Finite-size effects on open chaotic advection

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 73, Issue 2, 2006, Pages

  Vilela, Rafael D ^a   De Moura, Alessandro P S ^a   Grebogi, Celso ^b  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b UNIVERSITY OF ABERDEEN   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BUOYANCY; DYNAMICS; FLOW OF FLUIDS; PARAMETER ESTIMATION;

CHAOTIC FLOWS; CHAOTIC SADDLE; SPHERICAL PARTICLES; STOKES PARAMETER;

CHAOS THEORY;

EID: 33344479118     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.73.026302     Document Type: Article

References (27)

1. H. Aref, J. Fluid Mech. JFLSA7 0022-1120 143, 1 (1984).
2. M. Horner, G. Metcalfe, S. Wiggins, and J. M. Ottino, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112001006917 452, 199 (2002).
3. E. R. Abraham and M. M. Bowen, Chaos CHAOEH 1054-1500 10.1063/1.1481615 12, 373 (2002).
4. T.-Y. Koh and B. Legras, Chaos CHAOEH 1054-1500 10.1063/1.1480442 12, 382 (2002).
5. H. Kantz and P. Grassberger, Physica D PDNPDT 0167-2789 10.1016/0167-2789(85)90135-6 17, 75 (1985);
6. G.-H. Hsu, E. Ott, and C. Grebogi, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(88)90102-8 127, 199 (1988);
7. T. Tél, in Directions in Chaos, edited by, Hao Bai-Lin, (World Scientific, Singapore, 1990), Vol. 3, pp. 149-221.
8. G. Károlyi and T. Tél, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(97)00063-X 290, 125 (1997).
9. Finite-size effects are important not only for chaotic advection, but also in the turbulent regime. See, for instance, E. Balkovsky, G. Falkovich, and A. Fouxon, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.2790 86, 2790 (2001);
10. J. Bec, Phys. Fluids PHFLE6 1070-6631 10.1063/1.1612500 15, L81 (2003);
11. R. Reigada, F. Sagués, and J. M. Sancho, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.026307 64, 026307 (2001).
12. A. Babiano, J. H. E. Cartwright, O. Piro, and A. Provenzale, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.5764 84, 5764 (2000).
13. For the case of open chaotic advection of bubbles, see I. J. Benczik, Z. Toroczkai, and T. Tél, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.164501 89, 164501 (2002);
14. I. J. Benczik, Z. Toroczkai, and T. Tél, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.036303 67, 036303 (2003).
15. Z. Toroczkai, G. Károlyi, Pentek, T. Tél, and C. Grebogi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.500 80, 500 (1998);
16. G. Károlyi, Pentek, Z. Toroczkai, T. Tél, and C. Grebogi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.59.5468 59, 5468 (1999);
17. T. Tél, T. Nishikawa, A. E. Motter, C. Grebogi, and Z. Toroczkai, Chaos CHAOEH 1054-1500 10.1063/1.1626391 14, 72 (2004).
18. There are situations where finite-sizeness leads to fractality. In this context, reactions were studied in the following papers: T. Nishikawa, Z. Toroczkai, and C. Grebogi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.038301 87, 038301 (2001);
19. T. Nishikawa, Z. Toroczkai, C. Grebogi, and T. Tél, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.026216 65, 026216 (2002).
20. M. R. Maxey and J. Riley, Phys. Fluids PFLDAS 0031-9171 10.1063/1.864230 26, 883 (1983).
21. H. Aref, S. W. Jones, S. Mofina, and I. Zawadzki, Physica D PDNPDT 0167-2789 10.1016/0167-2789(89)90147-4 37, 423 (1989).
22. J. H. E. Cartwright, M. O. Magnasco, and O. Piro, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.045203 65, 045203 (R) (2002).
23. J. H. E. Cartwright, M. O. Magnasco, and O. Piro, Chaos CHAOEH 1054-1500 10.1063/1.1480441 12, 489 (2002);
24. J. H. E. Cartwright, M. O. Magnasco, O. Piro, and I. Tuval, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.264501 89, 264501 (2002).
25. A. E. Motter, Y.-C. Lai, and C. Grebogi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.056307 68, 056307 (2003).
26. For the effects of projecting fractal measures of n -dimensional dynamical systems onto subspaces of Rn, see B. R. Hunt and V. Y. Kaloshin, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/10/5/002 10, 1031 (1997), and references therein.
27. J. Jacobs, E. Ott, and C. Grebogi, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(97)00037-7 108, 1 (1997).