Frequency response of the swept-wing three-dimensional boundary layer

Three dimensional boundary layers are well known for being subject to the growth of perturbations and transition to turbulence well below the linear stability threshold. Both their linear stability and the temporal transient growth have been analyzed in previous studies. In this work we focus on the response of the swept-wing attachment-line boundary layer to periodic external forcing — e.g. incoming turbulence or wall roughness — and we analyze the response amplitude in multiple system norms. In particular, the induced $||\cdot||_2$ norm (aka singular value norm) identifies the peak gain at a given forcing frequency. The input-output gain and the spacial structures associated with each frequency are identified by singular value decomposition and discussed.