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Weakly nonlinear analysis of boundary layer receptivity to free-stream disturbances
KTH, Superseded Departments, Mechanics.ORCID iD: 0000-0002-4346-4732
KTH, Superseded Departments, Mechanics.ORCID iD: 0000-0001-7864-3071
2002 (English)In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 14, no 4, 1426-1441 p.Article in journal (Refereed) Published
Abstract [en]

The intent of the present paper is to study the receptivity of a zero pressure gradient boundary layer to free-stream disturbances with the aim to isolate the essential features involved in the generation of streamwise streaks. A weakly nonlinear formulation based on a perturbation expansion in the amplitude of the disturbance truncated at second order is used. It is shown that the perturbation model provide an efficient tool able to disentangle the sequence of events in the receptivity process. Two types of solutions are investigated: the first case amounts to the receptivity to oblique waves generated by a wave-like external forcing term oscillating in the free stream, the second the receptivity to free-stream turbulence-like disturbances, represented as a superposition of modes of the continuous spectrum of the Orr-Sommerfeld and Squire operators. A scaling property of the governing equations with the Reynolds number is also shown to be valid. The relation between this nonlinear receptivity process and previously investigated linear ones is also discussed.

Place, publisher, year, edition, pages
2002. Vol. 14, no 4, 1426-1441 p.
Keyword [en]
URN: urn:nbn:se:kth:diva-12899DOI: 10.1063/1.1456062ISI: 000174319200016OAI: diva2:319561
QC 20100518Available from: 2010-05-18 Created: 2010-05-18 Last updated: 2010-05-18Bibliographically approved
In thesis
1. Study of generation, growth and breakdown of streamwise streaks in a Blasius boundary layer.
Open this publication in new window or tab >>Study of generation, growth and breakdown of streamwise streaks in a Blasius boundary layer.
2001 (English)Licentiate thesis, comprehensive summary (Other scientific)
Abstract [en]

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.

Place, publisher, year, edition, pages
Stockholm: Mekanik, 2001. vii, 17 p.
Trita-MEK, ISSN 0348-467X ; 2001:10
Fluid mechanics, laminar-turbulent transition, boundary layer flow, transient growth, streamwise streaks, lift-up effect, receptivity, free-stream turbulence, streak instability, secondary instability, Direct Numerical Simulation.
urn:nbn:se:kth:diva-1256 (URN)
QC 20100518Available from: 2001-09-24 Created: 2001-09-24 Last updated: 2010-05-18Bibliographically approved

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