Distinguished scaling and UTSD structure in weak shock reflection at nearly glancing incidence

July 23, 2026Transport Phenomena

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This research aims to explore the reflection of weak shocks from rigid walls at nearly glancing incidences and determine the governing parameters.
Analyzed weak shock reflection using the unsteady transonic small-disturbance equation under distinguished scaling M = 1 + λα².
Calculated the physical trajectory angle and detachment values based on the Mach-number strength scale and parameters derived from the UTSD equations.
Derived self-similar reductions and formal adjoint solvability expressions for corrections and characterizations.
Identified that the inner reflection region in weak shocks is governed by a single parameter a₀ = 1/(2√λ).
Established a relationship between the distinguished scaling and detachment value, finding λ_d = 1/8 for Guderley–Mach reflection when λ > 1/8.
Formulated an expression for the physical trajectory angle involving the Mach-number strength scale and canonical UTSD trajectory function.

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Investigates weak shock reflection behavior in nearly glancing incidences, suggesting unique scaling properties.

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Justin Kin Jun Hew (2026) studied this question.

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