Causality in the shock wave/turbulent boundary layer interaction

TL;DR

This study investigates the physical mechanisms behind low-frequency unsteadiness in shock wave/turbulent boundary layer interactions at Mach 2, revealing a causal feedback loop and upstream traveling waves through numerical simulations and spectral analysis.

Contribution

It introduces a novel analysis of causality and feedback mechanisms in shock interactions using transfer functions and spectral decomposition, supported by large-eddy simulation data.

Findings

Low-frequency unsteadiness is mainly two-dimensional and can be isolated by spanwise averaging.

Transfer functions reveal a feedback mechanism between downstream flow and shock fluctuations.

Spectral modes confirm upstream traveling waves and enable energy reconstruction in the interaction zone.

Abstract

The mechanisms governing the low-frequency unsteadiness in the shock wave/turbulent boundary layer interaction at Mach 2 are considered. The investigation is conducted based on the numerical database issued from large-eddy simulations covering approximately 300 cycles of the low-frequency shock fluctuations. The evaluation of the spectrum in the interaction zone indicates that the broadband low-frequency unsteadiness is predominantly two-dimensional, and can be isolated via spanwise averaging. Empirically derived transfer functions are computed using the averaged flow field, and indicate the occurrence of a feedback mechanism between downstream flow regions and shock fluctuations. The transfer functions are also used as an estimation tool to predict the shock motion accurately; for the largest streamwise separation between input and output signals, correlations above 0.6 are observed between predicted and LES data. Computation of spectral proper orthogonal decomposition (SPOD) modes confirms the existence of upstream traveling waves in the leading spectral mode. Finally, the spectral modes obtained using selected flow regions downstream of the shock enable the reconstruction of a significant portion of the energy in the interaction zone. The current results shed further light on the physical mechanisms driving the shock motion, pointing towards a causal behavior between downstream areas and the characteristic unsteady fluctuations at the approximate shock position.