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  • 1. Abreu, L. I.
    et al.
    Cavalieri, A. V. G.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Vinuesa, Ricardo
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Reduced-order models to analyse coherent structures in turbulent pipe flow2019In: 11th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2019, International Symposium on Turbulence and Shear Flow Phenomena, TSFP , 2019Conference paper (Refereed)
    Abstract [en]

    Fully resolved direct numerical simulations, performed with a high-order spectral-element method, are used to study coherent structures in turbulent pipe flow at friction Reynolds numbers Reτ = 180 and 550 (El Khoury et al., 2013). The database was analysed using spectral proper orthogonal decomposition (SPOD) so as to identify dominant coherent structures, most of which are of streaky shape. As a reduced-order model for such structures, the linearised flow response to harmonic forcing was computed, and the analysed singular modes of the resolvent operator were analysed. For turbulent flows, this approach amounts to considering the non-linear terms in the Navier–Stokes system as an unknown forcing, treated convenienty as external. Resolvent analysis then allows an identification of the optimal forcing and most amplified flow response; the latter may be related to observed relevant structures obtained by SPOD, especially if the gain between forcing and response is much larger than what is found for suboptimal forcings or if the non-linear forcing is white noise. Results from SPOD and resolvent analysis were extracted for several combinations of frequencies, streamwise and azimuthal wavenumbers. For both Reynolds numbers, good agreement between SPOD and resolvent modes was observed for parameter combinations where the lift-up mechanism is present: optimal forcing from resolvent analysis represents streamwise vortices and the associated response are streaky structures.

  • 2. Abreu, L. I.
    et al.
    Cavalieri, A. V. G.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    Vinuesa, Ricardo
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    Wavepackets in turbulent flow over a NACA 4412 airfoil2018In: 31st Congress of the International Council of the Aeronautical Sciences, ICAS 2018, International Council of the Aeronautical Sciences , 2018Conference paper (Refereed)
    Abstract [en]

    Turbulent flow over a NACA 4412 airfoil with an angle of attack AoA = 5◦ was analysed using an incompressible direct numerical simulation (DNS) at chord Reynolds number of Rec = 4 · 105. Snapshots of the flow field were analysed using the method of Spectral Proper Orthogonal Decomposition (SPOD) in frequency domain, in order to extract the dominant coherent structures of the flow. Focus is given to two-dimensional disturbances, known to be most relevant for aeroacoustics. The leading SPOD modes show coherent structures forming a wavepacket, with significant amplitudes in the trailing-edge boundary layer and in the wake. To model coherent structures in the turbulent boundary layer, the optimal harmonic forcing and the associated linear response of the flow were obtained using the singular value decomposition of the linear resolvent operator. The resolvent analysis shows that the leading SPOD modes can be associated to most amplified, linearised flow responses. Furthermore, coherent structures in the wake are modelled as the Kelvin-Helmholtz mode from linear stability theory (LST). 

  • 3. Abreu, Leandra, I
    et al.
    Cavalieri, Andre V. G.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Vinuesa, Ricardo
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Resolvent modelling of near-wall coherent structures in turbulent channel flow2020In: International Journal of Heat and Fluid Flow, ISSN 0142-727X, E-ISSN 1879-2278, Vol. 85, article id 108662Article in journal (Refereed)
    Abstract [en]

    Turbulent channel flow was analysed using direct numerical simulations at friction Reynolds numbers Re-tau = 180 and 550. The databases were studied using spectral proper orthogonal decomposition (SPOD) to identify dominant near-wall coherent structures, most of which turn out to be streaks and streamwise vortices. Resolvent analysis was used as a theoretical approach to model such structures, as it allows the identification of the optimal forcing and most amplified flow response; the latter may be related to the observed relevant structures obtained by SPOD, especially if the gain between forcing and response is much larger than what is found for suboptimal forcings or if the non-linear forcing is white noise. Results from SPOD and resolvent analysis were compared for several combinations of frequencies and wavenumbers. For both Reynolds numbers, the best agreement between SPOD and resolvent modes was observed for the cases where the lift-up mechanism from resolvent analysis is present, which are also the cases where the optimal resolvent gain is dominant. These results confirm the outcomes in our previous studies (Abreu et al., 2019; Abreu et al., 2020), where we used a DNS database of a pipe flow for the same Reynolds numbers.

  • 4.
    Abreu, Leandra, I
    et al.
    Sao Paulo State Univ UNESP, Campus Sao Joao da Boa Vista, BR-13876750 Sao Joao da Boa Vista, SP, Brazil.;Inst Tecnol Aeronaut, Div Engn Aeronaut, BR-12228900 Sao Jose Dos Campos, SP, Brazil..
    Cavalieri, Andre V. G.
    Inst Tecnol Aeronaut, Div Engn Aeronaut, BR-12228900 Sao Jose Dos Campos, SP, Brazil..
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Vinuesa, Ricardo
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Stability, Transition and Control.
    Spectral proper orthogonal decomposition and resolvent analysis of near-wall coherent structures in turbulent pipe flows2020In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 900, article id A11Article in journal (Refereed)
    Abstract [en]

