Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-01-09T06:28:54.013Z Has data issue: false hasContentIssue false
  • English
  • Français

Three-dimensional convection in a horizontal fluid layer subjected to a constant shear

Published online by Cambridge University Press:  26 April 2006

R. M. Clever  and
F. H. Busse
R. M. Clever
Affiliation:
Institute of Geophysics and Planetary Physics, University of California at Los Angeles, CA, USAand Institute of Physics, University of Bayreuth, 858 Bayreuth, Germany
F. H. Busse
Affiliation:
Institute of Geophysics and Planetary Physics, University of California at Los Angeles, CA, USAand Institute of Physics, University of Bayreuth, 858 Bayreuth, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

Rayleigh-Bénard convection in the presence of a plane Couette flow is investigated by numerical computations. From earlier work it is well known that longitudinal rolls are preferred at the onset of convection and that at Prandtl numbers of the order unity or less these rolls become unstable with respect to the wavy instability which introduces wavy distortions perpendicular to the axis of the rolls. In the present analysis the three-dimensional flows arising from these distortions are studied and their stability is considered. A main result is the subcritical existence of three-dimensional flows at Rayleigh numbers far below the critical value for onset of convection.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 234 , January 1992 , pp. 511 - 527
Copyright
© 1992 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

Asai, T. 1970 Three-dimensional features of thermal convection in a plane Couette flow. J. Met. Soc. Japan 48, 18–29.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. 1978 Nonlinear properties of convection. Rep. Prog. Phys. 41, 1929–1967.Google Scholar
Busse, F. H. 1981 Transition to turbulence in Rayleigh—Bénard convection. Chapter 5. In Hydrodynamic Instabilities and the Transition to Turbulence (ed. H. L. Swinney & J. P. Gollub), chap. 5. Springer.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon.
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. 1977 Instability of longitudinal convection rolls in an inclined layer. J. Fluid Mech. 81, 107–127.Google Scholar
Clever, R. M. & Busse, F. H. 1991 Instabilities of longitudinal rolls in the presence of Poiseuille flow. J. Fluid Mech. 229, 517–529.Google Scholar
Clever, R. M., Busse, F. H. & Kelly, R. E. 1977 Instabilities of longitudinal convection rolls in Couette flow. Z. Angew. Math. Phys. 28, 771–783 (referred to herein as CBK).Google Scholar
Domaradzki, J. A. & Metcalfe, R. W. 1988 Direct numerical simulations of the effects of shear on turbulent Rayleigh—Bénard convection. J. Fluid Mech. 193, 499–531.Google Scholar
Gallagher, A. P. & Mercer, A. McD. 1965 On the behaviour of small disturbances in plane Couette flow with a temperature gradient. Proc. R. Soc. Lond. A 286, 117–128.Google Scholar
Kuettner, J. P. 1971 Cloud bands in the Earth's atmosphere. Tellus 23, 404–425.Google Scholar
Nagata, M. 1990 Three-dimensional finite amplitude solutions in plane Couette flow: bifurcation from infinity. J. Fluid Mech. 217, 519–527.Google Scholar
Or, A. C. & Busse, F. H. 1987 Convection in a rotating cylindrical annulus. Part 2. Transition to symmetric and vacillating flow. J. Fluid Mech. 174, 313–326.Google Scholar
Orszag, S. A. & Patera, A. T. 1983 Secondary instability of wall-bounded shear flows. J. Fluid Mech. 128, 347–385.Google Scholar
Pfeffer, R. L. & Chiang, Y. 1967 Two kinds of vacillation in rotating laboratory experiments. Mon. Weath. Rev. 95, 75–82.Google Scholar
Reichardt, H. 1959 Gesetzmäßigkeiten der geradlinigen turbulenten Couetteströmung. Mitt. Max-planck-Institut für Strömungsforschung, Göttingen, Nr. 22.