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Study of generation, growth and breakdown of streamwise streaks in a Blasius boundary layer.
KTH, Superseded Departments, Mechanics.ORCID iD: 0000-0002-4346-4732
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.
Series
Trita-MEK, ISSN 0348-467X ; 2001:10
Keyword [en]
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.
Identifiers
URN: urn:nbn:se:kth:diva-1256OAI: oai:DiVA.org:kth-1256DiVA: diva2:7064
Presentation
(English)
Note
QC 20100518Available from: 2001-09-24 Created: 2001-09-24 Last updated: 2010-05-18Bibliographically approved
List of papers
1. Weakly nonlinear analysis of boundary layer receptivity to free-stream disturbances
Open this publication in new window or tab >>Weakly nonlinear analysis of boundary layer receptivity to free-stream disturbances
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.

Keyword
ORR-SOMMERFELD EQUATION, OPTIMAL PERTURBATIONS, CONTINUOUS-SPECTRUM, BYPASS TRANSITION, POISEUILLE FLOW, ENERGY GROWTH, SHEAR FLOWS, MECHANISM
Identifiers
urn:nbn:se:kth:diva-12899 (URN)10.1063/1.1456062 (DOI)000174319200016 ()
Note
QC 20100518Available from: 2010-05-18 Created: 2010-05-18 Last updated: 2017-12-12Bibliographically approved
2. On the breakdown of boundary layer streaks
Open this publication in new window or tab >>On the breakdown of boundary layer streaks
2001 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 428, 29-60 p.Article in journal (Refereed) Published
Abstract [en]

A scenario of transition to turbulence likely to occur during the development of natural disturbances in a flat-plate boundary layer is studied. The perturbations at the leading edge of the flat plate that show the highest potential for transient energy amplification consist of streamwise aligned vortices. Due to the lift-up mechanism these optimal disturbances lead to elongated streamwise streaks downstream, with significant spanwise modulation, Direct numerical simulations are used to follow the nonlinear evolution of these streaks and to verify secondary instability calculations. The theory is based on a linear Floquet expansion and focuses on the temporal, inviscid instability of these flow structures. The procedure requires integration in the complex plane, in the coordinate direction normal to the wall, to properly identify neutral modes belonging to the discrete spectrum. The streak critical amplitude, beyond which streamwise travelling waves are excited, is about 26% of the free-stream velocity. The sinuous instability mode (either the fundamental or the subharmonic, depending on the streak amplitude) represents the most dangerous disturbance. Varicose waves are more stable, and are characterized by a critical amplitude of about 37%. Stability calculations of streamwise streaks employing the shape assumption, carried out in a parallel investigation, are compared to the results obtained here using the nonlinearly modified mean fields; the need to consider a base flow which includes mean flow modification and harmonics of the fundamental streak is clearly demonstrated.

Keyword
PLANE COUETTE-FLOW, SELF-SUSTAINING PROCESS, NEAR-WALL TURBULENCE, SECONDARY INSTABILITY, SHEAR FLOWS, STREAMWISE VORTICES, GORTLER VORTICES, HYDRODYNAMIC STABILITY, BYPASS TRANSITION, POISEUILLE FLOW
Identifiers
urn:nbn:se:kth:diva-12915 (URN)10.1017/S0022112000002421 (DOI)000167012800002 ()
Note
QC 20100518Available from: 2010-05-18 Created: 2010-05-18 Last updated: 2017-12-12Bibliographically approved
3. Transition of streamwise streaks in zero-pressure-gradient boundary layers
Open this publication in new window or tab >>Transition of streamwise streaks in zero-pressure-gradient boundary layers
2002 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 472, 229-261 p.Article in journal (Refereed) Published
Abstract [en]

A transition scenario initiated by streamwise low- and high-speed streaks in a flat-plate boundary layer is studied. In many shear flows, the perturbations that show the highest potential for transient energy amplification consist of streamwise-aligned vortices. Due to the lift-up mechanism these optimal disturbances lead to elongated streamwise streaks downstream, with significant spanwise modulation. In a previous investigation (Andersson et al. 2001), the stability of these streaks in a zero-pressure-gradient boundary layer was studied by means of Floquet theory and numerical simulations. The sinuous instability mode was found to be the most dangerous disturbance. We present here the first simulation of the breakdown to turbulence originating from the sinuous instability of streamwise streaks. 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. The present scenario is compared with transition initiated by Tollmien-Schlichting waves and their secondary instability and by-pass transition initiated by a pair of oblique waves. The relevance of this scenario to transition induced by free-stream turbulence is also discussed.

Keyword
DIRECT NUMERICAL-SIMULATION, SELF-SUSTAINING PROCESS, PLANE POISEUILLE FLOW, CHANNEL FLOW, SECONDARY INSTABILITY, OPTIMAL PERTURBATIONS, BYPASS TRANSITION, REYNOLDS-NUMBER, TURBULENCE, STABILITY
Identifiers
urn:nbn:se:kth:diva-12916 (URN)10.1017/S0022112002002331 (DOI)000179810100010 ()
Note
QC 20100518Available from: 2010-05-18 Created: 2010-05-18 Last updated: 2017-12-12Bibliographically approved

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