A transitional hydrogen–air non-premixed impinging jet flame is studied using three-dimensional direct numerical simulation (DNS) and flamelet generated manifolds (FGM) based on detailed chemical kinetics. The simulations are used to investigate the buoyancy instability and the spatial and temporal patterns of the impinging jet flame. The computational domain employed has a size of 4 jet diameters in the streamwise direction and 12 jet diameters in the cross-streamwise direction. The results presented in this study were performed using a uniform Cartesian grid with 200 × 600 × 600 points. Reynolds number used was Re = 2000, based on the inlet reference quantities. The spatial discretisation was carried out using a sixth-order accurate compact finite difference scheme and the discretised equations were advanced in time using a third-order accurate fully explicit compact-storage Runge–Kutta scheme. Results show that the buoyancy and jet shear instability lead to form both inner and outer vortical structures in the primary and wall jet regions, thus complex spatial and temporal variations occur in the mixture fraction, progress variable and temperature fields. Moreover, DNS results suggest that the near-wall vortical structures play an important role in the near-wall heat transfer. These findings may provide useful guidelines for the near-wall combustion modelling using Reynolds-averaged Navier–Stokes modelling or large eddy simulation techniques.