A collection of secondary instability calculations in streaky boundary layers is presented. The data are retrieved from well-resolved numerical simulations of boundary layers forced by free-stream turbulence (FST), considering different geometries and FST conditions. The stability calculations are performed before streak breakdown, taking place at various $Rey_x$ the Reynolds number based on the streamwise coordinate. Despite the rich streak population of various sizes, it is found that breaking streaks have similar aspect ratios, independently of the streamwise position where they appear. This suggests that wider streaks will break down further downstream than thinner ones, making the appearance of secondary instabilities somewhat independent of the streak's wavelength. Moreover, the large difference in the integral length scale among the simulations suggests that this aspect ratio is also independent of the FST scales. An explanation for this behaviour is provided by showing that these breaking streaks are in the range of perturbations that can experience maximum transient growth according to optimal disturbance theory. This could explain why, at a given streamwise position, there is a narrow spanwise wavelength range where streak breakdown is more likely to occur.

This thesis deals with the laminar-turbulent transition process in boundary layers induced by free-stream turbulence (FST), commonly referred to as bypass transition. The investigation has been carried out using direct numerical simulations (DNS), stability analysis, and control theory. The various aspects of bypass transition considered in this work can be grouped into two categories: open and closed-loop dynamics. 

The open-loop dynamics span from the inception to the breakdown of instabilities, driving the flow from a laminar to a turbulent state. A broader understanding of this process could inspire new and more accurate models for transition prediction, which is of great interest in many engineering applications. In this context, stability theory provides an excellent framework to study the pre-transitional flow. This work has confirmed the relevance of optimal disturbance theory in realistic flow conditions, and how its inexpensive computations can provide valuable information regarding the most 'dangerous' disturbances in terms of their amplification. The key role of streak secondary instabilities in bypass transition has also been studied. They constitute the main cause of transition in a flat plate simulation considering realistic wind tunnel conditions. By comparing the secondary instabilities leading to breakdown in different geometries and FST compositions, it has been found that their hosting streaks feature similar aspect ratios, regardless of their streamwise position. An explanation for this apparent size preference has been provided based on optimal growth and energy propagation due to non-linear interactions.

The closed-loop dynamics address how new inputs can steer the system to a desired state based on operational information extracted from the system. In boundary layers, delaying transition is an attractive idea for energy savings due to the lower drag associated with a laminar state. This work explores this possibility with the use of control theory in reduced-order models constructed solely on input/output data from DNS. The methods are restricted to being equally feasible in experiments. Here, streak attenuation is successfully achieved based only on wall measurements and wall localised actuation. It has been shown that the dissimilar performances regarding transition delay are connected to the controller's capabilities of acting on breaking streaks.

Denna avhandling behandlar den laminära-turbulenta övergångsprocessen i gränsskikt inducerad av friströmsturbulens (FST), vanligen kallad bypass-transition. Studien har genomförts med hjälp av direkta numeriska simuleringar (DNS), stabilitetsanalys och reglerteknik. Två typer av bypass-transition beaktas, omslagsprocessen utan reglerteknisk påverkan och med användning av reglerteknik. 

Omslagsprocessen utan användning av reglerteknik handlar till stor del om hur instabiliteter växer och bryter ner strömningen till turbulens.  En bredare förståelse av denna process kan resultera i bättre metoder för att förutsäga laminärt-turbulent omslag, vilket är av stort intresse i många tekniska tillämpningar. I detta sammanhang ger stabilitetsteori ett utmärkt ramverk för att studera strömningen före omslaget sker. Vårt arbete har bekräftat relevansen av sk ``optimal störningsteori'' i realistiska situationer, och hur de kan ge värdefull information om de mest ``farliga'' störningarna. Nyckelrollen av sekundärinstabiliteter har också studerats. De utgör huvudorsaken till övergången till turbulens för strömningen över vingar och plana plattor där strömningen i friströmmen innehåller tillräckligt med turbulens. Genom att jämföra sekundärinstabiliteterna som leder till sammanbrott i olika geometrier har det visat sig att långa strukturer av hög- och låghastighetsstråk med liknande förhållande mellan spännvidds och vertikal skalor är associerade med sammanbrott till turbulens. En förklaring för denna storlekspreferens baseras på optimal tillväxt tillsammans med icke-linjär interaktion mellan stråk med olika spännvidds skalor. 

