Direct numerical simulations were performed for the transitional and turbulent natural-convection boundary layer for air and water along a hot vertical flat plate. The numerical results for water well reproduce the vortex-like structures as observed experimentally in the thermal field for a high Prandtl-number fluid. When the calculated values are evaluated with the integral thickness of the velocity boundary layer as a length scale, the turbulence statistics such as heat transfer rate, mean velocity, mean temperature, intensity of velocity and temperature fluctuations, Reynolds shear stress and turbulent heat fluxes correspond relatively well with those obtained from the experiments for space-developing flows. This shows that the time-developing direct numerical simulation of the natural-convection boundary layer can provide details that are difficult to obtain in experiments. These data are of great importance to understand the turbulence structures. (C) 2009 Elsevier Ltd. All rights reserved.