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Abstract
Instability of thermocapillary convection has been studied by using a numerical code based on a control volume method. The momentum, continuity, and energy equations are solved in a cylindrical configuration with the thermocapillary boundary conditions at the free surface. The convective fluxes are calculated via an upwinding method, and the numerical values are updated via a single-step time marching method. We report the results obtained for two different Prandtl numbers (1 and 32). The disturbance growth has been determined during the transition from the axisymmetric to the oscillatory three-dimensional flow; the oscillatory modes, critical Reynolds numbers, and frequencies are compared with those obtained by stability analyses. Two different regimes occur in supercritical conditions: the oscillations initially emerge as a pulsating regime and, successively, become an azimuthally rotating structure. The latter is also subjected to further transitions characterized by an increase of the number of fundamental frequencies.