Modal analysis of the triadic interactions in the dynamics of a transitional shock wave boundary layer interaction

Abstract: This work is a numerical study of a transitional shock wave boundary layer interaction (SWBLI). The main goal is to improve our understanding of the well known low-frequency SWBLI unsteadiness and especially the suspected role of triadic interactions in the underlying physical mechanism. To this end, a Direct Numerical Simulation (DNS) is performed using high-order finite volume scheme equipped with a suitable shock capture procedure. The resulting database is then extensively post-processed in order to extract the main dynamical features of the interaction zone (involved characteristic frequencies, characteristics of the vortical structures, etc.). The dynamical organisation and space-time evolution of the flow at dominant frequencies are then further characterised by mean of a Spectral Proper Orthogonal Decomposition (SPOD) analysis. In order to study the role of triadic interactions occurring in the interaction region, a BiSpectral Mode Decomposition (BSMD) analysis is applied to the data base. It allows us to extract the significant triadic interactions, their location and the resulting physical spatial modes. Strong triadic interactions are detected in the downstream part of the separation bubble whose role on the low-frequency unsteadiness is characterised. All the results of the various analyses are then discussed and integrated to formulate a possible mechanism fuelling low-frequency SWBLI unsteadiness.