Quantifying spatiotemporal chaos in Rayleigh-Bénard convection

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

Volumn 85, Issue 4, 2012, Pages

  Karimi, A ^a   Paul, M R ^a  

^a Virginia Polytechnic Institute and State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOTIC DYNAMICS; CYLINDRICAL DOMAIN; FLUID CONVECTION; HIGH-DIMENSIONAL; HIGH-DIMENSIONAL CHAOS; LYAPUNOV EXPONENT; LYAPUNOV VECTORS; PARALLEL NUMERICAL SIMULATION; PATTERN DYNAMICS; SPATIOTEMPORAL CHAOS; STRANGE ATTRACTORS; SYSTEM SIZE; TIME DYNAMIC; TOPOLOGICAL FEATURES;

CHAOS THEORY; DIFFERENTIAL EQUATIONS; DYNAMICS; FRACTAL DIMENSION; LYAPUNOV FUNCTIONS;

LYAPUNOV METHODS;

EID: 84859526692     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.85.046201     Document Type: Article

References (40)

1. M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.65.851 65, 851 (1993).
2. E. N. Lorenz, J. Atmos. Sci. JAHSAK 0022-4928 10.1175/1520-0469(1963) 020<0130:DNF>2.0.CO;2 20, 130 (1963).
3. P. Holmes, J. L. Lumley, and G. Berkooz, Turbulence, Coherent Structures, Dynamical Systems, and Symmetry (Cambridge University Press, Cambridge, 1996).
4. C. R. Nugent, W. M. Quarles, and T. H. Solomon, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.218301 93, 218301 (2004). (Pubitemid 40011422)
5. M. Bar and M. Eiswirth, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.48.R1635 48, R1635 (1993).
6. H. D. I. Abarbanel, Analysis of Observed Chaotic Data (Springer, New York, 1996).
7. J. D. Farmer, E. Ott, and J. A. Yorke, Physica D PDNPDT 0167-2789 10.1016/0167-2789(83)90125-2 7, 153 (1983).
8. A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, Physica D PDNPDT 0167-2789 10.1016/0167-2789(85)90011-9 16, 285 (1985).
9. E. Ott, Chaos in Dynamical Systems (Cambridge University Press, New York, 1993).
10. E. Bodenschatz, W. Pesch, and G. Ahlers, Annu. Rev. Fluid Mech. ARVFA3 0066-4189 10.1146/annurev.fluid.32.1.709 32, 709 (2000). (Pubitemid 36145007)
11. D. A. Egolf, I. V. Melnikov, W. Pesch, and R. E. Ecke, Nature (London) NATUAS 0028-0836 10.1038/35008013 404, 733 (2000). (Pubitemid 30212394)
12. S. W. Morris, E. Bodenschatz, D. S. Cannell, and G. Ahlers, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71.2026 71, 2026 (1993).
13. J. D. Scheel and M. C. Cross, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.74.066301 74, 066301 (2006). (Pubitemid 44866721)
14. M. R. Paul, M. I. Einarsson, P. F. Fischer, and M. C. Cross, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.75.045203 75, 045203 (2007). (Pubitemid 46677027)
15. A. Jayaraman, J. D. Scheel, H. S. Greenside, and P. F. Fischer, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.74.016209 74, 016209 (2006). (Pubitemid 44147265)
16. G. Ahlers, S. Grossmann, and D. Lohse, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.81.503 81, 503 (2009).
17. K.-H. Chiam, M. R. Paul, M. C. Cross, and H. S. Greenside, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.67.056206 67, 056206 (2003).
18. H. S. Greenside, M. C. Cross, and W. M. Coughran Jr., Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.60.2269 60, 2269 (1988).
19. V. Croquette, P. Le Gal, and A. Pocheau, Phys. Scr. PHSTBO 0031-8949 10.1088/0031-8949/1986/T13/022 T13, 135 (1986).
20. A. Pocheau, V. Croquette, P. Le Gal, and C. Poitou, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/3/8/009 3, 915 (1987).
21. A. C. Newell, T. Passot, and M. Souli, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.64.2378 64, 2378 (1990).
22. A. C. Newell, T. Passot, and M. Souli, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112090003238 220, 187 (1990).
23. M. C. Cross and A. C. Newell, Physica D PDNPDT 0167-2789 10.1016/0167-2789(84)90181-7 10, 299 (1984). (Pubitemid 14601515)
24. G. Ahlers, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.33.1185 33, 1185 (1974).
25. M. R. Paul, M. C. Cross, P. F. Fischer, and H. S. Greenside, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.154501 87, 154501 (2001).
26. M. R. Paul, K.-H. Chiam, M. C. Cross, P. F. Fischer, and H. S. Greenside, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(03)00216-1 184, 114 (2003).
27. A. Duggleby and M. R. Paul, Comput. Fluids CPFLBI 0045-7930 10.1016/j.compfluid.2010.06.007 39, 1704 (2010).
28. P. F. Fischer and A. T. Patera, Annu. Rev. Fluid Mech. ARVFA3 0066-4189 10.1146/annurev.fl.26.010194.002411 26, 483 (1994).
29. P. F. Fischer, J. Comput. Phys. JCTPAH 0021-9991 10.1006/jcph.1997.5651 133, 84 (1997). (Pubitemid 127170079)
30. D. Ruelle, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01218566 87, 287 (1982).
31. M. P. Fishman and D. A. Egolf, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.054103 96, 054103 (2006). (Pubitemid 43270949)
32. A. Karimi and M. R. Paul, Chaos CHAOEH 1054-1500 10.1063/1.3496397 20, 043105 (2010).
33. C. S. O'Hern, D. A. Egolf, and H. S. Greenside, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.53.3374 53, 3374 (1996).
34. S. Tajima and H. S. Greenside, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.66.017205 66, 017205 (2002). (Pubitemid 40599122)
35. L. Sirovich and A. E. Deane, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S002211209100109X 222, 251 (1991).
36. G. A. Voth, G. Haller, and J. P. Gollub, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.254501 88, 254501 (2002).
37. G. Haller, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(00)00199-8 149, 248 (2001). (Pubitemid 32875760)
38. H. Kurtuldu, K. Mischaikow, and M. F. Schatz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.107.034503 107, 034503 (2011).
39. F. Ginelli, P. Poggi, A. Turchi, H. Chatè, R. Livi, and A. Politi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.130601 99, 130601 (2007). (Pubitemid 47480005)
40. D. Pazó, I. G. Szendro, J. M. López, and M. A. Rodríguez, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.78.016209 78, 016209 (2008).