Hostname: page-component-7479d7b7d-m9pkr Total loading time: 0 Render date: 2024-07-11T00:04:12.207Z Has data issue: false hasContentIssue false
  • English
  • Français

Two-dimensional oscillatory convection in a gravitationally modulated fluid layer

Published online by Cambridge University Press:  26 April 2006

R. Clever ,
G. Schubert  and
F. H. Busse
R. Clever
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90024, USA
G. Schubert
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90024, USA
F. H. Busse
Affiliation:
Physikalisches Institut, Universität Bayreuth, Postfach 101251, D8580 Bayreuth, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

A Galerkin method is used to study the two-dimensional modes of oscillatory convection in a gravitationally modulated fluid layer with rigid, isothermal boundaries heated either from below or from above. Nonlinear solutions are obtained for dimensionless frequencies ω (frequency is made non-dimensional with the timescale d2/κ where d is the depth of the fluid layer and κ is the thermal diffusivity) in the range 100–3000, dimensionless accelerations ε (εg is the amplitude of the externally imposed oscillatory vertical acceleration and g is the constant vertical acceleration of gravity) in the range of 1–104, and Prandtl numbers P in the range 0.71 (air) to 7 (water). The problem of convective onset is explored for a broader range of parameters than heretofore considered, including Prandtl numbers between 0.71 and 50. Both synchronous and subharmonic modes of convection are identified and it is found that finite-amplitude synchronous convection can be unstable to subharmonic modes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 253 , August 1993 , pp. 663 - 680
Copyright
© 1993 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., Hohenberg, P. C. & Lücke, M. 1985a Thermal convection under external modulation of the driving force. I. The Lorenz model. Phys. Rev. A 32, 3493–3518.Google Scholar
Ahlers, G., Hohenberg, P. C. & Lücke, M. 1985b Thermal convection under external modulation of the driving force. I. Experiments. Phys. Rev. A 32, 3519–3533.Google Scholar
Biringen, S. & Peltier, L. J. 1990 Numerical simulation of 3-D Bénard convection with gravitational modulation. Phys. Fluids A 2, 754–764.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
Burde, G. I. 1970 Numerical study of the onset of convection in a modulated field of external forces (in Russian). Izv. Akad. Nauk SSSR, Mekh. Zhid. Gazov, 2, 196.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon.
Davis, S. H. 1976 The stability of time-periodic flows. Ann. Rev. Fluid Mech 8, 57–74.Google Scholar
Donnelly, R. J. 1990 Externally modulated hydrodynamic systems. In Nonlinear Evolution of Spatio-Temporal Structures in Dissipative Continuous Systems (ed. F. H. Busse & L. Kramer), pp. 31–43. Plenum.
Douady, S. & Fauve, S. 1988 Pattern selection in Faraday instability. Europhys. Lett. 6, 221–226.Google Scholar
Ezerskii, A. B., Rabinovich, M. I. & Korotin, P. I. 1985 Random self-modulation of two-dimensional structures on a liquid surface during parametric-excitation. JETP Lett. 41, 157–160.Google Scholar
Faraday, M. 1831 Other forms and states assumed by fluids in contact with vibrating elastic surfaces. Phil. Trans. R. Soc. Lond. 121, 319–340.Google Scholar
Finucane, R. G. & Kelly, R. E. 1976 Onset of instability in a fluid layer heated sinusoidally from below. Intl J. Heat Mass Transfer 19, 71–85.Google Scholar
Gershuni, G. Z. & Zhukovitskii, E. M. 1976 Connective Stability of Incompressible Fluids (translated from the Russian by D. Louvish.) Jerusalem: Keter Publications.
Gresho, P. M. & Sani, R. L. 1970 The effects of gravity modulation on the stability of a heated fluid layer. J. Fluid Mech. 40, 783–806.Google Scholar
Hohenberg, P. C. & Swift, J. B. 1987 Hexagons & rolls in periodically modulated Rayleigh–Bénard convection. Phys. Rev. A 35, 3855–3873.Google Scholar
Meyer, C. W., Ahlers, G., Cannell, D. S., Hohenberg, P. C. & Swift, J. B. 1988 Pattern competition in temporally modulated Rayleigh-Bénard convection. Phys. Rev. Lett. 61, 947–950.Google Scholar
Meyer, C. W., Cannell, D. S. & Ahlers, G. 1992 Hexagonal and roll flow patterns in temporally modulated Rayleigh-Bénard convection. Phys. Rev. A 45, 8583–8604.Google Scholar
Niemela, J. J. & Donnelly, R. J. 1987 External modulation of Rayleigh-Bénard convection. Phys. Rev. Lett. 59, 2431–2434.Google Scholar
Ramshankar, R. & Gollub, J. P. 1991 Transport by capillary waves 2. Scalar dispersion and structure of the concentration field. Phys. Fluids A 3, 1344–1350.Google Scholar
Roppo, M. N., Davis, S. H. & Rosenblat, S. 1984 Bénard convection with time-periodic heating. Phys. Fluids 27, 796–803.Google Scholar
Rosenblat, S. & Herbert, D. M. 1970 Low-frequency modulation of thermal instability. J. Fluid Mech. 43, 385–398.Google Scholar
Rosenblat, S. & Tanaka, G. A. 1971 Modulation of thermal convection instability. Phys. Fluids 14, 1319–1322.Google Scholar
Venezian, G. J. 1969 Effect of modulation on the onset of thermal convection. J. Fluid Mech. 35, 243–254.Google Scholar