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Edge states and transition to turbulence in boundary layers
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The focus of this thesis is the numerical study of subcritical transition to turbulence in boundary-layer flows. For the most part, boundary layers with uniform suction are considered. Constant homogeneous suction counteracts the spatial growth of the boundary layer, rendering the flow parallel. This enables research approaches which are not feasible in the context of spatially developing flows.

In the first part, the laminar–turbulent separatrix of the asymptotic suction boundary layer (ASBL) is investigated numerically by means of an edge-tracking algorithm. The obtained edge states experience recurrent dynamics, going through calm and bursting phases. The self-sustaining mechanism bears many similarities with the classical regeneration cycle of near-wall turbulence. The recurrent simple structure active during calm phases is compared to the nucleation of turbulence events in bypass transition originating from delocalised initial conditions. The implications on the understanding of the bypass-transition process and the edge state's role are discussed.

Based on this understanding, a model is constructed which predicts the position of the nucleation of turbulent spots during free-stream turbulence induced transition in spatially developing boundary-layer flow. This model is used together with a probabilistic cellular automaton (PCA), which captures the spatial spreading of the spots, correctly reproducing the main statistical characteristics of the transition process.

The last part of the thesis is concerned with the spatio-temporal aspects of turbulent ASBL in extended numerical domains near the onset of sustained turbulence. The different behaviour observed in ASBL, i.e. absence of sustained laminar–turbulent patterns, which have been reported in other wall-bounded flows, is associated with different character of the large-scale flow. In addition, an accurate quantitative estimate for the lowest Reynolds number with sustained turbulence is obtained

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2016. , 45 p.
Series
TRITA-MEK, ISSN 0348-467X ; 2016:08
Keyword [en]
boundary layer, transition to turbulence, direct numerical simulation, edge state, free-stream turbulence, bypass transition, probabilistic cellular automaton, turbulence at the onset, laminar–turbulent coexistence, laminarisation
National Category
Fluid Mechanics and Acoustics
Research subject
Engineering Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-186038ISBN: 978-91-7595-977-1 (print)OAI: oai:DiVA.org:kth-186038DiVA: diva2:925008
Public defence
2016-05-19, F3, Lindstedtsvägen 26, Stockholm, 10:15 (English)
Opponent
Supervisors
Note

QC 20160429

Available from: 2016-04-29 Created: 2016-04-29 Last updated: 2016-05-03Bibliographically approved
List of papers
1. Localized edge states in the asymptotic suction boundary layer
Open this publication in new window or tab >>Localized edge states in the asymptotic suction boundary layer
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2013 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 717, no R6Article in journal (Refereed) Published
Abstract [en]

The dynamics on the laminar-turbulent separatrix is investigated numerically for boundary-layer flows in the subcritical regime. Constant homogeneous suction is applied at the wall, resulting in a parallel asymptotic suction boundary layer (ASBL). When the numerical domain is sufficiently extended in the spanwise direction, the coherent structures found by edge tracking are invariably localized and their dynamics shows bursts that drive a remarkable regular or irregular spanwise dynamics. Depending on the parameters, the asymptotic dynamics on the edge can be either periodic in time or chaotic. A clear mechanism for the regeneration of streaks and streamwise vortices emerges in all cases and is investigated in detail.

Keyword
boundary layers, instability, nonlinear dynamical systems
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-122354 (URN)10.1017/jfm.2013.20 (DOI)000317421600006 ()2-s2.0-84878528716 (Scopus ID)
Note

QC 20130522

Available from: 2013-05-22 Created: 2013-05-20 Last updated: 2017-12-06Bibliographically approved
2. Complexity of localised coherent structures in a boundary-layer flow
Open this publication in new window or tab >>Complexity of localised coherent structures in a boundary-layer flow
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2014 (English)In: The European Physical Journal E Soft matter, ISSN 1292-8941, E-ISSN 1292-895X, Vol. 37, no 32Article in journal (Refereed) Published
Abstract [en]

We study numerically transitional coherent structures in a boundary-layer flow with homogeneous suction at the wall (the so-called asymptotic suction boundary layer ASBL). The dynamics restricted to the laminar-turbulent separatrix is investigated in a spanwise-extended domain that allows for robust localisation of all edge states. We work at fixed Reynolds number and study the edge states as a function of the streamwise period. We demonstrate the complex spatio-temporal dynamics of these localised states, which exhibits multistability and undergoes complex bifurcations leading from periodic to chaotic regimes. It is argued that in all regimes the dynamics restricted to the edge is essentially low-dimensional and non-extensive.

