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Oscillatory convection in vertical slots

Published online by Cambridge University Press:  20 April 2006

J. N. Koster
Affiliation:
Kernforschungszentrum Karlsruhe, Institut für Reaktorbauelemente, Postfach 3640, 7500 Karlsruhe 1, Federal Republic of Germany
U. MÜLler
Affiliation:
Kernforschungszentrum Karlsruhe, Institut für Reaktorbauelemente, Postfach 3640, 7500 Karlsruhe 1, Federal Republic of Germany

Abstract

Convective flow phenomena in slender vertical slots with larger vertical than horizontal dimension, i.e. Hele Shaw slots, heated from below and subject to specified lateral boundary conditions, are investigated experimentally. Temperature fields in the liquid were visualized by holographic interferometry. Power-density spectra of local time-dependent thermocouple signals are calculated.

In these slender slots different steady and time-dependent convection patterns develop with increasing Rayleigh number. The range of oscillatory convective flow exhibits periodic, quasiperiodic or non-periodic structures including possible frequency locking, subharmonics and intermittency. Quasiperiodic and periodic oscillations reappear at higher Rayleigh numbers, with non-periodic flows occurring in-between. These time-dependent flows appear to be caused by an instability of thermal boundary layers at the horizontal walls. Finally, at still higher Rayleigh numbers a reverse transition to a steady-state flow pattern is observed. The transitions between steady and non-steady flows are characterized by hysteresis.