    Direct numerical simulations, performed with a high-order spectral-element method, are used to study coherent structures in turbulent pipe flow at friction Reynolds numbers Re-tau = 180 and 550. The database was analysed using spectral proper orthogonal decomposition (SPOD) to identify energetically dominant coherent structures, most of which turn out to be streaks and quasi-streamwise vortices. To understand how such structures can be modelled, the linear flow responses to harmonic forcing were computed using the singular value decomposition of the resolvent operator, using the mean field as a base flow. The SPOD and resolvent analysis were calculated for several combinations of frequencies and wavenumbers, allowing the mapping out of similarities between SPOD modes and optimal responses for a wide range of relevant scales in turbulent pipe flows. In order to explore physical reasons behind the agreement between both methods, an indicator of lift-up mechanism in the resolvent analysis was introduced, activated when optimal forcing is dominated by the wall-normal and azimuthal components, and associated response corresponds to streaks of streamwise velocity. Good agreement between leading SPOD and resolvent modes is observed in a large region of parameter space. In this region, a significant gain separation is found in resolvent analysis, which may be attributed to the strong amplification associated with the lift-up mechanism, here understood as nonlinear forcing terms leading to the appearance of streamwise vortices, which in turn form high-amplitude streaks. For both Reynolds numbers, the observed concordances were generally for structures with large energy in the buffer layer. The results highlight resolvent analysis as a pertinent reduced-order model for coherent structures in wall-bounded turbulence, particularly for streamwise elongated structures corresponding to near-wall streamwise vortices and streaks.

  • 5.
    Abreu, Leandra, I
    et al.
    Sao Paulo State Univ UNESP, Campus Sao Joao Boa Vista, BR-13876750 Sao Joao Da Boa Vista, SP, Brazil.;Inst Tecnol Aeronaut, Div Engn Aeronaut, BR-12228900 Sao Jose Dos Campos, SP, Brazil..
    Tanarro, Alvaro
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Cavalieri, Andre V. G.
    Inst Tecnol Aeronaut, Div Engn Aeronaut, BR-12228900 Sao Jose Dos Campos, SP, Brazil..
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Vinuesa, Ricardo
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Hanifi, Ardeshir
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Spanwise-coherent hydrodynamic waves around flat plates and airfoils2021In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 927, article id A1Article in journal (Refereed)
    Abstract [en]

    We investigate spanwise-coherent structures in the turbulent flow around airfoils, motivated by their connection with trailing-edge noise. We analyse well-resolved large-eddy simulations (LES) of the flow around NACA 0012 and NACA 4412 airfoils, both at a Reynolds number of 400 000 based on the chord length. Spectral proper orthogonal decomposition performed on the data reveals that the most energetic coherent structures are hydrodynamic waves, extending over the turbulent boundary layers around the airfoils with significant amplitudes near the trailing edge. Resolvent analysis was used to model such structures, using the mean field as a base flow. We then focus on evaluating the dependence of such structures on the domain size, to ensure that they are not an artefact of periodic boundary conditions in small computational boxes. To this end, we performed incompressible LES of a zero-pressure-gradient turbulent boundary layer, for three different spanwise sizes, with the momentum-thickness Reynolds number matching those near the airfoils trailing edge. The same coherent hydrodynamic waves were observed for the three domains. Such waves are accurately modelled as the most amplified flow response from resolvent analysis. The signature of such wide structures is seen in non-premultiplied spanwise wavenumber spectra, which collapse for the three computational domains. These results suggest that the spanwise-elongated structures are not domain-size dependent for the studied simulations, indicating thus the presence of very wide structures in wall-bounded turbulent flows.

  • 6.
    Abreu, Leandra I.
    et al.
    Divisão de Engenharia Aeronáutica, Instituto Tecnológico de Aeronáutica, 12228-900, São José dos Campos, SP, Brazil.
    Tanarro, Alvaro
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Cavalieri, André V.G.
    Divisão de Engenharia Aeronáutica, Instituto Tecnológico de Aeronáutica, 12228-900, São José dos Campos, SP, Brazil.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Superseded Departments (pre-2005), Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Vinuesa, Ricardo
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Hanifi, Ardeshir
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Superseded Departments (pre-2005), Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Wavepackets in turbulent flows around airfoilsManuscript (preprint) (Other academic)
    Abstract [en]

    Motivated by the recent analysis by Sano et al. 2019, Phys. Rev. Fluids, vol. 4, p. 094602, of spanwise-coherent structures in the turbulent flow around airfoils and their connection to trailing-edge noise, we carry out a thorough characterisation of such structures in three simulation databases. We analyse two different numerical simulations of incompressible flow in turbulent regime, both at chord Reynolds number of 400,000: a large-eddy simulation for a NACA 0012 profile at zero angle of attack, and a direct numerical simulation for a NACA 4412 airfoil with an angle of attack of 5 degrees. Snapshots of the flow field were analysed using Spectral Proper Orthogonal Decomposition (SPOD), in order to extract the dominant coherent structures of the flow. Focus is given to  the aforementioned spanwise-coherent fluctuations, which two-dimensional disturbances in the computational domain due to the use of periodic boundary conditions. The leading SPOD modes show that the most energetic coherent structures are wavepackets, extending over the whole turbulent boundary layers around the airfoils with significant amplitudes near the trailing-edge. Higher amplitudes are observed in the region of  stronger adverse pressure gradient at the suction side of the NACA 4412 airfoil. To understand how such structures in the turbulent field can be modelled, the linear response of the flow using the singular value decomposition of the linearised resolvent operator was performed, using the mean field as a base flow and considering a locally parallel approximation. Such analysis shows that the leading SPOD modes can be associated to optimal, linearised flow responses, particularly for stations far from the trailing edge; the latter introduces a discontinuity in boundary conditions, and the locally parallel approximation becomes questionable. We then focus on evaluating the dependence of such wavepackets on the domain size, to ensure that these structures are not an artifact of the use of periodic boundary conditions in small computational boxes. To do so, we performed an incompressible LES of a zero-pressure gradient turbulent boundary layer (ZPGTBL), for three different spanwise sizes: Lz=32 δ*, Lz=64 δ* and Lz=128 δ*, where δ* is a reference displacement thickness in a region of developed turbulent flow, with Reynolds number matching the values in the airfoil simulations. The signature of such wavepackets is seen in non-premultiplied spanwise wavenumber spectra, which reaches, for the three domain sizes, a plateau for spanwise wavelengths going to infinity (or wavenumbers going to zero); this plateau is representative of the spanwise-coherent structures seen in the airfoil simulations. Similar SPOD and resolvent analyses were carried out for the zero spanwise wavenumber of the ZPGTBL, and the same coherent wavepackets were observed for the three domains, with very similar amplitudes. Such wavepackets were also accurately modelled using the optimal resolvent response. These results confirm that the spanwise-elongated structures are not domain-size dependent for the studied simulations, and are thus a feature of turbulent boundary layers.

