Regions and Boundaries for Diffracting Shock Wave Systems

Abstract

AbstractThis paper examines, as completely as possible, the wave systems that may occur when a plane shock wave i diffracts over a concave corner. For a perfect gas, a particular wave system is specified by three parameters (γ, ϵi, ωo), which are respectively the ratio of the specific heats γ, the inverse strength ϵi of i, and its angle of incidence ωo. The topology of the (ϵi, ωo) plane is studied for a given γ (gas), and regions or domains corresponding to each wave system are delineated. Exact expressions are given for the boundaries of many of these regions. Although it is plausible that the boundaries represent the transition conditions between the wave systems, a detailed analysis shows that the situation is sometimes more complicated than might be expected. A new transition criterion, which may be valid for diffraction over flexible surfaces, is presented. For very weak shocks (ϵi > 0.8328 in air), it is found that Mach reflexion cannot exist, and in its place a continuous wave system is indicated.