  This study aims to shed light on hypersonic attachment-line instabilities
with large sweep Mach numbers. Highly swept flows over a cold cylinder that
give rise to large sweep Mach numbers are studied. High fidelity base flows are
obtained by solving full Navier-Stokes equations with a high-order
shock-fitting method. Using local and global stability theories, an
attachment-line mode is found to be dominant for the laminar-turbulent
transition along the leading edge that agrees well with experimental
observations Gaillard1999. The behavior of this mode explains the reason why
the transition occurs earlier as the sweep Mach number is above 5. Also, this
attachment-line mode is absent if the base flow is calculated with
boundary-layer assumptions, indicating that the influence of inviscid flow
outside the boundary layer can not be ignored as is normally done. It is
clearly demonstrated that the global modes display the features of both
attachment-line modes, as in sweep Hiemenz flow, and cross-flow-like modes
further downstream along the surface. In contrast to incompressible flows, the
mode is shown to be of inviscid nature. Moreover, the leading-edge curvature
has a destabilizing effect on the attachment-line mode for large spanwise wave
numbers but a stabilizing effect for small spanwise wave numbers.