  • 7.
    Alarcón, José Faúndez
    et al.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Cavalieri, André
    Hanifi, Ardeshir
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Role of streak secondary instabilities on free stream turbulence-induced transitionManuscript (preprint) (Other academic)
  • 8.
    Alarcón, José Faúndez
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Cavalieri, André V.G.
    Aerodynamics Department, Instituto Tecnológico de Aeronáutica, 12228-900, São José dos Campos / SP, Brazil, SP.
    Hanifi, Ardeshir
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Role of streak secondary instabilities on free-stream turbulence-induced transition2024In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 988, article id A6Article in journal (Refereed)
    Abstract [en]

    We study the stability of a zero-pressure gradient boundary layer subjected to free-stream disturbances by means of local stability analysis. The dataset under study corresponds to a direct numerical simulation (DNS) of a flat plate with a sharp leading edge in realistic wind tunnel conditions, with a turbulence level of 3.45 % at the leading edge. We present a method to track the convective evolution of the secondary instabilities of streaks by performing sequential stability calculations following the wave packet, connecting successive unstable eigenfunctions. A scattered nature, in time and space, of secondary instabilities is seen in the stability calculations. These instabilities can be detected before they reach finite amplitude in the DNS, preceding the nucleation of turbulent spots, and whose appearance is well correlated to the transition onset. This represents further evidence regarding the relevance of secondary instabilities of streaks in the bypass transition in realistic flow conditions. Consistent with the spatio-temporal nature of this problem, our approach allows us to integrate directly the local growth rates to obtain the spatial amplification ratio of the individual instabilities, where it is shown that instabilities reaching an -factor in the range [2.5,4] can be directly correlated to more than 65 % of the nucleation events. Interestingly, it is found that high amplification is not only attained by modes with high growth rates, but also by instabilities with sustained low growth rates for a long time.

  • 9.
    Alarcón, José Faúndez
    et al.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Hanifi, Ardeshir
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    On the size of transitional boundary layer streaksManuscript (preprint) (Other academic)
  • 10.
    Alarcón, José Faúndez
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Morra, Pierluigi
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics.
    Hanifi, Ardeshir
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Disturbance growth on a NACA0008 wing subjected to free stream turbulence2022In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 944, article id A44Article in journal (Refereed)
    Abstract [en]

    The stability of an incompressible boundary layer flow over a wing in the presence of free stream turbulence (FST) has been investigated by means of direct numerical simulations and compared with the linearised boundary layer equations. Four different. FST conditions have been considered, which are characterised by their turbulence intensity levels and length scales. In all cases the perturbed flow develops into elongated disturbances of high and low streamwise velocity inside the boundary layer, where their spacing has been found to be strongly dependent on the scales of the incoming free stream vorticity. The breakdown of these streaks into turbulent spots from local secondary instabilities is also observed, presenting the same development as the ones reported in flat plate experiments. The disturbance growth, characterised by its root mean squares value, is found to depend not only on the turbulence level, but also on the FST length scales. Particularly, higher disturbance growth is observed for our cases with larger length scales. This behaviour is attributed to the preferred wavenumbers that can exhibit maximum transient growth. We study this boundary layer preference by projection of the flow fields at the leading edge onto optimal disturbances. Our results demonstrate that optimal disturbance growth is the main cause of growth of disturbances on the wing boundary layer.

  • 11.
    Alarcón, José Faúndez
    et al.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Sasaki, Kenzo
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Hanifi, Ardeshir
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Larsson, Roger
    Saab Aeronautics, Bröderna Ugglas gata, SE-58188, Linköping, Sweden, Bröderna Ugglas gata.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    REACTIVE CONTROL OF BYPASS TRANSITION IN A WING BOUNDARY LAYER2022In: 33rd Congress of the International Council of the Aeronautical Sciences, ICAS 2022, International Council of the Aeronautical Sciences , 2022, p. 3037-3047Conference paper (Refereed)
    Abstract [en]

    This investigation deals with the numerical implementation of a data-driven method for reactive control of the boundary-layer over a NACA0008 airfoil. The aim of this work is to evaluate the performance of controller in damping the flow disturbances and its efficiency in delaying laminar-turbulent transition. We focus our attention on the bypass transition scenario caused by free-stream turbulence. In this scenario, the perturbations in the wing boundary-layer develop into streaky structures. We show that this data-driven method is effective in decreasing the wall shear stress and disturbance energy at the objective location, and this damping is sustained downstream of the objective location. However, further downstream, the fluctuations grow again reaching amplitudes similar to those in the uncontrolled case.

