Abstract
Recent studies of the dynamics of low-dimensional nonlinear systems with chaotic solutions have produced very interesting and profound results with several implications in many disciplines dealing with nonlinear equations. However, the interest of fluid dynamicists in these studies stems primarily from the expectation that they will help us understand better the onset as well as dynamics of turbulence in fluid flows. At this time, much of this expectation remains untested, especially in ‘open’ or unconfined fluid flows. This work is aimed at filling some of this gap.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ruelle, D. & Takens, F., Commun. Math. Phys. 20, 167 (1971).
Newhouse, S., Ruelle, D. & Takens, F., Commun. Math. Phys. 64, 35 (1978).
Gollub, J.P. & Swinney, H.L., Phys. Rev. Lett. 35, 927 (1975).
Fenstermacher, P.R., Swinney, H.L. & Gollub, J.P., J. Fluid Mech. 94, 103 (1979).
Brandstäter, A., Swift, J., Swinney, H.L. & Wolf, A., Phys. Rev. Lett. 51, 1442 (1983).
Libchaber, A. & Maurer, J., J. de Physique 41, C3–57 (1980).
Libchaber, A., In Chaos and Statistical Methods (ed. Y. Kuramoto, Springer 1984), p.221.
Coles, D., J. Fluid Mech. 21, 385 (1965).
Sreenivasan, K.R. & Strykowski, P.J., In Turbulence and Chaotic Phenomena in Fluids (ed. T. Tatsumi), to appear.
Sreenivasan, K.R., In Nonlinear Dynamics of Transcritical Flows (ed. H. Oertel), to appear.
Takens, F., In Lecture Notes in Mathematics 898 (eds. D.A. Rand and L.S. Young, Springer-Verlag 1981), p.366.
Chaitin, G.J., Scientific American, 246, 47 (May issue, 1982).
Thomas, R.M., J. Fluid Mech. 57, 549 (1973).
Gorman, M., Reith, L.A. & Swinney, H.L., Ann. N.Y. Acad. Sci. 357, 10 (1980). 66
Gollub, J.P., & Benson, S.V., J. Fluid Mech. 100, 449 (1980).
Greborgi, C., Ott, E. & Yorke, J.A., Phys. Rev. Lett. 51, 339 (1983).
Haken, H., Advanced Synergetics, Springer 1984.
Sparrow, C., The Lorenz Equations, Springer 1982.
Miles, J.W., Physica D (to appear), 1984.
Matsumoto, K. & Tsuda, I., J. Stat. Phys. 31, 87 (1983).
Roux, J.-C., Turner, J.C., McCormick, W.D., & Swinney, H.L., In Nonlinear Problems: Present and Future (eds. A.R. Bishop, D.K. Campbell, B. Nicolaenko, North-Holland Publishing Co., 1982), p.409.
Roshko, A., J. Fluid Mech. 10, 345 (1961).
Schewe, G., J. Fluid Mech. 133, 265 (1983).
Tritton, D.J., J. Fluid Mech. 6, 241 (1959).
Berger, E., Z. Flugwiss. 12, 41 (1964).
Tritton, D.J., J. Fluid Mech. 45, 749 (1971).
Friehe, C.A., J. Fluid Mech. 100, 237 (1980).
Gaster, M., J. Fluid Mech. 38, 565 (1969).
Malraison, B., Atten, P., Berge, P. & Dubois, M., J. Physique Lett. 44, L-897 (1983).
Mandelbrot, B., The Fractal Geometry of Nature, Freeman & Co., New York, 1983.
Farmer, J.D., Ott, E. & Yorke, J.A., Physica 7D, 153 (1983).
Grassberger, P. & Procaccia, I., Phys. Rev. Lett. 50, 346 (1983).
Landau, L.D. & Lifshitz, E.M., Fluid Mechanics (volume 6 of the Course of Theoretical Physics), Pergamon Press, 1982.
Barrow, J.D., Phys. Reports, 85, 1 (1982).
Grassberger, P. & Procaccia, I., Prepublication report (1983).
Gerrard, J.H., Phil. Trans. Roy. Soc. Lond. 288A, 29 (1978).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1985 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sreenivasan, K.R. (1985). Transition and Turbulence in Fluid Flows and Low-Dimensional Chaos. In: Davis, S.H., Lumley, J.L. (eds) Frontiers in Fluid Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46543-7_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-46543-7_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-46545-1
Online ISBN: 978-3-642-46543-7
eBook Packages: Springer Book Archive