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RESEARCH PAPERS

On Oscillatory Instability of Convective Flows at Low Prandtl Number

[+] Author and Article Information
A. Yu. Gelfgat, P. Z. Bar-Yoseph, A. L. Yarin

Computational Mechanics Laboratory, Technion-Israel Institute of Technology, Haifa 32000, Israel

J. Fluids Eng 119(4), 823-830 (Dec 01, 1997) (8 pages) doi:10.1115/1.2819504 History: Received September 05, 1996; Revised June 23, 1997; Online January 22, 2008

Abstract

Numerical investigation of the oscillatory instability of convective flows in laterally heated rectangular cavities is presented. Cavities with no-slip isothermal vertical boundaries, no-slip adiabatic lower boundary, and stress-free adiabatic upper boundary are considered. Dependence of the critical Grashof number and the critical frequency of oscillations on the aspect ratio (A = length/height) of the cavity are investigated. The stability diagrams were obtained for the whole interval of the aspect ratio 1 ≤ A ≤ 10. The study was carried out for two values of the Prandtl number, Pr = 0 and 0.015. It was shown that the oscillatory instability sets in as a result of the Hopf bifurcation. It was found that at two different values of the Prandtl number considered the instability is caused by different infinitely small dominant perturbations, which means that the convective heat transfer strongly affects stability of the flow even for cases having small Prandtl number. No asymptotic behavior for large aspect ratios was found up to A = 10. Slightly supercritical oscillatory flows were approximated asymptotically by means of the weakly nonlinear analysis of the calculated bifurcation.

Copyright © 1997 by The American Society of Mechanical Engineers
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