  • 12. Amoignon, Olivier
    et al.
    Pralits, Jan O.
    Hanifi, Ardeshir
    Swedish Defence Research Agency.
    Berggren, M.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    Shape optimization for delay of laminar-turbulent transition2006In: AIAA Journal, ISSN 0001-1452, E-ISSN 1533-385X, Vol. 44, no 5, p. 1009-1024Article in journal (Refereed)
    Abstract [en]

    A method using gradient-based optimization is introduced for the design of wing profiles with the aim of natural laminar How, as well as minimum wave drag. The Euler equations of gasdynamics, the laminar boundary-layer equations for compressible flows on infinite swept wings, and the linear parabolized stability equations (PSE) are solved to analyze the evolution of convectively unstable disturbances. Laminar-turbulent transition is assumed to be delayed by minimizing a measure of the disturbance kinetic energy of a chosen disturbance, which is computed using the PSE. The shape gradients of the disturbance kinetic energy are computed based on the solutions of the adjoints of the state equations just named. Numerical tests are carried out to optimize the RAE 2822 airfoil with the aim to delay simultaneously the transition, reduce the pressure drag coefficient, and maintain the coefficients of lift and pitch moments. Constraints are also applied on the geometry. Results show a reduction of the total amplification of a large number of disturbances, which is assumed to represent a delay of the transition in the boundary layer. Because delay of the transition implies reduction of the viscous drag, the present method enables shape optimization to perform viscous drag reduction.

  • 13.
    Andersson, Paul
    et al.
    KTH, Superseded Departments (pre-2005), Mechanics.
    Brandt, Luca
    KTH, Superseded Departments (pre-2005), Mechanics.
    Bottaro, A
    Henningson, Dan Stefan
    KTH, Superseded Departments (pre-2005), Mechanics.
    On the breakdown of boundary layer streaks2001In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 428, p. 29-60Article in journal (Refereed)
    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.

  • 14.
    Bagheri, Shervin
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Brandt, Luca
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Henningson, Dan
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Input-output analysis, model reduction and control of the flat-plate boundary layer2009In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 620, p. 263-298Article in journal (Refereed)
    Abstract [en]

    The dynamics and control of two-dimensional disturbances in the spatially evolving boundary layer oil a flat plate are investigated from an input output viewpoint. A set-up of spatially localized inputs (external disturbances and actuators) and Outputs (objective functions and sensors) is introduced for the control design of convectively unstable flow configurations. From the linearized Navier Stokes equations with the inputs and outputs, controllable, observable and balanced modes are extracted using the snapshot method. A balanced reduced-order model (ROM) is constructed and shown to capture the input output behaviour of the linearized Navier Stokes equations. This model is finally used to design H-2-feedback controller to suppress the growth or two-dimensional perturbations inside the boundary layer.

  • 15.
    Bagheri, Shervin
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Henningson, Dan
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Hoepffner, J.
    Institut de Recherche sur les Phénomènes Hors Équilibre (IRPHÉ), CNRS-Université d'Aix-Marseille.
    Schmid, Peter
    Laboratoire d'Hydrodynamique (LadHyX), CNRS-École Polytechnique.
    Input-Output Analysis and Control Design Applied to a Linear Model of Spatially Developing Flows2009In: Applied Mechanics Review, ISSN 0003-6900, E-ISSN 1088-8535, Vol. 62, no 2Article in journal (Refereed)
    Abstract [en]

    This review presents a framework for the input-output analysis, model reduction, and control design for fluid dynamical systems using examples applied to the linear complex Ginzburg-Landau equation. Major advances in hydrodynamics stability, such as global modes in spatially inhomogeneous systems and transient growth of non-normal systems, are reviewed. Input-output analysis generalizes hydrodynamic stability analysis by considering a finite-time horizon over which energy amplification, driven by a specific input (disturbances/actuator) and measured at a specific output (sensor), is observed. In the control design the loop is closed between the output and the input through a feedback gain. Model reduction approximates the system with a low-order model, making modern control design computationally tractable for systems of large dimensions. Methods from control theory are reviewed and applied to the Ginzburg-Landau equation in a manner that is readily generalized to fluid mechanics problems, thus giving a fluid mechanics audience an accessible introduction to the subject.

  • 16.
    Bagheri, Shervin
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    Transition delay using control theory2011In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 369, no 1940, p. 1365-1381Article in journal (Refereed)
    Abstract [en]

    This review gives an account of recent research efforts to use feedback control for the delay of laminar-turbulent transition in wall-bounded shear flows. The emphasis is on reducing the growth of small-amplitude disturbances in the boundary layer using numerical simulations and a linear control approach. Starting with the application of classical control theory to two-dimensional perturbations developing in spatially invariant flows, flow control based on control theory has progressed towards more realistic three-dimensional, spatially inhomogeneous flow configurations with localized sensing/actuation. The development of low-dimensional models of the Navier-Stokes equations has played a key role in this progress. Moreover, shortcomings and future challenges, as well as recent experimental advances in this multi-disciplinary field, are discussed.

  • 17.
    Bagheri, Shervin
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Henningson, Dan
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    The global stability of the jet in crossflow2008Report (Other academic)
  • 18.
    Bagheri, Shervin
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Schmid, Peter J.
    Laboratoire d'Hydrodynamique (LadHyX), CNRS-Ecole Polytechnique.
    Henningson, Dan
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Global stability of a jet in crossflow2009In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 624, p. 33-44Article in journal (Refereed)
    Abstract [en]

    A linear stability analysis shows that the jet in crossflow is characterized by self-sustained global oscillations for a jet-to-crossflow velocity ratio of 3. A fully three-dimensional unstable steady-state solution and its associated global eigenmodes are computed by direct numerical simulations and iterative eigenvalue routines. The steady flow, obtained by means of selective frequency damping, consists mainly of a (steady) counter-rotating vortex pair (CVP) in the far field and horseshoe-shaped vortices close to the wall. High-frequency unstable global eigenmodes associated with shear-layer instabilities on the CVP and low-frequency modes associated with shedding vortices in the wake of the jet are identified. Furthermore, different spanwise symmetries of the global modes are discussed. This work constitutes the first simulation-based global stability analysis of a fully three-dimensional base flow.

