Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-06-06T20:56:13.230Z Has data issue: false hasContentIssue false
  • English
  • Français

Spatio-temporal regimes in Rayleigh–Bénard convection in a small rectangular cell

Published online by Cambridge University Press:  26 April 2006

M. A. Rubio ,
P. Bigazzi ,
L. Albavetti  and
S. Ciliberto
M. A. Rubio
Affiliation:
Istituto Nazionale di Ottica, Largo Enrico Fermi 6, 50125 Arcetri-Firenze, Italy Permanent address: Departamento de Fisica Fundamental, Facultad de Ciencias. U.N.E.D., Aptdo. Correos 60141. Madrid, 28080, Spain.
P. Bigazzi
Affiliation:
Istituto Nazionale di Ottica, Largo Enrico Fermi 6, 50125 Arcetri-Firenze, Italy
L. Albavetti
Affiliation:
Istituto Nazionale di Ottica, Largo Enrico Fermi 6, 50125 Arcetri-Firenze, Italy
S. Ciliberto
Affiliation:
Istituto Nazionale di Ottica, Largo Enrico Fermi 6, 50125 Arcetri-Firenze, Italy
Get access Rights & Permissions [Opens in a new window]

Abstract

By means of an original optical technique we have studied the spatio-temporal behaviour in a Rayleigh–Bénard convection experiment of small rectangular geometry. The experimental technique allows complete reconstruction of the temperature field integrated along the roll axis. Two main spatiotemporal regimes have been found, corresponding to localized oscillations and travelling waves respectively. Several parameters are proposed for the quantitative characterization of this complex behaviour.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 209 , December 1989 , pp. 309 - 334
Copyright
© 1989 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., Cannell, D. S. & Steinberg, V. 1985 Time dependence of flow patterns near the convective threshold in a cylindrical container. Phys. Rev. Lett. 54, 1373–1376.Google Scholar
Arecchi, F. T., Ciliberto, S. & Rubio, M. A. 1984 Oscillations and chaos on the free surface of a heated fluid. II Nuovo Cimento 3D, 793–802.Google Scholar
Badii, R. & Politi, A. 1985 Statistical description of chaotic attractors: the dimension function. J. Statist. Phys. 40, 725–750.Google Scholar
Berge, P. & Dubois, M. 1989 Study of unsteady convection through simultaneous velocity and interferometric measurements. J. Phys. Lett. Paris 40, L505–L509.Google Scholar
Bishop, A. R., Fesser, K., Lomdhal, P. S., Kerr, W. C., Williams, M. B. & Trullinger, S. E. 1983 Coherent spatial structure versus time chaos in a perturbed sine-Gordon system. Phys. Rev. Lett. 50, 1095–1098.Google Scholar
Bolton, E. W., Busse, F. H. & Clever, R. M. 1986 Oscillatory instabilities of convection rolls at intermediate Prandtl numbers. J. Fluid Mech. 164, 469–485.Google Scholar
Busse, F. H. 1987 Non linear properties of thermal convection. Rep. Prog. Phys. 41, 1929–1967.Google Scholar
Busse, F. H. & Whitehead, J. A. 1971 Instabilities of convection rolls in a high Prandtl number fluid. J. Fluid Mech. 47, 305–320.Google Scholar
Buzyna, G., Pfeffer, R. L. & Jung, R. 1984 Transition to geostrophic turbulence in a rotating differentially heated annulus of fluid. J. Fluid Mech. 145, 377–403.Google Scholar
Catton, I. 1970 Convection in a closed rectangular region: the onset of motion. Trans. ASME C: J. Heat Transfer 92, 186–188.Google Scholar
Catton, I. 1972 The effect of insulating vertical walls on the onset of motion in a fluid heated from below. J. Heat Mass Transfer 15, 665–672.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Dover.
Chate, H. & Manneville, P. 1987 Transition to turbulence via spatiotemporal intermittency. Phys. Rev. Lett. 58, 112–115.Google Scholar
Chu, T. Y. & Goldstein, R. J. 1973 Turbulent convection in a horizontal layer of water. J. Fluid Mech. 60, 141–159.Google Scholar
Ciliberto, S. 1987 Fractal dimension and metric entropy in extended systems. Europhys. Lett. 4, 685–690.Google Scholar
