| It has been acknowledged for a long time that the leading-edge boundary layer of a swept wing plays a critical role in the generation of skin friction. Instabilities in the swept leading-edge boundary layer can trigger the transition to a turbulent boundary layer already in the attachment-line region thereby increasing the overall skin friction substantially. Research has identified conditions for which this flow becomes linearly unstable. However, a concise linear stability theory is still lacking.; In this work we develop a linear stability theory for this flow. We derive, discuss, and classify the modal solutions of the global stability problem. The acquired knowledge is then used to study transient growth phenomena and the receptivity to free stream disturbances. We find that the complex structure of this flow forces us to generalize the classical concepts of transient growth and receptivity, leading us to unexpected conclusions.; In addition to these theoretical contributions we discuss the numerical methods that are used to study this flow. A direct numerical simulation based on a Fourier-Chebyshev spectral method is presented including a discussion of the fringe region technique. Special emphasis is put on a Hermite spectral method. This method serves equally well as both a numerical and an analytical tool. It is shown that the close interplay between the Hermite spectral method and the physics of the swept leading-edge boundary layer is the key to a full understanding of the linear dynamics of this flow. |
