The collision of two subsonic auto-ignition fronts with initial constant velocity was found to transit to detonation only when the collision angle was acute. The interaction of the reactive phase wave with inert hot layers constituted a singularity providing a continuous source of vorticity due to barocline effect. For an acute angle, this singularity that propagated at supersonic speed induced oblique pressure waves, of which resonance, due to the reactivity gradient geometry, near the center of the channel in the fresh gases accelerated the reactive wave fronts until transition to detonation. The numerical results of the present study, even if based on drastic assumptions, were at least in good qualitative consistency with experiments. The geometry of the reactivity gradients can thus provide another seed for the coupling between gas dynamics and heat release. Continuous pressure fluctuations and oblique shocks coming from vorticity sources and sheets from barocline effects can considerably enhance this transition. This path to transition could be complementary to that invoking mixing burning within premixed non-planar turbulent flame brush.