Analysis of the secondary instability of the incompressible flows over a swept wing

The crossflow instability of a three-dimensional (3-D) boundary layer is an important factor which affects the transition over a swept-wing. In this report, the primary instability of the incompressible flow over a swept wing is investigated by solving nonlinear parabolized stability equations (NPSE). The Floquet theory is applied to study the dependence of the secondary and high-frequency instabilities on curvature, Reynolds number and angle of swept (AOS). The computational results show that the curvature in the present case has no significant effect on the secondary instabilities. It is generally believed that the secondary instability growth rate increases with the magnitude of the nonlinear mode of crossflow vortex. But, at a certain state, when the Reynolds number is 3.2 million, we find that the secondary instability growth rate becomes smaller even when the magnitude of the nonlinear mode of the crossflow vortex is larger. The effect of the angle of swept at 35, 45 and 55 degrees, respectively, is also studied in the framework of the secondary linear stability theory. Larger angles of swept tend to decrease the spanwise spacing of the crossflow vortices, which correspondingly helps the stimulation of 'z' mode.