Flow transitions and instabilities have significant effects on the quality of the crystals. The flow and heat transfer in the LEC GaAs melt are numerically studied by a time-dependent and three-dimensional turbulent flow model. The effects of the change of the buoyancy and Marangoni force on the flow state are analyzed by changing the temperature difference between the crystal and the crucible walls. The results show that the flow will transform from axisymmetric steady flow to non-axisymmetric oscillatory flow when the temperature difference exceeds the critical value, and that the mechanism of the transition is attributed to the Marangoni instability. The critical temperature differences for the flow transitions corresponding to different melt depth H are numerically predicted. Several important characteristics of the non-axisymmetric buoyant-Marangoni convection are numerically observed and compared with that of the non-axisymmetric mixed convection coupled with crystal rotation. Flow transitions and instabilities have significant effects on the quality of the crystals. The flow and heat transfer in the LEC GaAs melt are numerically studied by a time-dependent and three-dimensional turbulent flow model. The effects of the change of the buoyancy and Marangoni force on the flow state is analyzed by changing the temperature difference between the crystal and the crucible walls. the results will show the the flow will transform from axisymmetric steady flow to non-axisymmetric oscillatory flow when the temperature difference exceeds the critical value, and that the mechanism of the transition is attributed to the Marangoni instability. Several critical characteristics of the non-axisymmetric buoyant-marangoni convection are numerically observed and compared with that of the non-axisymmetric mixed convection coupled with crystal rotation.