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Transition to time-dependent convection

Published online by Cambridge University Press:  29 March 2006

R. M. Clever  and
F. H. Busse
R. M. Clever
Affiliation:
Science Applications, Inc., El Segundo, California 90245
F. H. Busse
Affiliation:
Department of Planetary and Space Sciences, University of California, Los Angeles
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Abstract

Steady solutions in the form of two-dimensional rolls are obtained for convection in a horizontal layer of fluid heated from below as a function of the Rayleigh and Prandtl numbers. Rigid boundaries of infinite heat conductivity are assumed. The stability of the two-dimensional rolls with respect to three-dimensional disturbances is analysed. It is found that convection rolls are unstable for Prandtl numbers less than about 5 with respect to an oscillatory instability investigated earlier by Busse (1972) for the case of free boundaries. Since the instability is caused by the momentum advection terms in the equations of motion the Rayleigh number for the onset of instability increases strongly with Prandtl number. Good agreement with various experimental observations is found.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 65 , Issue 4 , 2 October 1974 , pp. 625 - 645
Copyright
© 1974 Cambridge University Press

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References

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. Proc. IUTAM-Symp., Herrenalb, 1969: 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. & Whitehead, J. A. 1971 Instabilities of convection rolls in a high Prandtl number fluid J. Fluid Mech. 47, 305–320.Google Scholar
Chan, G. L. 1972 Experimental investigations of cellular convection in low and moderate Prandtl number fluids. M.S. thesis, School of Engineering, University of California, Los Angeles.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford: Clarendon Press.
Denny, V. E. & Clever, R. M. 1974 Comparisons of Galerkin and finite-difference methods in highly nonlinear thermally driven flows. J. Comp. Phys. In press.Google Scholar
Eckhaus, W. 1965 Studies in Nonlinear Stability Theory. Springer.
Krishnamurt, R. 1970a On the transition to turbulent convection. Part 1. The transition from two- to three-dimensional flow J. Fluid Mech. 42, 295–307.Google Scholar
Krishnamurti, R. 1970b On the transition to turbulent convection. Part 1. The transition to time-dependent flow J. Fluid Mech. 42, 309–320.Google Scholar
Krishnamurti, R. 1974 Some further studies on the transition to turbulent convection J. Fluid Mech. 60, 285–303.Google Scholar
Plows, W. H. 1968 Some numerical results for two-dimensional steady laminar Bénard convection Phys. Fluids, 11, 1593–1599.Google Scholar
Schlüter, A., Lortz, D. & Busse, F. 1965 On the stability of steady finite amplitude convection J. Fluid Mech. 23, 129–144.Google Scholar
Willis, G. E. & Deardorff, J. W. 1970 The oscillatory motions of Rayleigh convection J. Fluid Mech. 44, 661–672.Google Scholar
Willis, G. E., Deardorff, J. W. & Somerville, R. C. J. 1972 Roll-diameter dependence in Rayleigh convection and its effect upon the heat flux J. Fluid Mech. 54, 351–367.Google Scholar