Med användning av reglerteknik adresserar vi hur aktuatorer kan styra systemet till ett önskat tillstånd baserat på information som via mätningar extraherats från systemet. I gränsskiktströmning är man intresserad av att fördröja övergång från laminärt till turbulent tillstånd för att åstadkomma energibesparingar genom det lägre motståndet ett laminärt tillstånd har. Detta arbete undersöker möjligheten att använda reglerteknik tillsammans med enkla modeller baserade på analys av på in/utdata från direktsimuleringarna. Metoderna är beskaffade så att de skulle kunna anvädas i en experimentellt. Vi dämpar de stråkstrukturer som finns i gränsskiktsströmningen framgångsrikt. Fördröjningen av laminär-turbulent omslag är kopplade till möjligheten att begränsa amplituden på de stråk som har störst sannolikhet att bryta samman till turbulens via sekundärinstabiliteter. 

We study the stability of a zero-pressure gradient boundary layer subjected to free-stream disturbances by means of local stability analysis. The dataset under study corresponds to a direct numerical simulation (DNS) of a flat plate with a sharp leading edge in realistic wind tunnel conditions, with a turbulence level of 3.45 % at the leading edge. We present a method to track the convective evolution of the secondary instabilities of streaks by performing sequential stability calculations following the wave packet, connecting successive unstable eigenfunctions. A scattered nature, in time and space, of secondary instabilities is seen in the stability calculations. These instabilities can be detected before they reach finite amplitude in the DNS, preceding the nucleation of turbulent spots, and whose appearance is well correlated to the transition onset. This represents further evidence regarding the relevance of secondary instabilities of streaks in the bypass transition in realistic flow conditions. Consistent with the spatio-temporal nature of this problem, our approach allows us to integrate directly the local growth rates to obtain the spatial amplification ratio of the individual instabilities, where it is shown that instabilities reaching an -factor in the range [2.5,4] can be directly correlated to more than 65 % of the nucleation events. Interestingly, it is found that high amplification is not only attained by modes with high growth rates, but also by instabilities with sustained low growth rates for a long time.

The stability of an incompressible boundary layer flow over a wing in the presence of free stream turbulence (FST) has been investigated by means of direct numerical simulations and compared with the linearised boundary layer equations. Four different. FST conditions have been considered, which are characterised by their turbulence intensity levels and length scales. In all cases the perturbed flow develops into elongated disturbances of high and low streamwise velocity inside the boundary layer, where their spacing has been found to be strongly dependent on the scales of the incoming free stream vorticity. The breakdown of these streaks into turbulent spots from local secondary instabilities is also observed, presenting the same development as the ones reported in flat plate experiments. The disturbance growth, characterised by its root mean squares value, is found to depend not only on the turbulence level, but also on the FST length scales. Particularly, higher disturbance growth is observed for our cases with larger length scales. This behaviour is attributed to the preferred wavenumbers that can exhibit maximum transient growth. We study this boundary layer preference by projection of the flow fields at the leading edge onto optimal disturbances. Our results demonstrate that optimal disturbance growth is the main cause of growth of disturbances on the wing boundary layer.

This investigation deals with the numerical implementation of a data-driven method for reactive control of the boundary-layer over a NACA0008 airfoil. The aim of this work is to evaluate the performance of controller in damping the flow disturbances and its efficiency in delaying laminar-turbulent transition. We focus our attention on the bypass transition scenario caused by free-stream turbulence. In this scenario, the perturbations in the wing boundary-layer develop into streaky structures. We show that this data-driven method is effective in decreasing the wall shear stress and disturbance energy at the objective location, and this damping is sustained downstream of the objective location. However, further downstream, the fluctuations grow again reaching amplitudes similar to those in the uncontrolled case.