On the onset of oscillatory convection in molten gallium

Abstract

The results of experimental and numerical investigations of the onset of oscillatory convection in a sidewall heated rectangular cavity of molten gallium are reported. Detailed comparisons are made between experimental observations and calculations from numerical simulations of a three-dimensional Boussinesq model. The onset of time-dependence takes place through supercritical Hopf bifurcations and the loci of critical points in the ($\hbox{\it Gr}, \hbox{\it Pr}$)-plane are qualitatively similar with excellent agreement between the frequencies of the oscillatory motion. This provides a severe test of the control of the experiment since the mode of oscillation is extremely sensitive to imperfections.

Detailed numerical investigations reveal that there are a pair of Hopf bifurcations which exist on two asymmetric states which themselves arise at a subcritical pitchfork from the symmetric state. There is no evidence for this in the experiment and this qualitative difference is attributed to non-Boussinesq perturbations which increase with $\hbox{\it Gr}$.

However, the antisymmetric spatial structure of the oscillatory state is robust and is present in both the experiment and the numerical model. Moreover, the detailed analysis of the numerical results reveals the origins of the oscillatory instability.