Abstract
It is shown that pipe-flow turbulence consists of transients. The “fractal” dimensions of the dynamical process are thus all zero. Nevertheless, this is compatible with Grassberger-Procaccia analyses suggesting the existence of a high-dimensional strange attractor. The usefulness of the Grassberger-Procaccia method to detect the aging of transients is demonstrated.
References
P. Grassberger, Information content and predictablity of lumped and distributed dynamical systems, inProceedings of the Conference on Chaos and Related Non-linear Phenomena, Kiryat Anavim, December 1986, preprint University of Wuppertal WU V 87-8.
H. G. Schuster,Deterministic Chaos (VCH Verlagsgesellschaft, Weinheim, 1988), Chapter 5.
P. Grassberger and I. Procaccia,Physica 9D:189 (1983).
H. L. Swinney and J. P. Gollup, eds.,Hydrodynamic Instabilities and the Transition to Turbulence (Springer, New York, 1985).
M. Nishioka, S. Ida, and Y. Ichikawa,J. Fluid Mech. 72:731 (1975).
L. Boberg and U. Brosa,Z. Naturforsch. 43a:697 (1988).
J. Guckenheimer and G. Buzyna,Phys. Rev. Lett. 51:1438 (1983).
B. Malraison, P. Atten, P. Berge, and M. Dubois,J. Phys. Lett. (Paris)44:L-897 (1983).
M. Giglio, S. Musazzi, and U. Perini,Phys. Rev. Lett. 53:2402 (1984).
A. Brandstäter, J. Swift, H. L. Swinney, A. Wolf, J. D. Framer, E. Jen, and P. J. Crutchfield,Phys. Rev. Lett. 51:1442 (1983).
A. Brandstäter, H. L. Swinney, and G. T. Chapman, inDimensions and Entropies in Chaotic Systems, G. Mayer-Kress, ed. (Springer, Berlin, 1986), p. 150.
M. Sieber,Phys. Lett. A 122:467 (1987).
C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang,Spectral Methods in Fluid Mechanics (Springer, New York, 1988).
O. Reynolds,Phil. Trans. 174:935 (1883).
I. J. Wygnanski and F. H. Champagne,J. Fluid Mech. 59:281 (1973).
J. Meseth,Arch. Mech. 26:391 (1974).
F. Takens, inDynamical Systems and Turbulence, D. A. Rand and L. S. Young, eds. (Springer, Berlin, 1981), p. 366.
O. E. Lanford, inHydrodynamic Instabilities and the Transition to Turbulence, H. L. Swinney and J. P. Gollup, eds. (Springer, New York, 1985).
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Brosa, U. Turbulence without strange attractor. J Stat Phys 55, 1303–1312 (1989). https://doi.org/10.1007/BF01041090
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DOI: https://doi.org/10.1007/BF01041090