Convection with heat flux prescribed on the boundaries of the system. I. The effect of temperature dependence of material properties
作者:
M.C. Depassier,
E.A. Spiegel,
期刊:
Geophysical & Astrophysical Fluid Dynamics
(Taylor Available online 1982)
卷期:
Volume 21,
issue 3-4
页码: 167-188
ISSN:0309-1929
年代: 1982
DOI:10.1080/03091928208209011
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
We study the bifurcation to steady two-dimensional convection with the heat flux prescribed on the fluid boundaries. The fluid is weakly non-Boussinesq on account of a slight temperature dependence of its material properties. Using expansions in the spirit of shallow water theory based on the preference for large horizontal scales in fixed flux convection, we derive an evolution equation for the horizontal structure of convective cells. In the steady state, this reduces to a simple nonlinear ordinary differential equation. When the horizontal scales of the cells exceed a certain critical size, the bifurcation to steady convection is subcritical and the degree of subcriticality increases with increasing cell size.
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