Reflections of weak shock waves over wedges are investigated mainly by considering disturbance propagation which leads to a flow non-uniformity immediately behind a Mach stem. The flow non-uniformity is estimated by the local curvature of a smoothly curved Mach stem, and is characterized not only by a pressure increase immediately behind the Mach stem on the wedge but also by a propagation speed. In the case of a smoothly curved Mach stem as is observed in a von Neumann Mach reflection; the pressure increase behind the Mach stem is approximately determined by Whitham's ray-shock theory. The propagation speed of the flow non-uniformity is approximated by Whitham's shock-shock relation. If the shock-shock does not catch up with a point where a curvature of the Mach stem vanishes, a von Neumann Mach reflection appears. The boundary on which the above-mentioned condition breaks results in the transition from a von Neumann Mach reflection to a simple Mach reflection. This idea leads to a transition criterion for a von Neumann Mach reflection, which is algebraically expressed by chi(1) = chi(s) where chi(1) is the trajectory angle of the point on the Mach stem where the local curvature vanishes and is approximately replaced by chi(g) - theta(w) (chi(g) is the angle of glancing incidence, and theta(w) is the apex angle of the wedge) and chi(s) is the trajectory angle of Whitham's shock-shock, measured from the surface of the wedge. For shock Mach numbers of 1.02 to 2.2 and a wedge angle from 0 degrees to 30 degrees, the domains of a von Neumann Mach reflection, simple Mach reflection and regular reflection are determined by experiment, numerical simulation and theory. The present transition criterion agrees well with experiments and numerical simulations.
