Summary
This paper focuses on a method proposed for diagnosing the presence of chaotic behaviour in physical systems directly from experimental time series. The procedure relies on the concept of short-term predictability of chaotic motions. From a statistical point of view, it is completely non-parametric and works whatever the distribution function of the data points may be. The method is robust to observational noise, and can distinguish merely linear stochastic processes,e.g., fractional Brownian motion, from truly non-linear deterministic systems. The capability of the method has been evaluated by applying it to intermittent gas-liquid flows in a horizontal pipe. A weak sign of deterministic chaos has been diagnosed in plug and slug flow regimes. Our analysis fully confirms the Ruelle-Takens view about the complexity in hydrodynamical systems. However, the weak sign of chaos is in contrast with the Lorenz type systems (strong chaos) and supports the idea of Kolmogorov about irregular motion in hydrodynamical systems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Packard N. H., Cructchfield J. P., Farmer J. D. andShaw R. S.,Phys. Rev. Lett.,45 (1980) 712.
Takens F.,Dynamical Systems and Turbulence, edited byD. A. Rand andL. S. Young (Springer-Verlag, Berlin) 1981.
Grassberger P. andProcaccia I.,Physica D,9 (1983) 189.
Mayer-Kress G. (Editor),Dimension and Entropies in Chaotic Systems (Springer-Verlag, New York, N.Y.) 1985.
Fowler A. C. andKember G.,Phys. Lett. A,175 (1993) 402.
Malinetski G. G., Potapov A. B., Rakhmanov A. I. andRodichev E. B.,Phys. Lett. A,179 (1993) 15.
Mandebrolt B. B.,The Fractal Geometry of Nature (Freeman, San Francisco) 1982.
Voss R. F.,Physica D,38 (1989) 362.
Serio C.,Nuovo Cimento B,107 (1992) 681.
Serio C.,Fractal 93: Fractals in the Natural and Applied Sciences, edited byM. M. Novak (Elsevier Science B. V. (North-Holland)) 1994, pp. 371–383.
Serio C.,Europhys. Lett.,27 (1994) 103.
Cuomo V., Serio C., Crisciani V. andFerraro A.,Tellus A,46 (1994) 299.
Farmer J. D. andSidorowich J. J.,Phys. Rev. Lett.,59 (1987) 845.
Sugihara G. andMay R. M.,Nature,344 (1990) 734.
Casdagli M.,J. R. Statist. Soc. B,54 (1991) 303.
Kennel M. B. andIsabelle S.,Phys. Rev. A,6 (1992) 3111.
Mao Z. S. andDukler A. E.,Int. J. Multiphase Flow,19 (1993) 377.
Hewitt G. F. andJayanti S.,Int. J. Multiphase Flow,19 (1993) 527.
Ruder Z. andHanratty T. J.,Int. J. Multiphase Flow,16 (1990) 233.
Drahoš J., Ebner L., Bradka F., Fialova M. andČermak J.,Proceedings of the International Conference on the Mechanics of Two-Phase Flows, National Taiwan University, Taipei 1989 (National Taiwan University, Taipei) 1989, pp. 351–355.
Box G. E. P. andJenkins G. M.,Time Series Analysis (Holden-Day, S. Francisco) 1976.
Ventsel A. D.,Teoria dei processi stocastici (Editori Riuniti, Edizioni MIR, Roma) 1983.
Bartlett M. S.,An Introduction to Stochastic Processes, with Special Reference to Methods and Applications (Cambridge University Press, Cambridge) 1955.
Drahoš J., Čermak J., Selucký K. andEbner L.,Chem. Eng. Process.,22 (1987) 45.
Nydal O. J., Pintus S. andAndreussi P.,Int. J. Multiphase Flow,18 (1992) 439.
Ruelle D. andTakens F.,Commun. Math. Phys.,20 (1971) 167.
Lorenz E. N.,J. Atmosph. Sci.,20 (1963) 130.
Arnol’d V. I.,Kolmogorov’s hydrodynamic attractors, in Turbulence and Stochastic Processes, edited byJ. C. R. Hunt,O. M. Phillips andD. Williams (The Royal Society, London) 1991, pp. 19–22.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Drahoš, J., Punčochář, M., Nino, E. et al. Finding chaos in experimental time series: The case of two-phase flow. Il Nuovo Cimento B 110, 1415–1428 (1995). https://doi.org/10.1007/BF02849840
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02849840