John Hunter, UC Davis

Abstract: Numerical solutions of weak-shock Mach reflections show a sequence of supersonic patches and triple points in a tiny region below the leading triple point. A basic question, with analogs to the existence of shock-free flows over transonic airfoils, is whether it is possible to have only a single shock-free supersonic patch and triple point behind the Mach stem, or must there be multiple triple points. We explore this question using the steady transonic small disturbance equation as the simplest model equation. Assuming the hodograph transformation is invertible near the triple point, we formulate an oblique derivative Tricomi problem for the Tricomi equation as a local description of shock-free flows behind the Mach stem and discuss its solvability.