Nonlinear transition in three-dimensional convection

Author:

Kessler R.

Abstract

Steady and oscillatory convection in a rectangular box heated from below are studied by means of a numerical solution of the three-dimensional, time-dependent Boussinesq equations. The effect of the rigid sidewalls of the box on the spatial structure and the dynamical behaviour of the flow is analysed. Both conducting and adiabatic sidewalls are considered. Calculated streamlines illustrate the three-dimensional structure of the steady flow with Prandtl numbers 0.71 and 7. The onset and the frequency of the oscillatory instability are calculated and compared with available experimental and theoretical data. With increasing Rayleigh number a subharmonic bifurcation and the onset of a quasi-periodic flow can be observed. A comparison of the different time-dependent solutions shows some interesting relations between the spatial structure and the dynamical behaviour of the confined flow.

Publisher

Cambridge University Press (CUP)

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Reference29 articles.

1. Feigenbaum, M. J. 1979 The onset spectrum of turbulence.Phys. Lett. A74,375–378.

2. Kessler, R. 1984 Vectorization of the Galerkin method. In Vectorization of Computer Programs with Applications to Computational Fluid Dynamics (ed. W. Gentzsch ), pp. 217–234.Vieweg.

3. Gollub, J. P. , Benson, S. V. & Steinman, J. 1980 A subharmonic route to turbulent convection.Ann. N.Y. Acad. Sci. 357,22–27.

4. Kessler, R. 1983 Oszillatorische Konvektion. dissertation, Universität Karlsruhe, West Germany (DFVLR-Rep. FB-84-14).

5. Frick, H. , Busse, F. H. & Clever, R. M. 1983 Steady three-dimensional convection at high Prandtl numbers.J. Fluid Mech. 127,141–153.

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