Superpersistent chaotic transients in physical space: Advective dynamics of inertial particles in open chaotic flows under noise

Physical Review Letters

Volumn 91, Issue 22, 2003, Pages

  Do, Younghae ^a   Lai, Ying Cheng ^a  

^a ARIZONA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHANNEL FLOW; CHAOS THEORY; COMPUTER SIMULATION; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; PERTURBATION TECHNIQUES; RANDOM PROCESSES; REYNOLDS NUMBER; VELOCITY; VISCOSITY OF LIQUIDS; VORTEX FLOW; WAKES;

CHAOTIC FLOW; NOISE-INDUCED SUPERPERSISTENT TRANSIENT; STOCHASTIC DIFFERENTIAL EQUATION; SUPERPERSISTENT CHAOTIC TRANSIENT;

FLUID MECHANICS;

EID: 0347949963     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.91.224101     Document Type: Article

References (22)

1. C. Grebogi, E. Ott, and J.A. Yorke, Phys. Rev. Lett. 50, 935 (1983); 10.1103/PhysRevLett.50.935
2. C. GrebogiE. OttJ.A. YorkeErgodic Theory Dynam. Syst. 5, 341 (1985).
3. Y.-C. Lai, C. Grebogi, J.A. Yorke, and S.C. Venkataramani, Phys. Rev. Lett. 77, 55 (1996).10.1103/PhysRevLett.77.55
4. J.P. Crutchfield and K. Kaneko, Phys. Rev. Lett. 60, 2715 (1988).10.1103/PhysRevLett.60.2715
5. V. Andrade, R. Davidchack, and Y.-C. Lai, Phys. Rev. EPLEEE8 61, 3230 (2000).10.1103/PhysRevE.61.3230
6. L. Zhu, A. Raghu, and Y.-C. Lai, Phys. Rev. Lett. 86, 4017 (2001).10.1103/PhysRevLett.86.4017
7. H. Aref, J. Fluid Mech.JFLSA7 143, 1 (1984).
8. J.M. Ottino, The Kinematics of Mixing: Stretching, Chaos and Transport (Cambridge University Press, Cambridge, 1989).
9. M.R. Maxey and J.J. Riley, Phys. Fluids 26, 883 (1983).10.1063/1.864230
10. Attractors for inertial particles in fluid flows have been known. See, for example, J. Rubin, C.K.R.T. Jones, and M. Maxey, J. Nonlinear Sci. 5, 337 (1995);
11. T.J. Burns, R.W. Davis, and E.F. Moore, J. Fluid Mech.JFLSA7 384, 1 (1999).10.1017/S002211209900419X
12. I.J. Benczik, Z. Toroczkai, and T. Tél, Phys. Rev. Lett. 89, 164501 (2002).10.1103/PhysRevLett.89.164501
13. There are numerous results in the mathematics literature concerning the persistence of attractors under noise. See, for example, D. Ruelle, Lect. Notes Math.LNMAA2 1007, 663 (1983). In this paper we are interested in what can happen physically to a chaotic attractor when it can no longer persist under random perturbations.
14. J.M. Österlund, A.V. Johansson, H.M. Nagib, and M.H. Hites, Phys. FluidsPHFLE6 12, 1 (2000); 10.1063/1.870250
15. J.M. Österlund, A.V. Johansson, and H.M. Nagib, Phys. FluidsPHFLE6 12, 2360 (2000).10.1063/1.1287660
16. G.I. Barenblatt, A.J. Chorin, and V.M. Prostokishin, Phys. FluidsPHFLE6 12, 2159 (2000).10.1063/1.1287613
17. J.C. Sommerer, H.-C. Ku, and H.E. Gilreath, Phys. Rev. Lett. 77, 5055 (1996).10.1103/PhysRevLett.77.5055
18. C. Jung, T. Tél, and E. Ziemniak, Chaos 3, 555 (1993).10.1063/1.165960
19. P.E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations (Springer-Verlag, Berlin, 1992).
20. A.E. Motter and Y.-C. Lai, Phys. Rev. EPLEEE8 65, 015205 (2002).10.1103/PhysRevE.65.015205
21. C.W. Gardiner, Handbook of Stochastic Methods (Springer-Verlag, New York, 1997).
22. T. Shinbrot, M.M. Alvarez, J.M. Zalc, and F.J. Muzzio, Phys. Rev. Lett. 86, 1207 (2001).10.1103/PhysRevLett.86.1207