  • 19.
    Bagheri, Shervin
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Åkervik, Espen
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Brandt, Luca
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Matrix-free methods for the stability and control of boundary layers2009In: AIAA Journal, ISSN 0001-1452, E-ISSN 1533-385X, Vol. 47, no 5, p. 1057-1068Article in journal (Refereed)
    Abstract [en]

    This paper presents matrix-free methods for the stability analysis and control design of high-dimensional systems arising from the discretized linearized Navier-Stokes equations. The methods are applied to the two-dimensional spatially developing Blasius boundary-layer. A critical step in the process of systematically investigating stability properties and designing feedback controllers is solving very large eigenvalue problems by storing only velocity fields at different times instead of large matrices. For stability analysis, where the entire dynamics of perturbations in space and time is of interest, iterative and adjoint-based optimization techniques are employed to compute the global eigenmodes and the optimal initial conditions. The latter are the initial conditions yielding the largest possible energy growth over a finite time interval. The leading global eigenmodes take the shape of Tollmien-Schlichting wavepackets located far downstream in streamwise direction, whereas the leading optimal disturbances are tilted structures located far upstream in the boundary layer. For control design on the other hand, the input-output behavior of the system is of interest and the snapshot-method is employed to compute balanced modes that correctly capture this behavior. The inputs are external disturbances and wall actuation and the outputs are sensors that extract wall shear stress. A low-dimensional model that capture the input-output behavior is constructed by projection onto balanced modes. The reduced-order model is then used to design a feedback control strategy such that the growth of disturbances are damped as they propagate downstream.

  • 20.
    Bagheri, Shervin
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Åkervik, Espen
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Brandt, Luca
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Henningson, Dan Stefan
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Input-output analysis and control design of spatially developing shear flows2008In: 5th AIAA Theoretical Fluid Mechanics Conference, 2008Conference paper (Refereed)
    Abstract [en]

    A framework for the input-output analysis, model reduction and control design of spatially developing shear flows is presented using the Blasius boundary-layer flow as an example. An input-output formulation of the governing equations yields a flexible formulation for treating stability problems and for developing control strategies that optimize given objectives. Model reduction plays an important role in this process since the dynamical systems that describe most flows are discretized partial differential equations with a very large number of degrees of freedom. Moreover, as system theoretical tools, such as controllability, observability and balancing has become computationally tractable for large-scale systems, a systematic approach to model reduction is presented.

  • 21. Belson, Brandt A.
    et al.
    Semeraro, Onofrio
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    Rowley, Clarence W.
    Henningson, Dan Stefan
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    Feedback control of instabilities in the two-dimensional Blasius boundary layer: The role of sensors and actuators2013In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 25, no 5, p. 054106-1-054106-17Article in journal (Refereed)
    Abstract [en]

    We analyze the effects of different types and positions of actuators and sensors on controllers' performance and robustness in the linearized 2D Blasius boundary layer. The investigation is carried out using direct numerical simulations (DNS). To facilitate controller design, we find reduced-order models from the DNS data using a system identification procedure called the Eigensystem Realization Algorithm. Due to the highly convective nature of the boundary layer and corresponding time delays, the relative position of the actuator and sensor has a strong influence on the closed-loop dynamics. We address this issue by considering two different configurations. When the sensor is upstream of the actuator, corresponding to disturbance-feedforward control, good performance is observed, as in previous work. However, feedforward control can be degraded by additional disturbances or uncertainties in the plant model, and we demonstrate this. We then examine feedback controllers in which the sensor is a short distance downstream of the actuator. Sensors farther downstream of the actuator cause inherent time delays that limit achievable performance. The performance of the resulting feedback controllers depends strongly on the form of actuation introduced, the quantities sensed, and the observability of the structures deformed by the controller's action. These aspects are addressed by varying the spatial distribution of actuator and sensor. We find an actuator-sensor pair that is well-suited for feedback control, and demonstrate that it has good performance and robustness, even in the presence of unmodeled disturbances.

  • 22.
    Beneitez Galan, Miguel
    et al.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Stability, Transition and Control. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Duguet, Yohann
    LIMSI-CNRS, Université Paris-Saclay, P91405 Orsay, France.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Stability, Transition and Control. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Modeling the collapse of the edge when two transition routes compete2020In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 102, no 5, article id 053108Article in journal (Refereed)
    Abstract [en]

    The transition to turbulence in many shear flows proceeds along two competing routes, one linked with finite-amplitude disturbances and the other one originating from a linear instability, as in, e.g., boundary layer flows. The dynamical systems concept of an edge manifold has been suggested in the subcritical case to explain the partition of the state space of the system. This investigation is devoted to the evolution of the edge manifold when linear stability is added in such subcritical systems, a situation poorly studied despite its prevalence in realistic fluid flows. In particular, the fate of the edge state as a mediator of transition is unclear. A deterministic three-dimensional model is suggested, parametrized by the linear instability growth rate. The edge manifold evolves topologically, via a global saddle-loop bifurcation of the underlying invariant sets, from the separatrix between two attraction basins to the mediator between two transition routes. For larger instability rates, the stable manifold of the saddle point increases in codimension from 1 to 2 after an additional local pitchfork node bifurcation, causing the collapse of the edge manifold. As the growth rate is increased, three different regimes of this model are identified, each one associated with a flow case from the recent hydrodynamic literature. A simple nonautonomous generalization of the model is also suggested in order to capture the complexity of spatially developing flows.

