Comparative Study of Linear Interaction Analysis and DNS for Shock-Vorticity Interaction: Scaling of Non-Linear Terms

Abstract

Interaction of shock waves with turbulence is a complex problem in high-speed flows. Linear interaction analysis (LIA) is a theoretical tool used to predict the shock-induced turbulence amplification. It is based on the elementary interaction of a two-dimensional disturbance wave with a normal shock. In this work, we assess the accuracy of LIA when compared to high-order numerical simulation of shock-vorticity wave interaction. We present results for a range of upstream wave amplitudes and orientations, at different shock Mach numbers. The deviation between LIA and DNS is, as expected, a strong function of wave inclination angle and mean flow Mach number. We perform secondorder error analysis using Rankine-Hugoniot relations to find scaling parameters that can characterize these deviations. We find that the deviations scale with the square of the sine of the downstream vorticity wave angle at a given Mach number and with the square of the mean compression ratio across the shock at a given upstream incidence angle.