STEADY AND OSCILLATORY BUOYANT THERMOCAPILLARY CONVECTION

This paper reviews some aspects of our recent work pertinent to the ch aracter and stability of two dimensional and three dimensional thermoc apillary and buoyant thermocapillary flows in a fixed rectangular cavi ty. For two dimensional calculations, the flow is assumed isothermal a t the two vertical boundaries and adiabatic at the others. Three dimen sional calculations include an assumed periodicity in the axial direct ion with planes of symmetry separating respective calculation regions. In all cases, thermocapillarity influences flow through a tangential shear boundary condition at the free surface. The limit of small Capil lary number (Ca --> 0) is assumed and thus the free-surface is nondefo rmable to leading order. Terrestrial calculations of buoyant convectio n, with no thermocapillary effects, exhibit a Hopf bifurcation at some predictable, critical Grashof number. However, numerical calculations which incorporated thermocapillarity in microgravity rectangular syst ems with imposed flat free surfaces have been generally steady. Three dimensional calculations were utilized to show a spatial bifurcation i n the combined leading order problem while two dimensional calculation s were utilized to investigate the influence of increasing thermocapil larity on the Hopf bifurcation in the combined leading order problem.