Thermocapillary convection with undeformable curved surfaces in open cylinders

Thermocapillary convection driven by a uniform heat flux in an open cylindrical container of unit aspect ratio is investigated by two- and three-dimensional numerical simulations. The undeformable free surface is either flat or curved as determined by the fluid volume (V⩽1) and the Young–Laplace equation. Convection is steady and axisymmetric at sufficiently low values of the Reynolds number (Re) with either flat or curved interfaces. Only steady convection is possible at any Re in strictly axisymmetric computations. Transition to oscillatory three-dimensional motions occurs as Re increases beyond a critical value dependent on Pr and V. Two pulsating and three rotating waves are observed at the free surface with a flat and a concave surface, respectively. The numerical results with either flat or curved free surfaces are in good quantitative agreement with space experiments.