Dynamic free-surface deformations in axisymmetric thermocapillary convection in open cylindrical annuli

Thermocapillary convection in an open cylindrical annulus heated from the inside wall is investigated by two-dimensional numerical simulations. The deformable free surface is obtained as a solution of the coupled transport equations at fixed Prandtl and aspect ratio. Only steady convection can be realized in this axisymmetric computations with either non-deformable or deformable surfaces. Dynamic free-surface deformations do not induce transitions to oscillatory convection even at large Reynolds numbers. Free surfaces are convex near the cold wall due to the stagnation point, and concave near the hot wall. Free surface deformation increases with increasing Ca at a fixed Re. Two peaks appear at the free surface with low Re, while additional ripples, four peaks, occur at larger Re. Thermocapillary convection in the open annulus interior is insensitive to variations in Ca