Linear and nonlinear development of perturbations in the asymptotic suction boundary layer

Abstract: Turbulent processes play an important role in most flow systems. To optimize and control these flows, knowledge about the mechanisms that leads to and maintains turbulence is crucial. Boundary layers with wall suction are known to delay/prevent transition as well as separation. Therefore it is a promising example of passive flow control which may reduce losses in many industrial energy conversion systems. Of particular interest is the asymptotic suction boundary layer (ASBL). It is reached downstream of a Blasius boundary layer (BBL) as spatially uniform and steady suction is applied over a large area. This flow is parallel, has an analytically well-defined velocity profile and hence serves as an ideal model flow to evaluate transition mechanisms. Experimentally, a common observation for boundary layers subject to free stream turbulence is that streamwise elongated structures (streaks) pre-date transition to turbulence. Moreover, streaks appear also well into the turbulent regime. In this perspective, a studyon the formation, growth and instability of streaks should provide insight on the stabilising effects of wall suction. This licentiate thesis is devoted to theoretical studies of the ASBL. The focus lies in investigating the mechanisms involved in disturbance growth and transition, but also on the comparison with the corresponding suction-free flow (i.e. the BBL). The thesis consists of three papers. In the first paper, the transient growth of streaks is studied. The streak is created by the lift-up of a localized initial disturbance given by a delta function, and the Orr-Sommerfeld/Squire system of equations is solved as an initial value problem for both the ASBL and the BBL. An analytical solution is obtained for the ASBL, for which disturbances initiated in the free-stream is found to move towards the wall with the suction velocity. A parameter study shows that the most amplified disturbances are obtained when placed inside the boundary layer, and that the overall largest growth is obtained for the BBL. In the second paper, the nonlinear evolution of a localized model disturbance is followed and compared for the two flow cases. The model prescribes an identical wall-normal velocity for these flow cases, thus the slight difference obtained originate only from the Squire equation. In the last paper, the transition process in the ASBL is studied by means of temporal direct numerical simulations. Several scenarios are investigated and the most competitive in terms of transition for the lowest initial energy is outlined.