Keyword
boundary layers, nonlinear dynamical systems, edge states, multistability, period doubling, Pomeau-Manneville intermittency
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-141345 (URN)10.1140/epje/i2014-14032-3 (DOI)000335160300002 ()2-s2.0-84901942755 (Scopus ID)
Note

QC 20140602

Available from: 2014-02-13 Created: 2014-02-13 Last updated: 2017-12-06Bibliographically approved
3. Edge states as mediators of bypass transition in boundary-layer flows
Open this publication in new window or tab >>Edge states as mediators of bypass transition in boundary-layer flows
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2016 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645Article in journal (Refereed) Submitted
Abstract [en]

The concept of edge state is investigated in the asymptotic suction boundary layer in relation with the receptivity process to noisy perturbations and the nucleation of turbulent spots. Edge tracking is first performed numerically, without imposing any discrete symmetry, in a large computational domain allowing for full spatial localisation of the perturbation velocity. The edge state is a three-dimensional localised structure recurrently characterised by a single low-speed streak that experiences erratic bursts and planar shifts. This recurrent streaky structure is then compared with predecessors of individual spot nucleation events, triggered by non-localised initial noise. The present results suggest a nonlinear picture, rooted in dynamical systems theory, of the nucleation process of turbulent spots in boundary-layer flows, in which the localised edge states play the role of state-space mediator.

Keyword
boundary layers, transition to turbulence, nonlinear dynamical systems
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-185958 (URN)
Note

QS 201605

Available from: 2016-04-29 Created: 2016-04-29 Last updated: 2017-11-30Bibliographically approved
4. Bypass transition and spot nucleation in boundary layers
Open this publication in new window or tab >>Bypass transition and spot nucleation in boundary layers
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2016 (English)Manuscript (preprint) (Other academic)
Abstract [en]

The spatio-temporal aspects of the transition to turbulence are considered in the case of a boundary-layer flow developing above a flat plate exposed to free-stream turbulence. Combining results on the receptivity to free-stream turbulence with the nonlinear concept of a transition threshold, a physically motivated model suggests a spatial distribution of spot nucleation events. To describe the evolution of turbulent spots a probabilistic cellular automaton is introduced, with all parameters directly fitted from numerical simulations of the boundary layer. The nucleation rates are then combined with the cellular automaton model, yielding excellent quantitative agreement with the statistical characteristics for different free-stream turbulence levels. We thus show how the recent theoretical progress on transitional wall-bounded flows can be extended to the much wider class of spatially developing boundary-layer flows.

Keyword
boundary layers, bypass transition, free-stream turbulence, edge of chaos, cellular automaton
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-186034 (URN)
Note

QS 201605

Available from: 2016-04-29 Created: 2016-04-29 Last updated: 2016-05-31Bibliographically approved
5. Turbulence collapse in a suction boundary layer
Open this publication in new window or tab >>Turbulence collapse in a suction boundary layer
2016 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 795, 356-379 p.Article in journal (Refereed) Published
Abstract [en]

Turbulence in the asymptotic suction boundary layer is investigated numerically at the verge of laminarisation using direct numerical simulation. Following an adiabatic protocol, the Reynolds number Re is decreased in small steps starting from a fully turbulent state until laminarisation is observed. Computations in a large numerical domain allow in principle for the possible coexistence of laminar and turbulent regions. However, contrary to other subcritical shear flows, no laminar–turbulent coexistence is observed, even near the onset of sustained turbulence. High-resolution computations suggest a critical Reynolds number Reg≈270, below which turbulence collapses, based on observation times of O(105) inertial time units. During the laminarisation process, the turbulent flow fragments into a series of transient streamwise-elongated structures, whose interfaces do not display the characteristic obliqueness of classical laminar–turbulent patterns. The law of the wall, i.e. logarithmic scaling of the velocity profile, is retained down to Reg, suggesting a large-scale wall-normal transport absent in internal shear flows close to the onset. In order to test the effect of these large-scale structures on the near-wall region, an artificial volume force is added to damp spanwise and wall-normal fluctuations above y+=100, in viscous units. Once the largest eddies have been suppressed by the forcing, and thus turbulence is confined to the near-wall region, oblique laminar–turbulent interfaces do emerge as inother wall-bounded flows, however only transiently. These results suggest that oblique stripes at the onset are a prevalent feature of internal shear flows, but will not occur in canonical boundary layers, including the spatially growing ones.

Place, publisher, year, edition, pages
Cambridge University Press, 2016
Keyword
intermittency, turbulent boundary layers, turbulent transition
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-186037 (URN)10.1017/jfm.2016.205 (DOI)000374964700016 ()
Note

QC 20160510

Available from: 2016-04-29 Created: 2016-04-29 Last updated: 2017-11-30Bibliographically approved

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