Abstract
SummaryResults of a bifurcation analysis of the test cases prescribed for the GAMM Workshop on the Numerical Simulation of Oscillatory Convection in Low Prandtl Number Fluids are presented. An oscillatory instability which arises at a Hopf bifurcation in the solution of the steady-state equations is identified. The critical Grashof number and frequency are predicted by solving an extended system of steady equations that locates exactly the Hopf bifurcation point, and the variation with Prandtl number is determined. The effect on the threshold of different thermal and viscous conditions on the upper surface is assessed. Under certain conditions a stable steady flow is found to co-exist with the oscillatory flow.
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