  • 23.
    Beneitez Galan, Miguel
    et al.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Duguet, Yohann
    Univ Paris Saclay, LIMSI, CNRS, P91405, Orsay, France..
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Engineering Mechanics.
    Edge manifold as a Lagrangian coherent structure in a high-dimensional state space2020In: Physical Review Research, E-ISSN 2643-1564, Vol. 2, no 3, article id 033258Article in journal (Refereed)
    Abstract [en]

    Dissipative dynamical systems characterized by two basins of attraction are found in many physical systems, notably in hydrodynamics where laminar and turbulent regimes can coexist. The state space of such systems is structured around a dividing manifold called the edge, which separates trajectories attracted by the laminar state from those reaching the turbulent state. We apply here concepts and tools from Lagrangian data analysis to investigate this edge manifold. This approach is carried out in the state space of autonomous arbitrarily high-dimensional dissipative systems, in which the edge manifold is reinterpreted as a Lagrangian coherent structure (LCS). Two different diagnostics, finite-time Lyapunov exponents and Lagrangian descriptors, are used and compared with respect to their ability to identify the edge and their scalability. Their properties are illustrated on several low-order models of subcritical transition of increasing dimension and complexity, as well on well-resolved simulations of the Navier-Stokes equations in the case of plane Couette flow. They allow for a mapping of the global structure of both the state space and the edge manifold based on quantitative information. Both diagnostics can also be used to generate efficient bisection algorithms to approach asymptotic edge states, which outperform classical edge tracking.

  • 24.
    Beneitez Galan, Miguel
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Duguet, Yohann
    LIMSI-CNRS, UPR 3251, Université Paris-Saclay, Orsay, F-91403, France Abstract.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Edge tracking in spatially developing boundary layer flows2019In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 881, p. 164-181Article in journal (Refereed)
    Abstract [en]

    Recent progress in understanding subcritical transition to turbulence is based on the concept of the edge, the manifold separating the basins of attraction of the laminar and the turbulent state. Originally developed in numerical studies of parallel shear flows with a linearly stable base flow, this concept is adapted here to the case of a spatially developing Blasius boundary layer. Longer time horizons fundamentally change the nature of the problem due to the loss of stability of the base flow due to Tollmien-Schlichting (TS) waves. We demonstrate, using a moving box technique, that efficient long-time tracking of edge trajectories is possible for the parameter range relevant to bypass transition, even if the asymptotic state itself remains out of reach. The flow along the edge trajectory features streak switching observed for the first time in the Blasius boundary layer. At long enough times, TS waves co-exist with the coherent structure characteristic of edge trajectories. In this situation we suggest a reinterpretation of the edge as a manifold dividing the state space between the two main types of boundary layer transition, i.e. bypass transition and classical transition.

  • 25.
    Beneitez Galan, Miguel
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Duguet, Yohann
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics.
    Finite-time stability of an edge trajectory in the Blasius boundary layerManuscript (preprint) (Other academic)
  • 26.
    Beneitez Galan, Miguel
    et al.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Duguet, Yohann
    LISN-CNRS, Campus Universitaire d'Orsay, Université Paris-Saclay, F-91400 Orsay, France.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Instability of the optimal edge trajectory in the Blasius boundary layer2023In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 971, article id A42Article in journal (Refereed)
    Abstract [en]

    In the context of linear stability analysis, considering unsteady base flows is notoriously difficult. A generalisation of modal linear stability analysis, allowing for arbitrarily unsteady base flows over a finite time, is therefore required. The recently developed optimally time-dependent (OTD) modes form a projection basis for the tangent space. They capture the leading amplification directions in state space under the constraint that they form an orthonormal basis at all times. The present numerical study illustrates the possibility to describe a complex flow case using the leading OTD modes. The flow under investigation is an unsteady case of the Blasius boundary layer, featuring streamwise streaks of finite length and relevant to bypass transition. It corresponds to the state space trajectory initiated by the minimal seed; such a trajectory is unsteady, free from any spatial symmetry and shadows the laminar-turbulent separatrix for a finite time only. The finite-time instability of this unsteady base flow is investigated using the 8 leading OTD modes. The analysis includes the computation of finite-time Lyapunov exponents as well as instantaneous eigenvalues, and of the associated flow structures. The reconstructed instantaneous eigenmodes are all of outer type. They map unambiguously the spatial regions of largest instantaneous growth. Other flow structures, previously reported as secondary, are identified with this method as relevant to streak switching and to streamwise vortical ejections. The dynamics inside the tangent space features both modal and non-modal amplification. Non-normality within the reduced tangent subspace, quantified by the instantaneous numerical abscissa, emerges only as the unsteadiness of the base flow is reduced.

