Hostname: page-component-745bb68f8f-hvd4g Total loading time: 0 Render date: 2025-01-27T16:42:54.009Z Has data issue: false hasContentIssue false
  • English
  • Français

Transition from periodic to chaotic thermal convection

Published online by Cambridge University Press:  20 April 2006

John B. McLaughlin  and
Steven A. Orszag
John B. McLaughlin
Affiliation:
Department of Chemical Engineering, Clarkson College of Technology, Potsdam, N.Y. 13676, U.S.A.
Steven A. Orszag
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

The transition to turbulence in Bénard convection in a layer of air bounded by rigid conducting walls is studied by numerical solution of the three-dimensional time-dependent Boussinesq equations. The wavy instability of rolls is compared with available experimental and theoretical results. The subsequent transition to chaotic convection is shown to occur for Rayleigh numbers larger than about 9000. The role of symmetry-breaking perturbations in the production of chaos is clarified.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 122 , September 1982 , pp. 123 - 142
Copyright
© 1982 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ahlers, G. & Behringer, R. P. 1978 Phys. Rev. Lett. 40, 712–716.
Ahlers, G. & Behringer, R. P. 1979 Prog. Theor. Phys. Suppl. 64, 180–201.
Busse, F. H. & Clever, R. M. 1979 J. Fluid Mech. 91, 319–335.
Chirikov, B. V. 1959 Atomnaya Energiya 6, 630.
Clever, R. M. & Busse, F. H. 1974 J. Fluid Mech. 65, 625–645.
Clever, R. M. & Busse, F. H. 1978 J. Appl. Math. & Phys. 29, 711–714.
Curry, J. H., Herring, J. R., Loncaric, J. & Orszag, S. A. 1982 Order and disorder in two and three dimensional Bénard convection. To be published.
Ford, J. & Lunsford, G. H. 1970 Phys. Rev. A 1, 59–70.
Gollub, J. P. & Benson, S. H. 1980 J. Fluid Mech. 100, 449–470.
Herbert, T. 1976 Periodic secondary motions in a plane channel. In Proc. 5th Int. Conf. on Numerical Methods in Fluid Dynamics (ed. A. I. van de Vooren & P. J. Zandbergen). Lecture Notes in Physics, vol. 59, p. 235. Springer.
Herbert, T. 1977 Finite amplitude stability of plane parallel flows. In Laminar-Turbulent Transition, AGARD Conf. Proc. no. 224, pp. 3–1–3–10.
Krishnamurti, R. 1973 J. Fluid Mech. 60, 285–303.
Landau, L. D. & Lifschitz, E. M. 1959 Fluid Mechanics. Pergamon.
Lanford, O. 1982 In Proc. 1981 Les Houches Summer School of Physics. North-Holland.
Laufer, J. 1954 The structure of turbulence in fully developed pipe flow. NASA Rep. no. 1174.Google Scholar
Lipps, F. B. 1976 J. Fluid Mech. 75, 113–148.
Marcus, P. S. 1981 J. Fluid Mech. 103, 241–255.
Mclaughlin, J. M. & Martin, P. C. 1975 Phys. Rev. A 12, 186–203.
Newhouse, S., Ruelle, D. & Takens, F. 1978 Commun. Math. Phys. 64, 35–40.
Orszag, S. A. 1971 J. Fluid Mech. 50, 689.
Orszag, S. A. & Kells, L. C. 1980 J. Fluid Mech. 96, 159–205.
Orszag, S. A. & Patera, A. T. 1981 Subcritical transition to turbulence in planar shear flows. In Transition and Turbulence (ed. R. E. Meyer), pp. 127–145. Academic.
Ruelle, D. & Takens, F. 1971 Commun. Math. Phys. 20, 167–192.
Toomre, J., Gough, D. O. & Spiegel, E. A. 1977 J. Fluid Mech. 79, 1–31.
Willis, G. E. & Deardorff, J. W. 1970 J. Fluid Mech. 44, 661–672.
Willis, G. E., Deardorff, J. W. & Somerville, R. C. J. 1972 J. Fluid Mech. 54, 351.