Modal Analysis of the Triadic Interactions in the Dynamics of a Transitional Shock Wave Boundary Layer Interaction

This work is a numerical study of a transitional shock wave boundary layerinteraction (SWBLI). The main goal is to improve our understanding of the wellknown low-frequency SWBLI unsteadiness and especially the suspected role oftriadic interactions in the underlying physical mechanism. To this end, aDirect Numerical Simulation (DNS) is performed using high-order finite volumescheme equipped with a suitable shock capture procedure. The resulting databaseis then extensively post-processed in order to extract the main dynamicalfeatures of the interaction zone (involved characteristic frequencies,characteristics of the vortical structures, etc.). The dynamical organisationand space-time evolution of the flow at dominant frequencies are then furthercharacterised by mean of a Spectral Proper Orthogonal Decomposition (SPOD)analysis. In order to study the role of triadic interactions occurring in theinteraction region, a BiSpectral Mode Decomposition (BSMD) analysis is appliedto the data base. It allows us to extract the significant triadic interactions,their location and the resulting physical spatial modes. Strong triadicinteractions are detected in the downstream part of the separation bubble whoserole on the low-frequency unsteadiness is characterised. All the results of thevarious analyses are then discussed and integrated to formulate a possiblemechanism fuelling low-frequency SWBLI unsteadiness.