  • 27.
    Blanco, Diego C. P.
    et al.
    Inst Tecnol Aeronaut, Div Engn Aerosp, BR-12228900 Sao Jose Dos Campos, SP, Brazil..
    Hanifi, Ardeshir
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Cavalieri, Andre V. G.
    Inst Tecnol Aeronaut, Div Engn Aerosp, BR-12228900 Sao Jose Dos Campos, SP, Brazil..
    Linear and nonlinear receptivity mechanisms in boundary layers subject to free-stream turbulence2024In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 979, article id A31Article in journal (Refereed)
    Abstract [en]

    Large-eddy simulations of a flat-plate boundary layer, without a leading edge, subject to multiple levels of incoming free-stream turbulence are considered in the present work. Within an input-output model, where nonlinear terms of the incompressible Navier-Stokes equations are treated as an external forcing, we manage to separate inputs related to perturbations coming through the intake of the numerical domain, whose evolution represents a linear mechanism, and the volumetric nonlinear forcing due to triadic interactions. With these, we perform the full reconstruction of the statistics of the flow, as measured in the simulations, to quantify pairs of wavenumbers and frequencies more affected by either linear or nonlinear receptivity mechanisms. Inside the boundary layer, different wavenumbers at near-zero frequency reveal streaky structures. Those that are amplified predominantly via linear interactions with the incoming vorticity occur upstream and display transient growth, while those generated by the nonlinear forcing are the most energetic and appear in more downstream positions. The latter feature vortices growing proportionally to the laminar boundary layer thickness, along with a velocity profile that agrees with the optimal amplification obtained by linear transient growth theory. The numerical approach presented is general and could potentially be extended to any simulation for which receptivity to incoming perturbations needs to be assessed.

  • 28.
    Brandt, Luca
    et al.
    KTH, Superseded Departments (pre-2005), Mechanics.
    Cossu, C.
    Chomaz, J. M.
    Huerre, P.
    Henningson, Dan S.
    KTH, Superseded Departments (pre-2005), Mechanics.
    On the convectively unstable nature of optimal streaks in boundary layers2003In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 485, p. 221-242Article in journal (Refereed)
    Abstract [en]

    The objective of the study is to determine the absolute/convective nature of the secondary instability experienced by finite-amplitude streaks in the flat-plate boundary layer. A family of parallel streaky base flows is defined by extracting velocity profiles from direct numerical simulations of nonlinearly saturated optimal streaks. The computed impulse response of the streaky base flows is then determined as a function of streak amplitude and streamwise station. Both the temporal and spatio-temporal instability properties are directly retrieved from the impulse response wave packet, without solving the dispersion relation or applying the pinching point criterion in the complex wavenumber plane. The instability of optimal streaks is found to be unambiguously convective for all streak amplitudes and streamwise stations. It is more convective than the Blasius boundary layer in the absence of streaks; the trailing edge-velocity of a Tollmien-Schlichting wave packet in the Blasius boundary layer is around 35% of the free-stream velocity, while that of the wave packet riding on the streaky base flow is around 70%. This is because the streak instability is primarily induced by the spanwise shear and the associated Reynolds stress production term is located further away from the wall, in a larger velocity region, than for the Tollmien-Schlichting instability. The streak impulse response consists of the sinuous mode of instability triggered by the spanwise wake-like profile, as confirmed by comparing the numerical results with the absolute/convective instability properties of the family of two-dimensional wakes introduced by Monkewitz (1988). The convective nature of the secondary streak instability implies that the type of bypass transition studied here involves streaks that behave as amplifiers of external noise.

  • 29.
    Brandt, Luca
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Cossu, C
    Henningson, Dan S
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Chomaz, J M
    Huerre, P
    Numerical studies of streak instability in boundary layers2006In: Sixth IUTAM Symposium on Laminar-Turbulent Transition / [ed] Govindarajan, R, DORDRECHT: SPRINGER , 2006, Vol. 78, p. 121-126Conference paper (Refereed)
    Abstract [en]

    Numerical results on the stability of boundary layers in the presence of streaks, assumed steady and spanwise periodic, are presented. The instability features are retrieved both from stability analysis and from the numerical simulation of the flow impulse response. It is found that the presence of streaks of moderate amplitudes is able to quench the viscous Tollmien-Schlichting waves. However, a threshold exists beyond which secondary inflectional instabilities occur. Streaky basic flows unstable to both sinuous and varicose perturbations are considered. To gain physical understanding of the instability mechanisms the equation for the perturbation kinetic energy is analysed. To investigate the sinuous instability modes an analytical model streak is also proposed.

  • 30.
    Brandt, Luca
    et al.
    KTH, Superseded Departments (pre-2005), Mechanics.
    Henningson, Dan S.
    KTH, Superseded Departments (pre-2005), Mechanics.
    Direct numerical simulations of streak breakdown in boundary layers2004In: Direct and Large-Eddy Simulation V, Proceedings / [ed] Friedrich, R; Geurts, BJ; Metais, O, 2004, Vol. 9, p. 175-196Conference paper (Refereed)
    Abstract [en]

    Numerical simulations of bypass transition in Blasius boundary layers are presented. The breakdown of streamwise streaks is first considered in the case of the steady, spanwise periodic basic flows arising from the nonlinear saturation of optimal perturbations and then in the case of transition in boundary layers subject to free-stream turbulence. Similarity and differences with previous work are discussed.

  • 31.
    Brandt, Luca
    et al.
    KTH, Superseded Departments (pre-2005), Mechanics.
    Henningson, Dan Stefan
    KTH, Superseded Departments (pre-2005), Mechanics.
    Transition of streamwise streaks in zero-pressure-gradient boundary layers2002In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 472, p. 229-261Article in journal (Refereed)
    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.

  • 32.
    Brandt, Luca
    et al.
    KTH, Superseded Departments (pre-2005), Mechanics.
    Henningson, Dan Stefan
    KTH, Superseded Departments (pre-2005), Mechanics.
    Ponziani, D
    Weakly nonlinear analysis of boundary layer receptivity to free-stream disturbances2002In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 14, no 4, p. 1426-1441Article in journal (Refereed)
    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.

