Proceedings of the Royal Society of London A Mathematical and Physical Sciences · 1949 · 180 citations · 0 references
Natural SciencesPhysicsAcousticsFluid DynamicsFluid MechanicsAcoustic Wave PropagationDiffractionShock ResponseShock WavesAcoustic Field TheoryMach Number EffectsShock DynamicsShock Wave InteractionsShock Wave PropagationShock Wave StructureShock-wave DiffractionShock-wave Interaction
The study aims to provide a foundation for later analyses of flow around walls with non‑small corner angles. Using a linearized anisentropic flow theory, the authors model a plane shock encountering a small‑angle corner, computing the shock shape and wall pressure distribution for Mach numbers from 1 to infinity. They find that a convex corner produces pure diffraction while a concave corner yields Mach reflection, and that weak shocks connect to acoustic theory.
The behaviour of a plane shock, of any strength, travelling along a wall, when it reaches a corner where the wall turns through a small angle δ , is investigated mathematically by use of a linearized theory of anisentropic flow (§§ 2 to 5). At a convex corner pure diffraction occurs; at a concave corner Mach reflexion (§8). The shape of the shock (§6) and the pressure distribution over the wall (§7) are calculated for a variety of shock Mach numbers from 1 to ∞. The connexion, for weak shocks, with acoustic theory, is displayed (§9). The work will be used in later parts to assist in a hypothetical description of the flow when δ is not small.