Abstract <p>The paper presents a numerical analysis of the combustion dynamics in ultralean hydrogen–air mixtures under terrestrial gravity. The effect of convective flows formed during the buoyant rise of the combustion kernel on its spatial structure is studied. Based on the performed analysis, the mechanisms and conditions for the local flame quenching and transition to a downward flame propagation limit are proposed. The upward motion of the hot combustion kernel under buoyancy force leads to a toroidal vortex that defines axial gas-dynamic flow and continuous inflow of the cold, unburnt mixture to the bottom part of the combustion kernel. The structure of the toroidal vortex, along with the associated axial flow and strain, determines the possibility of downward flame propagation along with the heat losses, which may result in local flame quenching. Obtained results supplement existing knowledge on the role of convection in the combustion near the lean flammability limits.</p>