The transient state of natural convection in a vertical cylindrical enclosure is studied numerically for water at high Rayleigh numbers, extending into values characteristic of the turbulent flow regime. Several two-equation turbulence models are used for this purpose. Heating is provided along the cylindrical surface at a constant heat flux, with the horizontal bounding surfaces being adiabatic and the development of stratification is studied. Such a configuration is very relevant to thermal storage tanks or solar thermal system vessels and the study aims at providing insight into the behavior of the system at the boundary between laminar and turbulent flow so that the appropriate numerical treatment may be adopted in future studies. The main aspect ratio considered is L/D = 1 and the Rayleigh number (based on the length L) varies in the range 10(10) greater than or equal to Ra greater than or equal to 10(13) for laminar flow and 5 x 10(13) greater than or equal to Ra greater than or equal to 10(15) for turbulent flow, values for which previous data in the literature are all but non-existent. The attainment of a quasi-steady state is achieved after the fluid undergoes an oscillating pattern where secondary flows alternately appear and vanish. These patterns affect the development of stratification in the vessel, Low-Reynolds k-epsilon models predict eventually a relaminarization at large times, but models employing the high-Re form of the k-epsilon model obtain sustained or very slowly decaying turbulence instead. Comparisons are made with experimental results where applicable.