Stability and transition in the suction boundary layer and other shear flows

Abstract: 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.

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