Origin of hysteresis in shock wave reflection

TL;DR

This paper explains the hysteresis observed in shock wave reflection transitions by proposing a higher-dimensional surface model where stable configurations correspond to valley lines, validated by experiments and simulations.

Contribution

It introduces a novel higher-dimensional surface perspective to understand hysteresis in shock wave reflection transitions, linking saddle-node bifurcations to transition points.

Findings

The hysteresis loop is a projection of a higher-dimensional valley surface.

Stable reflection configurations align with minimal values on the surface.

Experimental and numerical results support the proposed model.

Abstract

We report the mechanism of the hysteresis in the transition between Regular and Mach reflections. A new discovery is that, the hysteresis loop is in fact the projection of a higher dimensional path, i.e. the valley lines in the surface of dissipation, of which minimal values correspond to stable reflection configurations. Since the saddle-nodes bifurcate the valleies of the surface, they are actually the transition points of the two reflections. Furthermore, the predicted reflection configurations agree well with the experimental and numerical results, which is a validation of this theory.