Nonlinear reflection of weak shock waves from a rough surface in air

Abstract

Irregular reflection of weak acoustic shock waves occurs under the framework of the von Neumann paradox. In this study, the influence of the surface roughness on the reflection pattern was studied experimentally using spark-generated spherically divergent N-waves of 1.4 cm length reflecting from rigid rough surfaces in air. Dimensions of the roughness were varied from 20 up to 500 μm for different surfaces. A Mach-Zehnder interferometry method was used to reconstruct the pressure waveforms near the surface. The reconstruction was performed by applying the inverse Abel transform to the phase of the signal measured by the interferometer. It was shown that the height of the Mach stem became shorter for surfaces with larger dimensions of the roughness and disappeared when the surface roughness was large enough. Such tendency was also observed in simulations based on the Euler equations where the acoustic source was introduced as a Gaussian-envelope energy injection and the roughness was either sinusoidal or random and described by a Gaussian correlation function. [Work supported by RSF-17-72-10277 and by the Labex CeLyA of Universite de Lyon, operated by the French National Research Agency (ANR-10-LABX-0060/ ANR-11-IDEX-0007).]Irregular reflection of weak acoustic shock waves occurs under the framework of the von Neumann paradox. In this study, the influence of the surface roughness on the reflection pattern was studied experimentally using spark-generated spherically divergent N-waves of 1.4 cm length reflecting from rigid rough surfaces in air. Dimensions of the roughness were varied from 20 up to 500 μm for different surfaces. A Mach-Zehnder interferometry method was used to reconstruct the pressure waveforms near the surface. The reconstruction was performed by applying the inverse Abel transform to the phase of the signal measured by the interferometer. It was shown that the height of the Mach stem became shorter for surfaces with larger dimensions of the roughness and disappeared when the surface roughness was large enough. Such tendency was also observed in simulations based on the Euler equations where the acoustic source was introduced as a Gaussian-envelope energy injection and the roughness was either sinusoidal or r...