Experimental and Numerical Study of Shock Front Perturbation Decay

Abstract

Perturbations on shock fronts appear in many gas-dynamic configurations, including shock tubes, shock focusing problems, and reactive flows. As a perturbed shock propagates, its front progressively recovers a more planar shape, but the decay rate of finite-amplitude perturbations remains unclear. The objective of this work is to quantify the decay rate of perturbations on inert shock fronts and to identify the physical mechanism responsible for this decay. Three complementary approaches are used: shock tube experiments, two-dimensional Euler simulations, and Geometrical Shock Dynamics calculations. In all three cases, the perturbation amplitude is measured using the Mach-number difference ΔM across the triple-point structure, separating the stronger Mach shock region from the weaker incident shock region. The results show that ΔM decays approximately as 1/t. This behavior is observed consistently in the experiments, Euler simulations, and GSD calculations. The measured decay is therefore closer to the nonlinear 1/t scaling discussed by Whitham than to the t⁻³ᐟ² or t⁻¹ᐟ² decay laws previously reported from linear theory and early experimental interpretations. The agreement between the three approaches shows that the decay is governed by nonlinear wave dynamics along the shock front. In particular, the Mach-number profile along the front can be interpreted as the superposition of two N-wave-like disturbances propagating in opposite directions. The 1/t decay of these N-waves provides a physical explanation for the observed scaling.

This work provides experimental, numerical, and theoretical evidence that finite-amplitude perturbations on inert shock fronts decay according to a nonlinear 1/t law.