A numerical study of natural convection in cavity filled with air has been carried out under large temperature gradient. The flows under study are generated by a heated solid body located close to the bottom wall in a rectangular cavity with cold vertical walls and insulated horizontal walls. They have been investigated by direct simulations using a two-dimensional finite volume numerical code solving the time-dependent Navier-Stokes equations under the low Mach number approximation. This model permits to take into account large temperature variations unlike the classical Boussinesq model which is valid only for small temperature differences. We were particularly interested in the first transitions which occur when the Rayleigh number is increased for flows in cavities of aspect ratio A = 1, 2,4. Starting from a steady state, the results obtained for A = 1 and A = 4 show that the first transition occurs through a supercritical Hopf bifurcation. The induced disturbances determined for weakly supercritical regimes indicate the existence of two instability types driven by different physical mechanisms: shear and buoyancy-driven instabilities, according to whether the flow develops in a square or in a tall cavity. For A = 2, the flow undergoes a pitchfork bifurcation leading to an asymmetric steady state which in turn becomes periodic via a supercritical Hopf bifurcation point. In both cases, the flow is found to be strongly deflected towards one vertical wall and instabilities are found to be of shear layers type. (c) 2006 Elsevier Ltd. All rights reserved.