<p>Transition from laminar to turbulent flow has beentraditionally studied in terms of exponentially growingeigensolutions to the linearized disturbance equations.However, experimental findings show that transition may occuralso for parameters combinations such that these eigensolutionsare damped. An alternative non-modal growth mechanism has beenrecently identified, also based on the linear approximation.This consists of the transient growth of streamwise elongateddisturbances, mainly in the streamwise velocity component,called streaks. If the streak amplitude reaches a thresholdvalue, secondary instabilities can take place and provoketransition. This scenario is most likely to occur in boundarylayer flows subject to high levels of free-stream turbulenceand is the object of this thesis. Different stages of theprocess are isolated and studied with different approaches,considering the boundary layer flow over a flat plate. Thereceptivity to free-stream disturbances has been studiedthrough a weakly non-linear model which allows to disentanglethe features involved in the generation of streaks. It is shownthat the non-linear interaction of oblique waves in thefree-stream is able to induce strong streamwise vortices insidethe boundary layer, which, in turn, generate streaks by thelift-up effect. The growth of steady streaks is followed bymeans of Direct Numerical Simulation. After the streaks havereached a finite amplitude, they saturate and a new laminarflow, characterized by a strong spanwise modulation isestablished. Using Floquet theory, the instability of thesestreaks is studied to determine the features of theirbreakdown. The streak critical amplitude, beyond which unstablewaves are excited, is 26% of the free-stream velocity. Theinstability appears as spanwise (sinuous-type) oscillations ofthe streak. The late stages of the transition, originating fromthis type of secondary instability, are also studied. We foundthat the main structures observed during the transition processconsist of elongated quasi-streamwise vortices located on theflanks of the low speed streak. Vortices of alternating signare overlapping in the streamwise direction in a staggeredpattern.</p><p><strong>Descriptors:</strong>Fluid mechanics, laminar-turbulenttransition, boundary layer flow, transient growth, streamwisestreaks, lift-up effect, receptivity, free-stream turbulence,nonlinear mechanism, streak instability, secondary instability,Direct Numerical Simulation.</p> / QC 20100518

Transition from laminar to turbulent flow has beentraditionally studied in terms of exponentially growingeigensolutions to the linearized disturbance equations.However, experimental findings show that transition may occuralso for parameters combinations such that these eigensolutionsare damped. An alternative non-modal growth mechanism has beenrecently identified, also based on the linear approximation.This consists of the transient growth of streamwise elongateddisturbances, mainly in the streamwise velocity component,called streaks. If the streak amplitude reaches a thresholdvalue, secondary instabilities can take place and provoketransition. This scenario is most likely to occur in boundarylayer flows subject to high levels of free-stream turbulenceand is the object of this thesis. Different stages of theprocess are isolated and studied with different approaches,considering the boundary layer flow over a flat plate. Thereceptivity to free-stream disturbances has been studiedthrough a weakly non-linear model which allows to disentanglethe features involved in the generation of streaks. It is shownthat the non-linear interaction of oblique waves in thefree-stream is able to induce strong streamwise vortices insidethe boundary layer, which, in turn, generate streaks by thelift-up effect. The growth of steady streaks is followed bymeans of Direct Numerical Simulation. After the streaks havereached a finite amplitude, they saturate and a new laminarflow, characterized by a strong spanwise modulation isestablished. Using Floquet theory, the instability of thesestreaks is studied to determine the features of theirbreakdown. The streak critical amplitude, beyond which unstablewaves are excited, is 26% of the free-stream velocity. Theinstability appears as spanwise (sinuous-type) oscillations ofthe streak. The late stages of the transition, originating fromthis type of secondary instability, are also studied. We foundthat the main structures observed during the transition processconsist of elongated quasi-streamwise vortices located on theflanks of the low speed streak. Vortices of alternating signare overlapping in the streamwise direction in a staggeredpattern. Descriptors:Fluid mechanics, laminar-turbulenttransition, boundary layer flow, transient growth, streamwisestreaks, lift-up effect, receptivity, free-stream turbulence,nonlinear mechanism, streak instability, secondary instability,Direct Numerical Simulation. / QC 20100518

<p>Disturbances introduced in wall-bounded .ows can grow andlead to transition from laminar to turbulent .ow. In order toreduce losses or enhance mixing in energy systems, afundamental understanding of the .ow stability is important. Inlow disturbance environments, the typical path to transition isan exponential growth of modal waves. On the other hand, inlarge disturbance environments, such as in the presence of highlevels of free-stream turbulence or surface roughness,algebraic growth of non-modal streaks can lead to transition.In the present work, the stability of wall-bounded .ows isinvestigated by means of linear stability equations valid bothfor the exponential and algebraic growth scenario. Anadjoint-based optimization technique is used to optimize thealgebraic growth of streaks. The exponential growth of waves ismaximized in the sense that the envelope of the most ampli.edeigenmode is calculated. Two wall-bounded .ows areinvestigated, the Falkner–Skan boundary layer subject tofavorable, adverse and zero pressure gradients and the Blasiuswall jet. For the Falkner–Skan boundary layer, theoptimization is carried out over the initial streamwiselocation as well as the spanwise wave number and the angularfrequency. Furthermore, a uni.ed transition-prediction methodbased on available experimental data is suggested. The Blasiuswall jet is matched to the measured .ow in an experimentalwall-jet facility. Linear stability analysis with respect tothe growth of two-dimensional waves and streamwise streaks areperformed and compared to the experiments. The nonlinearinteraction of introduced waves and streaks and the .owstructures preceding the .ow breakdown are investigated bymeans of direct numerical simulations.</p><p>Descriptors: Boundary layer, wall jet, algebraic growth,exponential growth, lift-up e.ect, streamwise streaks,Tollmien-Schlichting waves, free-stream turbulence, roughnesselement, transition prediction, Parabolized StabilityEquations, Direct Numerical Simulation.</p>

Disturbances introduced in wall-bounded .ows can grow andlead to transition from laminar to turbulent .ow. In order toreduce losses or enhance mixing in energy systems, afundamental understanding of the .ow stability is important. Inlow disturbance environments, the typical path to transition isan exponential growth of modal waves. On the other hand, inlarge disturbance environments, such as in the presence of highlevels of free-stream turbulence or surface roughness,algebraic growth of non-modal streaks can lead to transition.In the present work, the stability of wall-bounded .ows isinvestigated by means of linear stability equations valid bothfor the exponential and algebraic growth scenario. Anadjoint-based optimization technique is used to optimize thealgebraic growth of streaks. The exponential growth of waves ismaximized in the sense that the envelope of the most ampli.edeigenmode is calculated. Two wall-bounded .ows areinvestigated, the Falkner–Skan boundary layer subject tofavorable, adverse and zero pressure gradients and the Blasiuswall jet. For the Falkner–Skan boundary layer, theoptimization is carried out over the initial streamwiselocation as well as the spanwise wave number and the angularfrequency. Furthermore, a uni.ed transition-prediction methodbased on available experimental data is suggested. The Blasiuswall jet is matched to the measured .ow in an experimentalwall-jet facility. Linear stability analysis with respect tothe growth of two-dimensional waves and streamwise streaks areperformed and compared to the experiments. The nonlinearinteraction of introduced waves and streaks and the .owstructures preceding the .ow breakdown are investigated bymeans of direct numerical simulations. Descriptors: Boundary layer, wall jet, algebraic growth,exponential growth, lift-up e.ect, streamwise streaks,Tollmien-Schlichting waves, free-stream turbulence, roughnesselement, transition prediction, Parabolized StabilityEquations, Direct Numerical Simulation. / NR 20140805