Non-uniqueness of solutions in asymptotically self-similar shock reflections

TL;DR

This paper investigates how initial conditions influence shock reflection types in self-similar flows, revealing that the flow's history affects whether regular or Mach reflection occurs, with significant differences based on start-up conditions.

Contribution

It demonstrates that shock reflection outcomes depend on initial start-up conditions, showing non-uniqueness in solutions for the same flow parameters.

Findings

Shock reflection type depends on start-up conditions.

Transition angles differ between straight and curved wedge tips.

Flow 'remembers' initial conditions, affecting shock behavior.

Abstract

The present study addresses the self-similar problem of unsteady shock reflection on an inclined wedge. The start-up conditions are studied by modifying the wedge corner and allowing for a finite radius of curvature. It is found that the type of shock reflection observed far from the corner, namely regular or Mach reflection, depends intimately on the start-up condition, as the flow "remembers" how it was started. Substantial differences were found. For example, the type of shock reflection for an incident shock Mach number $M=6.6$ and an isentropic exponent $\gamma =1.2$ changes from regular to Mach reflection between $44^\circ$ and $45^\circ$ when a straight wedge tip is used, while the transition for an initially curved wedge occurs between $57^\circ$ and $58^\circ$.