Tokamak experiments have revealed that the L - H power threshold depends on the ion drift direction. This experimental result could be explained by resistive interchange micro-instabilities in the SOL. It is shown that the sheath resistance near the target plates depends on the direction of the longitudinal SOL current. In conjunction with the curvature of the toroidal magnetic field and the ion drift direction, these effects lead to an asymmetry in the turbulence near the plasma edge; hence a different L - H power threshold is required to reduce this turbulence.