Type
Research Article
Copyright
© 1984 Cambridge University Press

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References

Ahlers, G. & Behringer, R. P. 1978a Evolution of turbulence from the Rayleigh—Bénard instability Phys. Rev. Lett. 40, 712716.Google Scholar
Ahlers, G. & Behringer, R. P. 1978b The Rayleigh—Bénard instability and the evolution of turbulence Prog. Theor. Phys. Suppl. 64, 186201.Google Scholar
Bendat, J. S. & Piersol, A. G. 1971 Random data: Analysis and Measurement Procedures. Wiley.
Bergé, P. 1979 Experiments on hydrodynamic instabilities and the transition to turbulence. In Dynamical Critical Phenomena and Related Topics (ed. C. P. Enz). Lecture Notes in Physics, vol. 104, pp. 289308. Springer.
Bergé, P, & Dubois, M. 1978 Experimental study of the velocity field in Rayleigh—Bénard convection J. Fluid Mech. 85, 641653.Google Scholar
Bergé, P. & Dubois, M. 1979 Study of unsteady convection through simultaneous velocity and interferometric measurements J. Phys. Lett. (Paris) 40, L505L509.Google Scholar
Bergé, P., Dubois, M., Manneville, P. & Pomeau, Y. 1980 Intermittency in Rayleigh—Bénard convection J. Phys. Lett. (Paris) 41, L341L345.Google Scholar
Brigham, E. O. 1974 The Fast Fourier Transform. Prentice-Hall.
Busse, F. H. 1981 Transition to turbulence in Rayleigh-Bénard convection. In Hydrodynamic Instabilities and the Transition to Turbulence (ed. H. L. Swinney & J. P. Gollub), pp. 97137. Springer.
Busse, F. H. & Whitehead, J. A. 1974 Oscillatory and collective instabilities in large Prandtl number convection J. Fluid Mech. 66, 6779.Google Scholar
Chandrasekhar, S. 1981 Hydrodynamic and Hydromagnetic Stability. Dover.
Chu, T. Y. & Goldstein, R. J. 1973 Turbulent convection in a horizontal layer of water J. Fluid Mech. 60, 141159.Google Scholar
Davis, S. H. 1967 Convection in a box: linear theory. J. Fluid Mech. 30, 465465.Google Scholar
Dubois, M. 1981 Approach of the turbulence in hydrodynamics instabilities. In Symmetries and Broken Symmetries in Condensed Matter Physics (ed. N. Boccara), pp. 91105. IDSET-Paris.
Dubois, M. & BERGÉ, P. 1981 Instabilités de couche limite dans un fluide en convection; évolution vers la turbulence J. Phys. (Paris) 42, 167174.Google Scholar
Frick, H. & Clever, R. M. 1980 Einfluß der Seitenwände auf das Einsetzen der Konvektion in einer horizontalen Flüssigkeitsschicht Z. angew. Math. Phys. 31, 502513.Google Scholar
Frick, H. & MÜLLER, U. 1983 Oscillatory Hele Shaw convection J. Fluid Mech. 126, 521532.Google Scholar
Gollub, J. P. & Benson, S. V. 1980 Many routes to turbulent convection J. Fluid Mech. 100, 449470.Google Scholar
Gollub, J. P., Benson, S. V. & Steinman, J. 1980 A subharmonic route to turbulent convection Ann. NY Acad. Sci. 357, 2227.Google Scholar
Gray, D. D. & Giorgini, A. 1976 The validity of the Boussinesq approximation for liquids and gases Intl J. Heat Mass Transfer 19, 545551.Google Scholar
Günther, C. 1981 Numerische Untersuchung der Naturkonvektion in einer von unten beheizten, schmalen Hele-Shaw Zelle. Kernforschungszentrum Karlsruhe, KfK-Rep. 3142.Google Scholar
Günther, C. 1982 Zur Identifikation von Lösungsverzweigungen bei der Naturkonvektion in einer von unten beheizten, schmalen Hele-Shaw Zelle Z. angew. Math. Mech. 62, T207T209.Google Scholar
Hirsch, I. E., Huberman, B. A. & Scalapino, D. J. 1982 Theory of intermittency Phys. Rev. A25, 519532.Google Scholar
Howard, L. N. 1964 Convection at high Rayleigh number. In Proc. 11th Intl Congr. Appl. Mech., München (ed. H. Görtler), pp. 11091115. Springer.
Koschmieder, E. L. 1981 Experimental aspects of hydrodynamic instabilities. In Order and Fluctuations in Equilibrium and Non-Equilibrium Statistical Mechanics (ed. E. Nicolis, G. Dewel & J. W. Turner), pp. 159188. Wiley.
Koster, J. N. 1980 Freie Konvektion in vertikalen Spalten. Dissertation, Universität Karlsruhe, West Germany (KfK-Rep. 3066).
Koster, J. N. 1983 Interferometric investigation of convection in Plexiglas boxes Experiments in Fluids 1, 121128.Google Scholar
Koster, J. N. & MÜLLER, U. 1980 Free convection in vertical slots. In Natural Convection in Enclosures (ed. I. Catton & K. E. Torrance), pp. 2730. ASME HTD-Vol. 8.
Koster, J. N. & MÜLLER, U. 1981 Time dependent free convection in vertical slots Phys. Rev. Lett. 47, 15991602.Google Scholar
Koster, J. N. & MÜLLER, U. 1982 Free convection in vertical gaps J. Fluid Mech. 125, 429451.Google Scholar
Libchaber, A. & Maurer, J. 1978 Local probe in a Rayleigh—Bénard experiment in liquid helium J. Phys. (Paris) 39, 369371.Google Scholar
Libchaber, A. & Maurer, J. 1980 Une expérience de Rayleigh—Bénard de géométrie réduite: multiplication, accrochage et démultiplication de fréquences. J. Phys. (Paris) 41, 5151.Google Scholar
Lyubimov, D. V., Putin, G. F. & Chernatynskii, V. I. 1977 On convective motions in a Hele-Shaw cell Sov. Phys. Dokl. 22, 360362.Google Scholar
Normand, C. Y., Pomeau, Y. & Velarde, M. G. 1977 Convective instability: a physicist's approach. Rev. Mod. Phys. 49, 581581.Google Scholar
Ostrovsky, Y. I., Butusov, M. M. & Ostrovskaya, G. V. 1980 Interferometry by Holography. Springer.
Putin, G. F. & Tkacheva, E. A. 1979 Experimental investigation of supercritical convective motions in a Hele-Shaw cell Fluid Dyn. (Izv. Akad. Nauk SSSR, Mekh. Zhid. i Gaza) 14, 15.Google Scholar
Rabinovich, M. I. 1980 Strange attractors in modern physics Ann. NY Acad. Sci. 357, 435452.Google Scholar
Stork, K. & MÜLLER, U. 1972 Convection in boxes: experiments. J. Fluid Mech. 54, 559559.Google Scholar
Vest, C. M. 1979 Holographic Interferometry. Wiley.