Statistics of stretching fields in experimental fluid flows exhibiting chaotic advection

Journal of Statistical Physics

Volumn 121, Issue 5-6, 2005, Pages 805-822

  Arratia, P E ^a   Gollub, J P ^a,b  

^a HAVERFORD COLLEGE   (United States)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Chaotic advection; Mixing in fluids; Stretching statistics

Indexed keywords

EID: 29044436776     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-005-8664-8     Document Type: Article

References (23)

1. R. T. Pierrehumbert, Large-scale horizontal mixing in planetary atmospheres, Phys. Fluids A 3:1250-1260 (1991).
2. T. Akira, R. A. Rogers, P. E. Hydon, and J. P. Butler, Chaotic mixing deep in the lung, Proc. Natl. Acad. Sci. 99:10173-10178 (2002).
3. G. K. Batchelor, The effect of homogeneous turbulence on material lines and surfaces, Proc. R Soc. London Ser. A 213:349-368 (1952).
4. H. Aref, Stirring by chaotic advection, J. Fluid Mech. 143:1-21 (1984).
5. J. M. Ottino, F. J. Muzzio, M. Tjahjadi, J. G. Franjione, S. C. Jana, and H. A. Kusch, Chaos, symmetry, and self-similarity: Exploiting order and disorder in mixing processes, Science 257:754-760 (1992).
6. X. Z. Tang and A. H. Boozer, Finite time Lyapunov exponent and advection-diffusion equation, Physica D 95:283-305 (1996).
7. G. A. Voth, G. Haller, and J. P. Gollub, Experimental measurements of stretching fields in fluid mixing, Phys. Rev. Lett. 88:254501 (2002).
8. J. M. Ottino, The Kinematics of Mixing: Stretching, Chaos, and Transport. (Cambridge University Press, 1989).
9. G. A. Voth, T. C. Saint, G. Dobler, and J. P. Gollub, Mixing rates and symmetry breaking in two-dimensional chaotic flow, Phys. Fluids 15:2560-2566 (2003).
10. E. Ott and T. M. Antonsen, Fractal measures of passively convected vector fields and scalar gradients in chaotic fluid flows, Phys. Rev. A 39:3660-3671 (1989).
11. F. Varosi, T. M. Antonsen, and E. Ott, The spectrum of fractal dimensions of passively convected scalar gradients in chaotic fluid flows, Phys. Fluids A 3:1017-1028 (1991).
12. F. J. Muzzio, P. D. Swanson, and J. M. Ottino, The statistics of stretching and stirring in chaotic flows, Phys. Fluids 3:822-834 (1991).
13. M. A. Sepulveda, R. Badii, and E. Pollak, Spectral analysis of conservative dynamical systems, Phys. Rev. Lett. 63:1226-1229 (1989).
14. R. T. Pierrehumbert, Decay of passive scalars under the action of single scale smooth velocity fields in bounded two-dimensional domains: From non-self-similar probability distribution functions to self-similar eigenmodes, Phys. Rev. E. 66:056302 (2002).
15. E. R. Abraham and M. M. Bowen, Chaotic stirring by a mesoscale surface ocean-flow, Chaos 12:373-381 (2002).
16. A. Prasad and R. Ramaswamy, Characteristic distributions of finite-time Lyapunov exponents, Phys. Rev. E. 60:2761-2766 (1999).
17. V. I. Oseledec, A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems, Trans. Moscow. Math. Soc. 19:197-231 (1968).
18. A. Androver and M. Giona, Long-range correlation properties of area-preserving chaotic systems, Physica A 253:143-153 (1998).
19. D. Beigie, A. Leonard, and S. Wiggins, A global study of enhanced stretching and diffusion in chaotic tangles, Phys. Fluids A 3:1039-1050 (1991).
20. F. J. Muzzio, C. Meneveau, P. D. Swanson, and J. M. Ottino, Scaling and multifractal properties of mixing in chaotic flows, Phys. Fluids A 4:1439-1456 (1992).
21. J. G. Franjione and J. M. Ottino, Symmetry concepts for the geometric analysis of mixing flows, Phil. Trans. R. Soc. Land. A 338:301-323 (1992).
22. R. S. Ellis, Entropy, Large Deviations, and Statistical Mechanics (Springer-Verlag, New York, 1985).
23. T. Horita, H. Hata, and H. Mori, Long-time correlations and expansion-rate spectra of chaos in Hamiltonian systems, Prog. Theor. Phys. 83:1065-1070 (1990).