Ciliberto, S. & Bigazzi, P. 1988 Spatiotemporal intermittency in Rayleigh—Bénard convection. Phys. Rev. Lett. 60, 286–289.Google Scholar
Ciliberto, S., Francini, F. & Simonelli, F. 1985 Real time measurements of optical disuniformity fields. Optics Commun. 54, 251–256.Google Scholar
Ciliberto, S. & Gollub, J. P. 1984 Pattern competition leads to chaos. Phys. Rev. Lett. 52, 922–925.Google Scholar
Ciliberto, S. & Gollub, J. P. 1985 Chaotic mode competition in parametrically forced surface waves. J. Fluid Mech. 158, 381–398.Google Scholar
Ciliberto, S. & Rubio, M. A. 1987a Local oscillations, travelling waves and chaos in Rayleigh—Bénard convection. Phys. Rev. Lett. 58, 2652–2655.Google Scholar
Ciliberto, S. & Rubio, M. A. 1987b Chaos and order in the temperature field of Rayleigh—Bénard convection. Physica Scripta 36, 920–926.Google Scholar
Ciliberto, S. & Simonelli, F. 1986 Spatial structure of temporal chaos in Rayleigh—Bénard convection. Europhys. Lett. 2, 285–290.Google Scholar
Curry, J., Herring, J., Loncaric, J. & Orszag, S. A. 1984 Order and disorder in two-and three-dimensional Bénard convection. J. Fluid Mech. 147, 1–38.Google Scholar
Depassier, M. C. 1984 A note on the free boundary conditions in Rayleigh—Bénard convection between insulating boundaries. Phys. Lett. 102A, 359–361.Google Scholar
Depassier, M. C. & Spiegel, E. A. 1981 The large-scale structure of compressible convection. Astr. J. 86, 496–512.Google Scholar
Dubois, M. & Berge, P. 1988 Experimental study of the velocity field in Rayleigh—Bénard convection. J. Fluid Mech. 85, 641–653.Google Scholar
Dubois, M. & Berge, P. 1981 Instabilities de couche limite dans un fluide en convection: evolution vers la turbulence. J. Phys. Paris 42, 167–174.Google Scholar
Dubois, M., Rubio, M. A. & Berge, P. 1983 Experimental evidence of intermittencies associated with a subharmonic bifurcation. Phys. Rev. Lett. 51, 1446–1449.Google Scholar
Farmer, J. D., Ott, E. & Yorke, J. A. 1983 The dimension of chaotic attractors. Physica 7D, 153–180.Google Scholar
Giglio, M., Musazzi, S. & Perini, U. 1981 Transition to chaotic behaviour via a reproducible sequence of period doubling bifuractions. Phys. Rev. Lett. 47, 243–246.Google Scholar
Giglio, M., Musazzi, S. & Perini, U. 1984 Low dimensionality turbulent convection. Phys. Rev. Lett. 53, 2402–2404.Google Scholar
Gollub, J. P. & Benson, S. V. 1980 Many routes to turbulent convection. J. Fluid Mech. 100, 449–470.Google Scholar
Gollub, J. P. & McCarrier, A. R. 1982 Convection patterns in Fourier space. Phys. Rev. A 26, 3470–3476.Google Scholar
Grassberger, P. & Procaccia, I. 1983 Characterization of strange attractors. Phys. Rev. Lett. 50, 346–349.Google Scholar
Guckenheimer, J. & Buzyna, G. 1983 Dimension measurements for geostrophic turbulence. Phys. Rev. Lett. 51, 1438–1441.Google Scholar
Guckenheimer, J. & Holmes, T. 1983 Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Springer.
Heutmaker, M. S., Fraenkel, P. N. & Gollub, J. P. 1985 Convection patterns: time evolution of the wave-vector field. Phys. Rev. Lett. 54, 1369–1372.Google Scholar
Howard, L. N. & Krishnamurti, R. 1986 Large-scale flow in turbulent convection: a mathematical model. J. Fluid Mech. 170, 385–410.Google Scholar
Hyman, J. M. & Nicolaenko, B. 1986 The Kuramoto—Sivashinski equation: a bridge between PDE's and dynamical systems. Physica 18D, 113–126.Google Scholar
Kaneko, K. 1985 Spatiotemporal intermittency in coupled map lattices. Prog. Theor. Phys. 74, 1033–1944.Google Scholar
Kolodner, P., Passner, A., Surko, C. M. & Walden, R. W. 1986a Onset of oscillatory convection in a binary fluid mixture. Phys. Rev. Lett. 56, 2621–2624.Google Scholar
