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Oscillatory convection has been observed in recent experiments in a square, air-filled cavity with differentially heated sidewalls and conducting horizontal surfaces. The author shows that the onset of the oscillatory convection occurs at a Hopf bifurcation in the steady-state equations for free convection in the Boussinesq approximation. The location of the bifurcation point is found by solving an extended system of steady-state equations. The predicted critical Rayleigh number and frequency at the onset of oscillations are in excellent agreement with the values measured recently and with those of a time-dependent simulation. Four other Hopf bifurcation points are found near the critical point and their presence supports a conjectured resonance between traveling waves in the boundary layers and interior gravity waves in the stratified core.
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| Authors: |
Winters, K.H. (Harwell Lab., Didcot (England))
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| Publication Date: | 1987 Nov 01 |
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| OSTI Identifier: | 5476637 |
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| Resource Type: | Journal Article |
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| Resource Relation: | Journal Name: Journal of Heat Transfer (Transcations of the ASME (American Society of Mechanical Engineers), Series C); (United States); Journal Volume: 109:4 |
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| Country of Publication: | United States |
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| Language: | English |
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| Format: | Size: Pages: 894-898 |
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| Other Number(s): | Journal ID: ISSN 0022-1481; CODEN: JHTRA |
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| Subject: | 42 ENGINEERING; CAVITIES; NATURAL CONVECTION; FLOW MODELS; DOUBLE GLAZING; PRANDTL NUMBER; RAYLEIGH-TAYLOR INSTABILITY; SQUARE CONFIGURATION; TIME DEPENDENCE; CONFIGURATION; CONVECTION; COVERINGS; ENERGY TRANSFER; GLAZING; HEAT TRANSFER; INSTABILITY; MASS TRANSFER; MATHEMATICAL MODELS; RECTANGULAR CONFIGURATION |
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| Update Date: | 2009 Dec 16 |
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