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Morphological structures produced by mixing in chaotic flows

Nature volume 333, pages 419–425 (1988)Cite this article

Abstract

Fluid mixing is poorly understood. However, some of the main concepts can be captured by both computational and experimental studies of two-dimensional flows. The identification of coherent structures and how they change with variations of the governing parameters gives insight into the behaviour of chaotic systems and can serve as a model for a variety of problems found in nature.

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References

  1. Birkhoff, G. D. Acta Math. 43, 1–119 (1920).

    Article  Google Scholar 

  2. Moser, J. Stable and Random Motions in Dynamical Systems (Princeton University Press, 1973).

    MATH  Google Scholar 

  3. Khakhar, D. V., Rising, H. & Ottino, J. M. J. Fluid Mech. 172, 419–451 (1986).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  4. Chien, W.-L., Rising, H. & Ottino, J. M. J. Fluid Mech. 170, 355–377 (1986).

    Article  ADS  CAS  Google Scholar 

  5. Spencer, R. S. & Wiley, R. M. J. Coll. Sci. 6, 133–145 (1951).

    Article  CAS  Google Scholar 

  6. Arnold, V. I. Mathematical Methods of Classical Mechanics (Springer, New York, 1980).

    Google Scholar 

  7. Truesdell, C. & Toupin, R. A. in Handbuch der Physik vol. III/1 (ed. Flügge, S.) 226–793 (Springer, Berlin, 1960).

    Google Scholar 

  8. Aref, H. J. Fluid Mech. 143, 1–21 (1984).

    Article  ADS  MathSciNet  Google Scholar 

  9. Guckenheimer, J. & Holmes, P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vectors Fields (Springer, New York, 1983).

    Book  Google Scholar 

  10. Lichtenberg, A. J. & Liebermann, M. A. Regular and Stochastic Motion (Springer, New York, 1982).

    Google Scholar 

  11. Helleman, R. H. G. in Fundamental Problems in Statistical Mechanics (ed. Cohen, E. G. D.) 165–275 (North-Holland, Amsterdam, 1980).

    Google Scholar 

  12. Devaney, R. L. An Introduction to Chaotic Dynamical Systems (Benjamin/Cummings, Menlo Park, 1986).

    MATH  Google Scholar 

  13. Batchelor, G. K. An Introduction to Fluid Mechanics (Cambridge University Press, London, 1967).

    MATH  Google Scholar 

  14. Wannier, G. L. Q. Appl. Math. VIII, 1–32 (1950).

    Article  MathSciNet  Google Scholar 

  15. Chaiken, J., Chevray, R., Tabor, M. & Tan, Q. M. Proc. R. Soc. A408, 165–174 (1986).

    Article  ADS  CAS  Google Scholar 

  16. Aref, H. & Balachandar, S. Phys. Fluids 29, 3515–3521 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  17. Newhouse, S. E. Institut des Hautes Études Scientifiques. Publications Mathématiques 50, 101–151 (1979).

    Article  Google Scholar 

  18. Abraham, R. H. & Shaw, C. D. Dynamics-The Geometry of Behavior Pt 3, Fig. 6, 5.2.11 (Aerial Press, Santa Cruz, 1985).

    Google Scholar 

  19. Rising, H. thesis, Univ. Massachusetts (1988).

  20. Franjione, J. G. & Ottino, J. M. Phys. Fluids 30, 3641–3643 (1987).

    Article  ADS  Google Scholar 

  21. MacKay, R. S. thesis, Princeton Univ. (1982).

  22. Takens, F. Math. Ann. 188, 304–312 (1970).

    Article  MathSciNet  Google Scholar 

  23. Greene, J., J. math. Phys. 20, 1183–1201 (1979).

    Article  ADS  Google Scholar 

  24. Mather, J. N. Institut des Hautes Études Scientifiques. Publications Mathématiques 63, 153–204 (1986).

    Article  Google Scholar 

  25. Allègre, C. J. & Turcotte, D. L. Science 323, 123–127 (1986).

    Google Scholar 

  26. Hoffman, N. R. A. & MacKenzie, D. P. Geophys. J. R. astr. Soc. 82, 163–206 (1985).

    Article  ADS  CAS  Google Scholar 

  27. Veronis, G. Adv. appl. Mech. 13, 1–92 (1973).

    Article  Google Scholar 

  28. Rhines, P. B. A. Rev. Fluid Mech. 18, 433–497 (1983).

    Article  ADS  Google Scholar 

  29. Macagno, E. O. & Cristensen, J. A. Revs. Fluid Mech. 12, 139–158 (1980).

    Article  ADS  Google Scholar 

  30. Ottino, J. M. & Chella, R. Polym. Eng. Sci. 23, 357–379 (1983).

    Article  CAS  Google Scholar 

  31. Khakhar, D. V., Franjione, J. G. & Ottino, J. M. Chem. Engng. Sci. 42, 2909–2926 (1987).

    Article  CAS  Google Scholar 

  32. Sobey, I. C. Chem. Engng Sci. 40, 2129–2134 (1985).

    Article  Google Scholar 

  33. Roshko, A. Am. Inst. Aeron. Astron. 14, 1349–1357 (1976).

    Article  Google Scholar 

  34. Gibbs, J. W. The Collected Works of J. W. Gibbs Vol. II, Pt 1, 141–156 (Yale University Press, New Haven, 1948).

    Google Scholar 

  35. Devaney, R. L. Science 235, 342–345 (1987).

    Article  ADS  MathSciNet  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts, 01003, USA

    J. M. Ottino & C. W. Leong

  2. Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts, 01003, USA

    H. Rising

  3. Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts, 01003, USA

    P. D. Swanson

Authors
  1. J. M. Ottino
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  2. C. W. Leong
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  3. H. Rising
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  4. P. D. Swanson
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Ottino, J., Leong, C., Rising, H. et al. Morphological structures produced by mixing in chaotic flows. Nature 333, 419–425 (1988). https://doi.org/10.1038/333419a0

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