Information-theoretic causal inference for shock wave/boundary layer interaction

We performed direct numerical simulations on a shock wave/turbulent boundary layer interaction with freestream Mach number of 1.9, momentum thickness Reynolds number of 1327, and shock angle of 39.27 degrees. We investigated the causal relationships between a shock wave-induced separation bubble and a reflected shock wave based on information theory. The large separation bubbles are considered to induce oscillation of the shock wave. The proper orthogonal decomposition (POD) was applied to the DNS data to extract the characteristic spatial modes of both the separation bubble and the compression waves forming the reflected shock wave. The POD also extracted the time coefficients representing the time evolution of each spatial mode and yielding the transfer entropy between them. The transfer entropy was used to quantify the causality between each mode and revealed that the overall trend of a causal relationship from the separation bubble to the pressure field. These results indicate that the pressure waves emitted from the separation bubble propagate information to the reflected shock wave.