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The effects of thermal conditions on the cell sizes of two-dimensional convection

Published online by Cambridge University Press:  26 April 2006

Masaki Ishiwatari ,
Shin-Ichi Takehiro  and
Yoshi-Yuki Hayashi
Masaki Ishiwatari
Affiliation:
Department of Earth and Planetary Physics, Faculty of Science, University of Tokyo, Bunkyo, Tokyo, 113, Japan
Shin-Ichi Takehiro
Affiliation:
Department of Earth and Planetary Physics, Faculty of Science, University of Tokyo, Bunkyo, Tokyo, 113, Japan
Yoshi-Yuki Hayashi
Affiliation:
Department of Earth and Planetary Physics, Faculty of Science, University of Tokyo, Bunkyo, Tokyo, 113, Japan
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Abstract

The effects of thermal conditions on the patterns of two-dimensional Boussinesq convection are studied by numerical integration. The adopted thermal conditions are (i) the heat fluxes through both upper and lower boundaries are fixed, (ii) the same as (i) but with internal cooling, (iii) the temperature on the lower boundary and the heat flux through the upper boundary are fixed, (iv) the same as (iii) but with internal cooling, and (v) the temperatures on both upper and lower boundaries are fixed. The numerical integrations are performed with Ra = 104 and Pr = 1 over the region whose horizontal and vertical lengths are 8 and 1, respectively.

The results confirm that convective cells with the larger horizontal sizes tend to form under the conditions where the temperature is not fixed on any boundaries. Regardless of the existence of internal cooling, one pair of cells spreading all over the region forms in the equilibrium states. On the other hand, three pairs of cells form and remain when the temperature on at least one boundary is fixed. The formation of single pairs of cells appearing under the fixed heat flux conditions shows different features with and without internal cooling. The difference emerges as the appearance of a phase change, whose existence can be suggested by the weak nonlinear equation derived by Chapman & Proctor (1980).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 281 , 25 December 1994 , pp. 33 - 50
Copyright
© 1994 Cambridge University Press

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