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.