haller, G., and Marsden, J., " Pollution release tied to invariant manifolds: A case study for the coast of Florida., " Physica D 210, 1-20 (2005b).
24. Lekien, F. and Leonard, N. E., " Dynamically consistent Lagrangian coherent structures., " Experimental Chaos: 8th Experimental Chaos Conference, AIP Conf. Proc. 742, pp. 132-139 (2004).
25. Lekien, F. and Marsden, J., " Tricubic interpolation in three dimensions., " Int. J. Numer. Methods Eng. 63, 455-471 (2005).
26. Mancho, A. M., Small, D., and Wiggins, S., " Computation of hyperbolic trajectories and their stable and unstable manifolds for oceanographic flows represented as data sets., " Nonlinear Processes Geophys. 11, 17-33 (2004).
27. Ottino, J. M., The Kinematics of Mixing: Stretching, Chaos, and Transport (Cambridge University Press, New York, 1989).
28. Padberg, K., Ph.D. thesis, University of Paderborn, 2005.
29. Pierrehumbert, R. T., " Large-scale horizontal mixing in planetary-atmospheres., " Phys. Fluids A 3, 1250-1260 (1991).
30. Pierrehumbert, R. T. and Yang, H., " Global chaotic mixing on isentropic surfaces., " J. Atmos. Sci. 50, 2462-2480 (1993).
31. Rom-Kedar, V., " Transport rates of a class of 2-dimensional maps and flows., " Physica D 43, 229-268 (1990).
32. Rom-Kedar, V., Leonard, A., and Wiggins, S., " An analytical study of transport, mixing and chaos in an unsteady vortical flow., " J. Fluid Mech. 214, 347-394 (1990).
33. Rom-Kedar, V. and Wiggins, S., " Transport in 2-dimensional maps: Concepts, examples, and a comparison of the theory of Rom-Kedar and Wiggins with the Markov model of Mackay, Meiss, Ott, and Percival., " Physica D 51, 248-266 (1991).
34. Shadden, S. C., Dabiri, J. O., and Marsden, J. E., " Lagrangian analysis of fluid transport in empirical vortex rings., " Phys. Fluids 18, 047105 (2006).
35. Shadden, S. C., Lekien, F., and Marsden, J. E., " Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows., " Physica D 212, 271-304 (2005).
36. Smale, S., in Differential and Combinatorial Topology, edited by, S. S. Cairns, (Princeton University Press, Princeton, NJ, 1965).
37. Solomon, T. H. and Gollub, J. P., " Passive transport in steady Rayleigh-B́nard convection., " Phys. Fluids 31, 1372-1379 (1988).
38. Solomon, T. H. and Gollub, J. P., " Sheared boundary-layers in turbulent Rayleigh-B́nard convection., " Phys. Rev. Lett. 64, 2382-2385 (1990).
39. Solomon, T. H. and Gollub, J. P., " Thermal-boundary layers and heat-flux in turbulent convection: The role of recirculating flows., " Phys. Rev. A 43, 6683-6693 (1991).
40. Toner, M. and Poje, A. C., " Lagrangian velocity statistics of directed launch strategies in a Gulf of Mexico model., " Phys. Rev. A 43, 6683-6693 (2004).
41. Voth, G. A., Haller, G., and Gollub, J. P., " Experimental measurements of stretching fields in fluid mixing., " Phys. Rev. Lett. 88, 254501 (2002).
42. Wysham, D. B. and Meiss, J. D., " Iterative techniques for computing the linearized manifolds of quasiperiodic tori., " Chaos 16, 023129 (2006).