Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-02-05T07:08:05.015Z Has data issue: false hasContentIssue false
  • English
  • Français

Competing and coexisting dynamical states of travelling-wave convection in an annulus

Published online by Cambridge University Press:  26 April 2006

D. Bensimon ,
Paul Kolodner ,
C. M. Surko ,
Hugh Williams  and
V. Croquette
D. Bensimon
Affiliation:
AT & T Bell Laboratories, Murray Hill, NJ 07974, USA
Paul Kolodner
Affiliation:
AT & T Bell Laboratories, Murray Hill, NJ 07974, USA
C. M. Surko
Affiliation:
AT & T Bell Laboratories, Murray Hill, NJ 07974, USA Present address: Department of Physics and Institute for Nonlinear Science, University of California at San Diego, La Jolla, CA 92093, USA.
Hugh Williams
Affiliation:
AT & T Bell Laboratories, Murray Hill, NJ 07974, USA
V. Croquette
Affiliation:
AT & T Bell Laboratories, Murray Hill, NJ 07974, USA Present address: Ecole Normale Supérieure, 24, rue Lhomond, 75231 Paris, France.
Get access Rights & Permissions [Opens in a new window]

Abstract

We describe experiments on convection in binary fluid mixtures in a large-aspect-ratio annular container. In this geometry, the convective rolls align radially and travel azimuthally, providing a model of travelling waves in an extended one-dimensional nonlinear dynamical system. Several different stable non-equilibrium states can be produced in this experiment, and the competition between them leads to a wide variety of steady and time-dependent behaviour. The observed spatiotemporal behaviour may shed light on recent theories of the nature of stable nonlinear travelling-wave convection, the pinning of travelling waves, and the creation of spatiotemporal defects.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 217 , August 1990 , pp. 441 - 467
Copyright
© 1990 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. & Heinrichs, R. 1987 Convection in a binary mixture. Nucl. Phys. B (Proc. Suppl.) 2, 77–86.Google Scholar
Bensimon, D., Pumir, A. & Shraiman, B. I. 1989 Nonlinear theory of traveling wave convection in binary mixtures. J. Phys. Paris 50, 3089–3108.Google Scholar
Bensimon, D., Shraiman, B. I. & Croquette, V. 1988 Nonadiabatic effects in convection. Phys. Rev. A38, 5461–5464.Google Scholar
Brand, H. R., Hohenberg, P. C. & Steinberg, V. 1984 Codimension-2 bifurcations for convection in binary fluid mixtures. Phys. Rev. A30, 2548–2561.Google Scholar
Brand, H. R., Lomdahl, P. S. & Newell, A. C. 1986 Benjamin—Feir turbulence in convective binary fluid mixtures. Physica 23D, 345–361.Google Scholar
Brand, H. R. & Steinberg, V. 1984 Analog of the Benjamin—Feir instability near the onset of convection in binary fluid mixtures. Phys. Rev. A29, 2303–2304.Google Scholar
Bretherton, C. S. & Spiegel, E. A. 1983 Intermittency through modulational instability. Phys. Lett. 96A, 152–156.Google Scholar
Caldwell, D. R. 1974 Experimental studies on the onset of thermohaline convection. J. Fluid Mech. 64, 347–367.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
Chaté, H. & Manneville, P. 1987 Transition to turbulence via spatiotemporal intermittency. Phys. Rev. Lett. 58, 112–115.Google Scholar
Coullet, P., Elphick, C. & Repaux, D. 1987 Nature of spatial chaos. Phys. Rev. Lett. 58, 431–434.Google Scholar
Croquette, V. 1989 Convective pattern dynamics at low Prandtl number: Part I. Contemp. Phys. 30, 113–133.Google Scholar
Croquette, V., Le Gal, P., Pocheau, A. & Guglielmetti, R. 1986 Large-scale flow characterization in a Rayleigh—Bénard convective pattern. Europhys. Lett. 1, 393–399.Google Scholar
Cross, M. C. 1986 Traveling and standing waves in binary-fluid convection in finite geometries. Phys. Rev. Lett. 57, 2935–2938.Google Scholar
Cross, M. C. 1988 Structure of nonlinear traveling-wave states in finite geometries. Phys. Rev. A 38, 3593–3600.Google Scholar
Cross, M. C. & Kim, K. 1988 Linear instability and the codimension-2 region in binary fluid convection between rigid impermeable boundaries. Phys. Rev. A37, 3909–3920.Google Scholar
Deissler, R. J. 1985 Noise-sustained structure, intermittency, and the Ginzburg—Landau equation. J. Statist. Phys. 40, 371–395.Google Scholar
Deissler, R. J. & Brand, H. R. 1988 Generation of counterpropagating nonlinear interacting traveling waves by localized noise. Phys. Lett. A30, 293–298.Google Scholar
Fineberg, J., Moses, E. & Steinberg, V. 1988 Spatially and temporally modulated traveling-wave pattern in convecting binary mixtures. Phys. Rev. Lett. 61, 838–841.Google Scholar
Heinrichs, R., Ahlers, G. & Cannell, D. S. 1987 Traveling waves and spatial variation in the convection of a binary mixture. Phys. Rev. A35, 2761–2764.Google Scholar
