The temporal evolutions of small, streamwise elongated disturbances in the asymptotic suction boundary layer (ASBL) and the Blasius boundary layer (BBL) are compared. In particular, initial perturbations localized (δ-functions) in the wall-normal direction are studied, corresponding to an axi-symmetric jet coming out of a plane parallel to the flat plate. Analytical solutions are presented for the wall-normal and streamwise velocities in the ASBL case whereas both analytical and numerical methods are used for the BBL case. The initial position of the perturbation and its spanwise wave number are varied in a parameter study. We present results of maximum amplitudes obtained, the time to reach them, their position and optimal spanwise scales. Free-stream disturbances are shown to migrate towards the wall and reach their (negative) optimum inside the boundary layer. The migration is faster for the ASBL case and a larger amplitude is reached than for the BBL. For perturbations originating inside the boundary layer the amplitudes are overall larger and show the phenomenon of overshoot, i.e. positive amplitudes moving out of the boundary layer. The overall largest amplitudes are obtained for the BBL case, as in other studies, but it is shown that for free-stream disturbances initiated somewhere downstream the leading edge streak growth may be amplified due to suction since in the BBL the disturbance mainly advects above the boundary layer.

Bypass transition has been studied by theoretical and numerical procedures, with the asymptotic suction boundary layer (ASBL) in focus. As reference cases the Blasius boundary layer (BBL) and a free shear flow have been studied. In order to reduce energy losses associated with flow systems, it is a wish to avoid turbulence in these flows. It is thus necessary to have a fundamental understanding of the mechanisms behind bypass transition, which typically starts with the formation and growth of structures extended in the streamwise direction, so called streaks. One way of delaying the transition to turbulence is to apply wall suction, which is also known to stabilize streaks. In this work, it is shown that the stabilizing mechanism of wall suction is not unambiguous. A theoretical study on the linear evolution of streaks triggered by a localized disturbance is performed. Releasing the disturbance in the free-stream, it will migrate towards the wall and quickly be subject to shear. Consequently, this disturbance is amplified when applying wall suction, provided that for the suction-free case the growth of the BBL may be considered small. When initiating the disturbance inside the boundary layer, on the other hand, it is found that suction stabilizes the growth of such a streak. Also, the non-linear properties of suction are studied using a model with prescribed wall-normal disturbance velocity identical for the ASBL and the BBL. Despite the similarity, suction is shown to dampen the non-linear forcing of the perturbation. Moreover, the non-linear response is shown to favor the forcing of streamwise longitudinal (3D) structures and 2D waves. For the ASBL, also energy thresholds for transition of periodical disturbances have been determined by direct numerical simulations. The least energy required to reach transition is obtained when the initial flow field consists of two oblique waves, for which the threshold value is found to scale as Re^{-2.6}. For transition starting with streamwise vortices or random noise the threshold scales like Re^{-2.1} (Re being the Reynolds number), and the routes to transition are similar to that of other flows. A theoretical framework for evaluating the non-linear interaction terms of the normal- velocity/vorticity equations is also developed. This formulation allows for study of wave interaction throughout the whole wavenumber plane, i.e. for any given wave number of a disturbance. The framework has been applied to a free shear flow, which shows that primarily streamwise elongated structures and Tollmien-Schlichting waves are forced by the non-linear interactions. Besides that, the geometrical interpretation shows that the non-linear interaction involving normal vorticity is most potent for structures inter-angled by 90 degrees in the wavenumber plane.

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 study on 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.

Energy thresholds for transition to turbulence in an asymptotic suction boundary layer is calculated by means of temporal direct numerical simulations. The temporal assumption limits the analysis to periodic disturbances with horizontal wave numbers determined by the computational box size. Three well known transition scenarios are investigated: oblique transition, the growth and breakdown of streaks triggered by streamwise vortices, and the development of random noise. Linear disturbance simulations and stability diagnostics are also performed for a base flow consisting of the suction boundary layer and a streak. The scenarios are found to trigger transition by similar mechanisms as obtained for other flows. Transition at the lowest initial energy is provided by the oblique wave scenario for the considered Reynolds numbers 500, 800, and 1200. The Reynolds number dependence on the energy thresholds are determined for each scenario. The threshold scales like Re-2.6 for oblique transition and like Re-2.1 for transition initiated by streamwise vortices and random noise, indicating that oblique transition has the lowest energy threshold also for larger Reynolds numbers.