The dual solution stability gap bounded by sub- and supercritical geometric thresholds in steady shock reflection

TL;DR

This study identifies a stability gap between regular and Mach reflection in steady shock reflection, revealing conditions under which flow configurations transition dynamically, confirmed through numerical simulations.

Contribution

The paper introduces the concept of a dual-solution stability gap in shock reflection, highlighting the dynamic transition possibilities between regular and Mach reflections.

Findings

A stability gap exists between RR and MR in shock reflection.

Numerical simulations confirm dynamic transitions including RR to MR and vice versa.

Complex flow structures are observed during these transitions.

Abstract

In this paper, we examine the significance of the lower geometric limit, defined as the trailing-edge height at which the reflected shock grazes the trailing edge, for both regular reflection (RR) and Mach reflection (MR). We show that this lower limit for MR is greater than that for RR, within the dual-solution domain away from its lower and left boundaries. We thus identify a dual-solution stability gap lying between the subcritical threshold (the lower limit for RR) and the supercritical threshold (the lower limit for MR). Within this gap RR is stable while MR is unstable, implying a new dynamic transition possiblity there: a steady RR configuration (start flow) can undergo a dynamic transition to an unstable MR state (unstart flow) under suitable disturbance of density or other flow parameters. Numerical simulations confirm the existence of this stability gap and illustrate the time history of dynamic transitions, including (1) direct transitions from RR to MR to unstart flow, with complex flow structures such as hybrid MR-type VI shock interference and double MR -- MR reflections, and (2) inverted transitions, in which RR first shifts to MR and then returns back to RR.