Hohenberg, P. C. & Cross, M. C. 1987 An introduction to pattern formation in nonequilibrium systems. Fluctuations and Stochastic Phenomena in Condensed Matter (ed. L. Garrido), pp. 55–255. Springer.
Hurle, D. T. J. & Jakeman, E. 1971 Soret-driven thermosolutal convection. J. Fluid Mech. 47, 667–689.Google Scholar
Joets, A. & Ribotta, R. 1989 Localisation and defects in propagative ordered structures. J. Phys. Paris 50, C3/171-C3/180.Google Scholar
Knobloch, E. & Moore, D. R. 1988 Linear stability of experimental Soret convection. Phys. Rev. A37, 860–870.Google Scholar
Kolodner, P., Bensimon, D. & Surko, C. M. 1988a Traveling-wave convection in an annulus. Phys. Rev. Lett. 60, 1723–1726.Google Scholar
Kolodner, P., Passner, A., Surko, C. M. & Walden, R. W. 1986 Onset of oscillatory convection in a binary fluid mixture. Phys. Rev. Lett. 56, 2621–2624.Google Scholar
Kolodner, P., Passner, A., Williams, H. L. & Surko, C. M. 1987a The transition to finite-amplitude traveling-wave convection in binary fluid mixtures. Nucl. Phys. B (Proc. Suppl.) 2, 97–108.Google Scholar
Kolodner, P. & Surko, C. M. 1988 Weakly nonlinear traveling-wave convection. Phys. Rev. Lett. 61, 842–845.Google Scholar
Kolodner, P., Surko, C. M., Passner, A. & Williams, H. L. 1987b Pulses of oscillatory convection. Phys. Rev. A36, 2499–2502.Google Scholar
Kolodner, P., Surko, C. M. & Williams, H. 1989 Dynamics of traveling waves near the onset of convection in binary fluid mixtures. Physica 37D, 319–333.Google Scholar
Kolodner, P., Surko, C. M., Williams, H. L. & Passner, A. 1988b Two-frequency states at the onset of convection in binary fluid mixtures. In Propagation in Systems Far from Equilibrium (ed. J. E. Wesfreid, H. R. Brand, P. Manneville, G. Albinet & N. Boccara), pp. 282–255. Springer.
Kolodner, P., Williams, H. & Moe, C. 1988c Optical measurement of the Soret coefficient of ethanol/water solutions. J. Chem. Phys. 88, 6512–6524.Google Scholar
Kuramoto, Y. 1978 Diffusion-induced chaos in reaction systems. Suppl. Prog. Theor. Phys. 64, 346–367.Google Scholar
Linz, S. J. & Lücke, M. 1987 Convection in binary mixtures: a Galerkin model with impermeable boundary conditions. Phys. Rev. A35, 3997–4000.Google Scholar
Moses, E., Fineberg, J. & Steinberg, V. 1987 Multistability and confined traveling-wave patterns in a convecting binary mixture. Phys. Rev. A35, 2757–2760.Google Scholar
Moses, E. & Steinberg, V. 1986 Flow patterns and nonlinear behavior of traveling waves in a convecting binary fluid. Phys. Rev. A34, 693–696.Google Scholar
Moses, E. & Steinberg, V. 1988 Mass transport in propagating patterns of convection. Phys. Rev. Lett. 60, 2030–2033.Google Scholar
Nozaki, K. & Bekki, N. 1983 Pattern selection and spatiotemporal transition to chaos in the Ginzburg—Landau equation. Phys. Rev. Lett. 51, 2171–2174.Google Scholar
Platten, J. K. & Chavepeyer, G. 1973 Oscillatory motion in Bénard cell due to the Soret effect. J. Fluid Mech. 60, 305–319.Google Scholar
Platten, J. K. & Legros, J. C. 1984 Convection in Liquids. Springer.
Pomeau, Y. 1986 Front motion, metastability, and subcritical bifurcations in hydrodynamics. Physica 23D, 3–11.Google Scholar
Shraiman, B. I. 1986 Order, disorder, and phase turbulence. Phys. Rev. Lett. 57, 325–328.Google Scholar
Sivashinsky, G. I. 1977 Nonlinear analysis of hydrodynamic instability in laminar flame. I. Derivation of basic equations. Acta Astronaut. 4, 1177–1206.Google Scholar
Sivashinsky, G. I. 1979 On self-turbulization of a laminar flame. Acta Astronaut. 6, 569–591.Google Scholar
Solomon, T. H. & Gollub, J. P. 1988 Passive transport in steady Rayleigh—Bénard convection. Phys. Fluids 31, 1372–1379.Google Scholar
Steinberg, V., Fineberg, J., Moses, E. & Rehberg, I. 1989 Pattern selection and transition to turbulence in propagating waves. Physica 37D, 359–383.Google Scholar
Steinberg, V., Moses, E. & Fineberg, J. 1987 Spatio-temporal complexity at the onset of convection in a binary fluid. Nucl. Phys. B (Proc. Suppl.) 2, 109–123.Google Scholar
Surko, C. M. & Kolodner, P. 1987 Oscillatory traveling-wave convection in a finite container. Phys. Rev. Lett. 58, 2055–2058.Google Scholar
Thual, O. & Fauve, S. 1988 Localized structures generated by subcritical instabilities. J. Phys. Paris 49, 1829–1832.Google Scholar
Walden, R. W., Kolodner, P., Passner, A. & Surko, C. M. 1985 Traveling waves and chaos in convection in binary fluid mixtures. Phys. Rev. Lett. 55, 496–499.Google Scholar
Walden, R. W., Kolodner, P., Passner, A. & Surko, C. M. 1987 Heat transport by parallel-roll convection in a rectangular container. J. Fluid Mech. 185, 205–233.Google Scholar
Zielinska, B. J. A. & Brand, H. R. 1987 Exact solution of the linear stability problem for the onset of convection in binary fluid mixtures. Phys. Rev. A35, 4349–4353.Google Scholar