| The purpose of this study is to shed more light on the role of surface perturbations and the laminar separation bubble associated with them on the boundary-layer instability and to explore this important flow problem in fluid dynamics further. To accomplish this, the stability characteristics of the separated flow over a flat plate are studied first by means of finite-difference solutions to the unsteady Navier-Stokes (N-S) equations in two-dimensions in stream-function vorticity form using a direct matrix solver. The laminar separation bubble is generated by imposing a decelerated velocity profile at the farfield boundary of the integration domain. The resulting flow field is perturbed by introducing small-amplitude Tollmien-Schlichting (T-S) waves of various frequencies upstream of the bubble. The time-accurate analysis shows that the bubble acts as a strong amplifier of these flow disturbances. A highly nonlinear flow field is shown to develop downstream of the bubble, and strong vortex shedding are shown to occur. Consequently, the results of the direct numerical simulation differ noticeably from those of classic linear stability theory, Orr-Sommerfeld (O-S) solutions, proving that the nonparallel effects, together with the nonlinear interactions, are crucial in this flow problem.; Next, the stability characteristics of the separated flow over a hump are studied by solving the unsteady N-S equations in generalized coordinates numerically. A strong nonlinear interaction between the T-S wave and the separation bubble, formed on the lee-side of the hump, is shown to occur, and it results in periodic shedding of blobs of vorticity from the bubble. This nonlinear interaction, together with the nonparallel flow effects, leads to discrepancies between the growth of the T-S waves predicted by linear (parallel) stability theory and the growth observed in the present simulation. |
