Abstract
Various patterns arise in hydrodynamic systems during the approach to turbulence. Under a wide range of conditions, these patterns have a symmetry typical of crystals or quasicrystals. Pattern elements (cells) are divided by thin layers which form a web, within which the streamlines are chaotic. The web represents channels along which particle transport occurs in lattice structures that are associated with dynamical chaos.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Weyl, H. Symmetry (Princeton Univ. Press, 1952).
Chernikov, A. A., Sagdeev, R. Z., Usikov, D. A., Zakharov, M. Yu. & Zaslavsky, G. M. Nature 326, 559–563 (1987).
Gollub, J. P. & Benson, S. V. J. Fluid Mech. 100, 449–470 (1980).
Ott, E. Rev. mod. Phys. 53, 655–671 (1981).
Eckmann, J. P. Rev. mod. Phys. 53, 643–654 (1981).
Wesfreid, J. E. & Zaleski, S. in Cellular Structures in Instabilities 1–32 (eds Wesfreid, J. E. & Zaleski, S.) (Springer, Berlin, 1984).
Monin, A. S. Usp. Fiz. Nauk 150, 61–105 (1986).
Carlson, D. R., Windnall S. E. & Peeters, M. F. J. Fluid Mech. 121, 407–505 (1982).
Orszag, S. A. & Kells, L. S. J. Fluid Mech. 96, 159–205 (1980).
Orszag, S. A. & Patera, A. T. J. Fluid Mech. 128, 347–385 (1983).
Arnold, V. I. & Korkina, E. I. Vest. Mask. Univ. Mat. Mekh. 3, 43–46 (1983).
Arnold, V. I. Mathematical Methods in Classical Mechanics (Nauka, Moscow, 1979).
Dombre, T. et al. J. Fluid Mech. 167, 353–391 (1986).
Galloway, D. & Frisch, U. Geophys. astrophys. Fluid Dyn. 29, 13–18 (1984).
Galloway, D. & Frisch, U. Geophys. astrophys. Fluid Dyn. 36, 53–83 (1986).
Moffatt, H. K. & Proctor, M. R. E. J. Fluid Mech. 154, 493–507 (1985).
Aref, H. J. Fluid Mech. 143, 1–21 (1984).
Williams, G. P. J. atmos. Sci. 35, 1399–1426 (1978).
Hasegawa, A. J. phys. Soc. Japan 52, 1930–1934 (1983).
Hasegawa, A. Adv. Phys. 34, 1–42 (1985).
Zaslavsky, G. M., Sagdeev, R. Z. & Chernikov, A. A. Zh. eksp. tear. Fiz. 94, 102–115 (1988).
Meshalkin, L. D. & Sinai, Ya. G. Prikl. Mat. Mekh. 25, 1140–1143 (1961).
Sivashinsky, G. & Yakhot, V. Phys. Fluids 28, 1040–1042 (1986).
Zaslavsky, G. M. Chaos in Dynamic Systems (Harwood Acad. Publs, Chur-New York, 1985).
Chernikov, A. A., Sagdeev, R. Z., Usikov, D. A. & Zaslavsky, G. M. Phys. Letters 125A, 101–106 (1987).
Zaslavsky, G. M., Sagdeev, R. Z., Usikov, D. A. & Chernikov, A. A. Usp. Fiz. Nauk 156, 193–251 (1988).
Kleva, R. G. & Drake, J. F. Phys. Fluids 27, 1686–1698 (1984).
Rosenbluth, M. N., Berk, H. L., Doxas, I. & Horton, W. Phys. Fluids 30, 2636–2647 (1987).
Osipenko, M. V., Pogutse, O. P. & Chudin, N. V. Fiz. Plazmy 13, 953–960 (1987).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Beloshapkin, V., Chernikov, A., Natenzon, M. et al. Chaotic streamlines in pre-turbulent states. Nature 337, 133–137 (1989). https://doi.org/10.1038/337133a0
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1038/337133a0
This article is cited by
-
Rod-packing arrangements of invariant tori in solenoidal vector fields with cubic symmetries
Journal of Mathematical Chemistry (2022)
-
Formation of Coherent Structures in Kolmogorov Flow with Stratification and Drag
Acta Applicandae Mathematicae (2014)
-
Hyperbolic structure and stickiness effect: A case of a 2D area-preserving twist mapping
Science China Physics, Mechanics & Astronomy (2014)
-
Nonlinear analysis of stretch-twist-fold (STF) flow
Nonlinear Dynamics (2013)
-
Chaotic electron diffusion through stochastic webs enhances current flow in superlattices
Nature (2004)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.