Global receptivity of instability waves in the boundary layer on a high-speed blunt cone

Unstable waves in parallel and near-parallel compressible boundary layers are well studied and can be important to boundary layer transition on flight vehicles in low disturbance environments. What is less well understood are the processes that occur near leading edges or in complex regions of the flow where these waves are incepted. Understanding the early stages in the development of instabilities is key to enabling accurate transition models that do not require calibration with flight test data. In this work the global direct and adjoint eigenvalue problems for the linearized compressible Navier-Stokes equations are solved on a spherically blunted cone. The results provide insight into the evolution of waves which later become unstable and are reminiscent of Mack’s second mode as the boundary layer approaches a nearly parallel state. In addition to visualizing the 2D structure of these waves, their receptivity can be inferred from the adjoint eigenvectors which provide insight into important mechanisms governing their excitation due to disturbances in the freestream.