OSCILLATORY BUOYANT THERMOCAPILLARY FLOW

A computational study of the character and stability of two-dimensiona l buoyant thermocapillary flows, valid to leading order in capillary n umber (Ca), is conducted in the Grashof number (Gr), Reynolds number ( Re), aspect ratio, and Prandtl number (Pr) parameter space. Calculatio ns of thermocapillary convection for low Pr fluids have generally prod uced steady results. Calculations of pure buoyant convection (Re=0) ex hibit a Hopf bifurcation at Gr(cr) (no thermocapillarity) that is well understood. Thus, the combined thermocapillary buoyant problem is stu died to investigate the onset of oscillatory convection in the limit G r-->0. The unsteady natural convection pattern at fixed Gr>Gr(cr) is m odified only slightly for low values of Re. When thermocapillarity act s in conjunction with buoyancy (Re>0) it is stabilizing, in that the t ransition to unsteady flow occurs at Gr>Gr(cr), as defined for the str ictly buoyant problem. When thermocapillarity acts in opposition to bu oyancy (Re<0), it is destabilizing for relatively small values of \Re\ , but thermocapillarity ultimately dominates the convective pattern fo r larger \Re\, and the resulting flow is steady for the range of param eter values considered. Stability boundaries for the onset of oscillat ory convection in the Gr-Re plane are given for representative values of the cavity aspect ratio and Pr.