OSCILLATORY 2-DIMENSIONAL AND 3-DIMENSIONAL THERMOCAPILLARY CONVECTION

The character and stability of two- and three-dimensional thermocapill ary driven convection are investigated by numerical simulations. In tw o dimensions, Hopf bifurcation neutral curves are delineated for fluid s with Prandtl numbers (Pr) 10.0, 6.78, 4.4 and 1.0 in the Reynolds nu mber (Re)-cavity aspect ratio (A(x)) plane corresponding to Re less th an or equal to 1.3 x 10(4) and A(x) less than or equal to 7.0. It is f ound that time-dependent motion is only possible if A(x) exceeds a cri tical value, A(xcr), which increases with decreasing PI. There are two coexisting neutral curves for Pr greater than or equal to 4.4. Stream line and isotherm patterns are presented at different Re and A(x) corr esponding to stationary and oscillatory states. Energy analyses of osc illatory flows are performed in the neighbourhood of critical points t o determine the mechanisms leading to instability. Results are provide d for flows near both critical points of the first unstable region wit h A(x) 3.0 and Pr = 10. In three dimensions, attention is focused on t he influence of sidewalls, located at y = 0 and y = A(y), and spanwise motion on the transition. In general, sidewalls have a damping effect on oscillations and hence increase the magnitude of the first critica l Re. However, the existence of spanwise waves can reduce this critica l Re. At large aspect ratios A(x) = A(y) = 15, our results with Pr = 1 3.9 at the lower critical Reynolds number of the first unstable region are in good agreement with those from infinite layer linear stability analysis.