Kolodner, P., Walden, R. W., Passner, A. & Surko, C. M. 1986b Rayleigh—Bénard convection in an intermediate-aspect-ratio rectangular container. J. Fluid Mech. 163, 195–226.Google Scholar
Koster, J. N. & Müller, U. 1984 Oscillatory convection in vertical slots. J. Fluid Mech. 139, 363–390.Google Scholar
Krishnamurti, R. 1970a On the transition to turbulent convection. Part 1. The transition from two-to three-dimensional flow, J. Fluid Mech. 42, 295–307.Google Scholar
Krishnamurti, R. 1970b On the transition to turbulent convection. Part 2. The transition to time-dependent flow. J. Fluid Mech. 42, 309–320.Google Scholar
Libchaber, A., Laroche, C. & Fauve, S. 1982 Period doubling cascade in mercury, a quantitative measurement. J. Phys. Lett. Paris 43, L221–L216.Google Scholar
Linz, S. J., Luke, M., Muller, H. W. & Niederlander, J. 1988 Convection in binary fluid mixtures: travelling waves and lateral currents. Phys. Rev. A 38, 5727–5741.Google Scholar
Livi, R., Pettini, M., Ruffo, S., Sparpaglione, M. & Vulpiani, A. 1985 Equipartition threshold in nonlinear large Hamiltonian systems: the Fermi—Pasta—Ulam model. Phys. Rev. A 31, 1039–1045.CrossRefGoogle Scholar
Malraison, B., Atten, P., Berge, P. & Dubois, M. 1983 Dimension of strange attractors: an experimental determination for the chaotic regime of two chaotic systems. J. Phys. Lett. Paris 44, L897–L902.Google Scholar
Meron, E. & Procaccia, I. 1986 Theory of chaos in surface waves: the reduction from hydrodynamics to few-dimensional dynamics. Phys. Rev. Lett. 56, 1323–1326.Google Scholar
Moses, E. & Steinberg, V. 1986 Flow patterns and nonlinear behaviour of travelling waves in a convective binary fluid. Phys. Rev. A 34, 693–696.Google Scholar
Nicolaenko, B. 1987 Large scale spatial structures in two-dimensional turbulent flows. In Proc. Intl. Conf. on the Physics of Chaos and Systems far from equilibrium, CHAOS 87 (ed. M. Duong-Van). North-Holland.
Normand, Ch. Pomeau, Y. & Velarde, M. G. 1977 Conyective instability: a physicist's approach. Rev. Mod. Phys. 49, 581–624.Google Scholar
Oono, Y. & Kohmoto, M. 1985 Discrete model of chemical turbulence. Phys. Rev. Lett. 55, 2927–2931.Google Scholar
Oppo, G. L. & Kapral, R. 1986 Discrete models for the formation and evolution of spatial structures in dissipative systems. Phys. Rev. A 33, 4219–4231.Google Scholar
Pocheau, A., Croquette, V. & Le Gal, P. 1985 Turbulence in a cylindrical container of argon near threshold of convection. Phys. Rev. Lett. 55, 1094–1097.Google Scholar
Poyet, F. 1983 The Rayleigh—Bénard two-dimensional convection in a fluid between two plates of finite conductivity. PhD thesis, Columbia University.
Simonelli, F. & Gollub, J. P. 1988 In Chaos and Complexity (ed. A. Buiatti, S. Ciliberto, R. Livi & S. Ruffo). World Scientific.
Simonelli, F. & Gollub, J. P. 1989 Surface wave mode interactions: Effects of symmetry and degeneracy. J. Fluid Mech. 199, 471–494.Google Scholar
Stork, K. & Müller, U. 1972 Convection in boxes: experiments. J. Fluid Mech. 54, 599–611.Google Scholar
Stork, K. & Müller, U. 1975 Convection in boxes: an experimental investigation in vertical cylinders and annuli. J. Fluid Mech. 71, 233–240.Google Scholar
Takens, F. 1981 Detecting strange attractors in turbulence (ed. D. A. Rand & L. S. Young). In Lecture Notes in Mathematics, vol. 808, Springer.
Vastano, J. A. & Swinney, H. L. 1988 Information transport in spatiotemporal systems. Phys. Rev. Lett. 60, 1773–1776.Google Scholar
Walden, R., Kolodner, P., Passner, A. & Surko, C. M. 1984 Nonchaotic Rayleigh—Bénard convection with four and five inconmensurate frequencies. Phys. Rev. Lett. 53, 242–245.Google Scholar
Walden, R., Kolodner, P., Passner, A. & Surko, C. M. 1987 Heat transport by parallel roll convection in a rectangular container. J. Fluid Mech. 185, 205–234.Google Scholar