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Licentiate seminar

Study of generation, growth and breakdown of streamwise streaks in a Blasius boundary layer


Defendant Main Advisor Extra Advisor Date
Luca Brandt Dan Henningson 2001-06-06

Opponent
Peter Schmid, Department of Applied Mathematics, University of Washington

Evaluation committee

Abstract

Transition from laminar to turbulent flow has been traditionally studied in terms of exponentially growing eigensolutions to the linearized disturbance equations. However, experimental findings show that transition may occur also for parameters combinations such that these eigensolutions are damped. An alternative non-modal growth mechanism has been recently identified, also based on the linear approximation. This consists of the transient growth of streamwise elongated disturbances, mainly in the streamwise velocity component, called streaks. If the streak amplitude reaches a threshold value, secondary instabilities can take place and provoke transition. This scenario is most likely to occur in boundary layer flows subject to high levels of free-stream turbulence and is the object of this thesis. Different stages of the process are isolated and studied with different approaches, considering the boundary layer flow over a flat plate. The receptivity to free-stream disturbances has been studied through a weakly non-linear model which allows to disentangle the features involved in the generation of streaks. It is shown that the non-linear interaction of oblique waves in the free-stream is able to induce strong streamwise vortices inside the boundary layer, which, in turn, generate streaks by the lift-up effect. The growth of steady streaks is followed by means of Direct Numerical Simulation. After the streaks have reached a finite amplitude, they saturate and a new laminar flow, characterized by a strong spanwise modulation is established. Using Floquet theory, the instability of these streaks is studied to determine the features of their breakdown. The streak critical amplitude, beyond which unstable waves are excited, is 26% of the free-stream velocity. The instability appears as spanwise (sinuous-type) oscillations of the streak. The late stages of the transition, originating from this type of secondary instability, are also studied. We found that the main structures observed during the transition process consist of elongated quasi-streamwise vortices located on the flanks of the low speed streak. Vortices of alternating sign are overlapping in the streamwise direction in a staggered pattern.
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