A direct numerical simulation has been performed for the case of a natural convection flow between two differentially heated vertical walls for a range of Rayleigh numbers (5.4 x 10(5) < Ra < 5.0 x 10(6)). The simulation data are compared with experimental data of Dafa-Alla and Betts [Experimental study of turbulent natural convection in a tall cavity, Exp. Heat Transfer 9 (1996) 165-194] and the agreement is found to be acceptable, Given the numerical data we consider the scaling behaviour of the mean temperature, the mean velocity profile and of the profiles of various turbulence statistics. Point of departure is the approach proposed by George and Capp [A theory for natural convection turbulent boundary layers next to heated vertical surfaces, Int. J. Heat Mass Transfer 22 (1979) 813-826] who have formulated scaling relationships valid, respectively, in the near-wall inner layer and in the outer layer in the centre region of the channel. Matching of the scaling relationships in the overlap between the inner and outer region leads to explicit expressions which can be used as wall functions in computational procedures, The DNS data confirm the results of George and Capp for the scaling of the mean temperature profile. For the mean velocity profile our DNS data support another scaling in terms of a defect law for the velocity gradient in the inner layer. The scaling of George and Capp is also found to apply to the Reynolds stress, the temperature variance and the temperature fluxes. However, the velocity variances again seem to follow a different scaling.