Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-17T17:44:16.405Z Has data issue: false hasContentIssue false
  • English
  • Français

Oscillatory instabilities of convection rolls at intermediate Prandtl numbers

Published online by Cambridge University Press:  21 April 2006

E. W. Bolton ,
F. H. Busse  and
R. M. Clever
E. W. Bolton
Affiliation:
Department of Earth and Space Sciences and Institute of Geophysics and Planetary Physics, University of California at Los Angeles, Los Angeles, CA 90024, USA
F. H. Busse
Affiliation:
Department of Earth and Space Sciences and Institute of Geophysics and Planetary Physics, University of California at Los Angeles, Los Angeles, CA 90024, USA
R. M. Clever
Affiliation:
Department of Earth and Space Sciences and Institute of Geophysics and Planetary Physics, University of California at Los Angeles, Los Angeles, CA 90024, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The analysis of the instabilities of convection rolls in a fluid layer heated from below with no-slip boundaries exhibits a close competition between various oscillatory modes in the range 2 [lsim ] P [lsim ] 12 of the Prandtl number P. In addition to the even-oscillatory instability known from earlier work two new instabilities have been found, each of which is responsible for a small section of the stability boundary of steady rolls. The most interesting property of the new instabilities is their close relationship to the hot-blob oscillations known from experimental studies of convection. In the lower half of the Prandtl-number range considered the B02-mode dominates, which is characterized by two blobs each of slightly hotter and colder fluid circulating around in the convection roll in a spatially and time-periodic fashion. At higher Prandtl numbers the BE 1-mode dominates, which possesses one hot blob (and one cold blob) circulating with the convection velocity. Just outside the stability boundary there exist other growing modes exhibiting three or four blobs which may be observable in experiments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 164 , March 1986 , pp. 469 - 485
Copyright
© 1986 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. & Beheinger, R. P. 1978 Evolution of turbulence from the Rayleigh-Bénard instability. Phys. Rev. Lett. 40, 712–716.Google Scholar
Bolton, E. W. & Busse, F. H. 1985 Stability of convection rolls in a layer with stress-free boundaries. J. Fluid Mech. 150, 487–498.Google Scholar
Bolton, E. W., F. H. Busse & R. M. Clever 1983 An antisymmetric oscillatory instability of convection rolls. Bull. Am. Phys. Soc. 28, 1399.Google Scholar
Busse, F. H. 1967 On the stability of two-dimensional convection in a layer heated from below. J. Math. Phys. 46, 140–150.Google Scholar
Busse, F. H. 1971 Stability regions of cellular fluid flow. In Instability of Continuous Systems (ed. H. Leipholz), pp. 41–47. Springer.
Busse, F. H. 1972 The oscillatory instability of convection rolls in a low Prandtl number fluid. J. Fluid Mech. 52, 97–112.Google Scholar
Busse, F. H. 1978 Nonlinear properties of convection. Rep. Prog. Phys. 41, 1929–1967.Google Scholar
Busse, F. H. & Bolton, E. W. 1984 Instabilities of convection rolls with stress-free boundaries near threshold. J. Fluid Mech. 146, 115–125.Google Scholar
Busse, F. H. & Clever, R. M. 1979 Instabilities of convection rolls in a fluid of moderate Prandtl number. J. Fluid Mech. 91, 319–335.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
Busse, F. H. & Whitehead, J. A. 1974 Oscillatory and collective instabilities in large Prandtl number convection. J. Fluid Mech. 66, 67–79.Google Scholar
Clever, R. M. & Busse, F. H. 1974 Transition to time-dependent convection. J. Fluid Mech. 65, 625–645.Google Scholar
Clever, R. M. & Busse, F. H. 1978 Large wave length convection rolls in low Prandtl number fluids. Z. angew. Math. Phys. 29, 711–714.Google Scholar
Fauve, S., Laroche, C. & Libchaber, A. 1981 Effect of a horizontal magnetic field on convection instabilities in mercury. J. Physique Lett. 42, L455–L457.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. & Steinman, J. F. 1981 Doppler imaging of the onset of turbulent convection. Phys. Rev. Lett. 47, 505–508.Google Scholar
Kessler, R., Dallmann, V. & Oertel, H. 1984 Nonlinear transitions in Rayleigh—Bénard convection. In Turbulence and Chaotic Phenomena in Fluids (ed. T. Tatsumi), pp. 173–178. Elsevier.
Krishnamurti, R. 1970 On the transition to turbulent convection. Part 2. The transition to time-dependent flow. J. Fluid Mech. 42, 309–320.Google Scholar
Kolodner, P., Walden, R. W., Passner, A. & Surko, C. M. 1985 Stability of Rayleigh—Bénard convection patterns in a rectangular container. Preprint.
Rossby, H. T. 1966 An experimental study of Bénard convection with and without rotation. Ph.D. thesis, Massachusetts Institute of Technology.
Schlüter, A., Lortz, D. & Busse, F. 1965 On the stability of steady finite amplitude convection. J. Fluid Mech. 23, 129–144.Google Scholar
Walden, R. W., Kolodner, P., Passner, A. & Surko, C. M. 1984 Nonchaotic Rayleigh-Bénard convection with four and five incommensurate frequencies. Phys. Rev. Letts. 53, 242–245.Google Scholar
Willis, G. E. & Deardorff, J. W. 1967 Development of short-period temperature fluctuations in thermal convection. Phys. Fluids 10, 931–937.Google Scholar
Willis, G. E. & Deardorff, J. W. 1970 The oscillatory motions of Rayleigh convection. J. Fluid Mech. 44, 661–672.Google Scholar