2-DIMENSIONAL AND 3-DIMENSIONAL BUOYANT THERMOCAPILLARY CONVECTION

Results of steady, three-dimensional numerical calculations of combined buoyant and thermocapillary-driven convection in a cavity are presented. The flow is assumed to be spatially periodic along the cavity, isothermal at other vertical boundaries, and adiabatic at horizontal ones. The Prandtl number, Marangoni number to Grashof number ratio, and geometry are fixed while the Marangoni number is varied over sufficient range to demonstrate a bifurcation from two-dimensional to three-dimensional flow. Two-dimensional results obtained from full three-dimensional calculations are typical of solutions generated by two-dimensional codes, with all field variables independent of the assumed periodic direction. Three-dimensional solutions represent a distinct departure from projected two-dimensional solutions with velocity component parallel to the periodic direction comparable in magnitude to the other two components. The numerical results are in qualitative agreement with available experimental results.