The dual-solution stability gap and dynamic transition from steady regular reflection to unstable Mach reflection

For regular reflection (RR) and Mach reflection (MR), the critical parameter of the trailing-edge height ( HR,min ), at which the reflected shock grazes the trailing edge, is the critical condition for stable and unstable reflection. A proof of the statement that HR,min for MR is larger than HR,min for RR, within some region in the dual-solution domain, is important for confirming the existence of a dual-solution stability gap, within which RR is stable while MR is unstable. This proof is accomplished here by transitivity, with the intermediate value corresponding to the minimum height of the Mach stem. By establishing a bridge between the evaluation of HR,min for MR and that of the linear coefficients for Mach stem height variation with the trailing-edge height, we overcome the difficulty of quantifying HR,min exactly, and show that the difference between HR,min for MR and HR,min for RR is significant, meaning that there is a large enough dual-solution stability gap. The confirmation of this gap has further impact on shock transition, suggesting a new transition scenario: stable to unstable dynamic transition, i.e., within the dual-solution stability gap, a stable RR can undergo a dynamic transition to an unstable MR state (unstart flow) under suitable disturbance of the flow parameters. This dynamic transition is demonstrated here numerically. The time history of dynamic transitions displays (i) 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 (ii) inverted transitions, in which RR first shifts to MR and then returns back to RR.