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The temporal development of a model of high Rayleigh number convection

Published online by Cambridge University Press:  28 March 2006

J. W. Elder
J. W. Elder
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

The evolution of a model of the flow in a layer of fluid suddenly heated from below at a Rayleigh number sufficient for a laboratory flow to ultimately become turbulent is investigated with numerical experiments. The numerical study simulates the flow by means of the mean field equations along the lines of Herring's (1963, 1964) pioneering study but uses a different finite difference technique and concentrates attention on the flow development rather than on the final statistically steady state. These solutions are compared with previous and some new simulations in two dimensions. The solutions confirm Herring's work and in addition show that the mean field equations, and in particular the weak-coupling approximations, describe the gross features of the model sufficiently well for the mean field equations to be used with reasonable confidence in evolutionary studies.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 35 , Issue 3 , 20 February 1969 , pp. 417 - 437
Copyright
© 1969 Cambridge University Press

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References

Deardorf, J. W. & Willis, G. E. 1967a J. Fluid Mech. 28, 675.
Deardorff, J. W. & Willis, G. E. 1967b Quart. J. Roy. Met. Soc. 93, 166.
Elder, J. W. 1965 J. Fluid Mech. 23, 99.
Elder, J. W. 1966a Second Australasian Conference on Fluid Mechanics.
Elder, J. W. 1966b J. Fluid Mech. 24, 823.
Elder, J. W. 1968a J. Fluid Mech. 32, 69.
Elder, J. W. 1968b Sci. Prog. Oxf. 56, 1.
Herring, J. R. 1963 J. Atmos. Sci. 20, 325.
Herring, J. R. 1964 J. Atmos. Sci. 21, 277.
Malkus, W. V. R. 1954 Proc. Roy. Soc. A, 225, 185.
Priestley, C. H. B. 1954 Aust. J. Phys. 7, 177.
Spiegel, E. A. 1965 Proc. 5th Cosmical Gas Dynamics Symposium, Nice.
Townsend, A. A. 1959 J. Fluid Mech. 5, 209.