Abstract: The convective instabilities in semiconductor or oxide melts, significantly affect the quality of large crystals grown from the melts by the Czochralski method. This paper reviews our recent numerical studies of thermal convection in annular pools of low-Pr silicon melt and moderate-Pr silicone oil. The mechanisms of the convective instability are discussed and the critical conditions for the onset of three-dimensional flow are determined. The results show that the hydrothermal wave, characterized by curved spokes, is dominant in a shallow thin pool. In a thick pool of the low-Pr silicon melt, there appears a standing wave type of oscillatory longitudinal rolls, which moves in the azimuthal direction and looks very similar to the hydrothermal waves. In deep pools of moderate-Pr silicone oil, a three-dimensional steady flow pattern, consisting of pairs of counter-rotating longitudinal rolls, arises, which corresponds to the RayleighBenard instability
