Melt flows associated with a Czochralski crystal growth process was investigated to better understand the transition from a steady laminar regime to an unsteady one as the Grashof number increases. The kinetic energy of the flow as a function of time was examined as an indication of stability. Three-dimensional solutions were interpolated onto a two-dimensional unstructured mesh to compute the Reynolds average mean flow and its fluctuations. Our simulations showed that the transition to unsteady three-dimensional flow begins at a Grashof number of approximately 3.0 million. At higher Grashof numbers (e.g., 6.6 million), the melt flow is fully unsteady, three-dimensional turbulent flow. The simulations further indicated that the melt flow at a Grashof number of 6.6 million is statistically stable, which suggested the Reynolds quasi-steady assumption is valid in this case.