  • 33.
    Brandt, Luca
    et al.
    KTH, Superseded Departments (pre-2005), Mechanics.
    Schlatter, Philipp
    KTH, Superseded Departments (pre-2005), Mechanics.
    Henningson, Dan S.
    KTH, Superseded Departments (pre-2005), Mechanics.
    Transition in boundary layers subject to free-stream turbulence2004In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 517, p. 167-198Article in journal (Refereed)
    Abstract [en]

    The effect of high levels of free-stream turbulence on the transition in a Blasius boundary layer is studied by means of direct numerical simulations, where a synthetic turbulent inflow is obtained as superposition of modes of the continuous spectrum of the Orr-Sommerfeld and Squire operators. In the present bypass scenario the flow in the boundary layer develops streamwise elongated regions of high and low streamwise velocity and it is suggested that the breakdown into turbulent spots is related to local instabilities of the strong shear layers associated with these streaks. Flow structures typical of the spot precursors are presented and these show important similarities with the flow structures observed in previous studies on the secondary instability and breakdown of steady symmetric streaks. Numerical experiments are performed by varying the energy spectrum of the incoming perturbation. It is shown that the transition location moves to lower Reynolds numbers by increasing the integral length scale of the free-stream turbulence. The receptivity to free-stream turbulence is also analysed and it is found that two distinct physical mechanisms are active depending on the energy content of the external disturbance. If low-frequency modes diffuse into the boundary layer, presumably at the leading edge, the streaks Lire induced by streamwise vorticity through the linear lift-up effect. If, conversely, the free-stream perturbations are mainly located above the boundary layer a nonlinear process is needed to create streamwise vortices inside the shear layer. The relevance of the two mechanisms is discussed.

  • 34.
    Brethouwer, Geert
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Duguet, Yohann
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Johansson, Arne V.
    KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Recurrent Bursts via Linear Processes in Turbulent Environments2014In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 112, no 14, p. 144502-Article in journal (Refereed)
    Abstract [en]

    Large-scale instabilities occurring in the presence of small-scale turbulent fluctuations are frequently observed in geophysical or astrophysical contexts but are difficult to reproduce in the laboratory. Using extensive numerical simulations, we report here on intense recurrent bursts of turbulence in plane Poiseuille flow rotating about a spanwise axis. A simple model based on the linear instability of the mean flow can predict the structure and time scale of the nearly periodic and self-sustained burst cycles. Poiseuille flow is suggested as a prototype for future studies of low-dimensional dynamics embedded in strongly turbulent environments.

  • 35.
    Brito, Pedro P. C.
    et al.
    Inst Tecnol Aeronaut, Aerodynam Dept, Sao Jose Dos Campos, Brazil..
    Morra, Pierluigi
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Cavalieri, Andre V. G.
    Inst Tecnol Aeronaut, Aerodynam Dept, Sao Jose Dos Campos, Brazil..
    Araujo, Tiago B.
    Inst Tecnol Aeronaut, Aerodynam Dept, Sao Jose Dos Campos, Brazil..
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Hanifi, Ardeshir
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Experimental control of Tollmien-Schlichting waves using pressure sensors and plasma actuators2021In: Experiments in Fluids, ISSN 0723-4864, E-ISSN 1432-1114, Vol. 62, no 2, article id 32Article in journal (Refereed)
    Abstract [en]

    This manuscript presents a successful application of the inverse feed-forward control (IFFC) technique for control of the Tollmien-Schlichting (TS) waves over a wing profile placed in an open-circuit wind tunnel. Active cancellation of two-dimensional broadband TS disturbances is performed using a single dielectric barrier discharge (DBD) plasma actuator. The measurements required for the IFFC are performed with microphones, instead of hot wires often used for this purpose, in order to reduce the space occupied by the sensors and assess the suitability of simpler and cheaper devices. An attenuation of the TS-wave amplitude of one order of magnitude is achieved. Direct numerical simulations (DNS) are also performed and compared to the outcome of the experiments. The plasma-actuator model used in DNS is a mapping of the force field used by Fabbiane et al. (In: Proceedings of TSFP-9, Melbourne, 2015a) to the actual geometry, whereas the sensors (microphones) are modeled as pressure probes. Despite these modelling choices, a good agreement between the results of DNS and the experiments is achieved. However, the control performance is better in the DNS, with attenuation of three orders of magnitude of TS-wave amplitude. Further analysis of experiments and simulations shows that the limiting factor in the experiments is the ambient low-frequency acoustic waves in the wind tunnel. These waves are sensed by the microphones and act as noise in the analysis of TS-wave evolution and thus leading to lower coherence between sensors and actuators. This in turn leads to a suboptimal control kernel in the experiment.Please confirm if the inserted city and country are correct in Affiliations [Aff1, Aff2]. Amend if necessary.Confirmed. It is correct.Please confirm if the corresponding author is correctly identified. Amend if necessary.Confirmed. The corresponding author is Pedro P. C. Brito.

  • 36.
    Brynjell-Rahkola, Mattias
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Barman, Emelie
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Hanifi, Ardeshir
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    On the stability of a Blasius boundary layer subject to localized suction2017Report (Other academic)
    Abstract [en]

    In this work the problem of premature transition in boundary layers due to localized suction is revisited. A thorough study involving nonlinear direct numerical simulations, a three-dimensional linear stability analysis, a sensitivity study and a Koopman analysis is presented. The ensemble of these different techniques enables the origins of oversuction to be studied in great detail and provides new insight into the transition process of the flow. The configuration considered consists of an infinite row of widely separated suction pipes that are mounted to the plate at right angles. For the parameter range investigated, the flow inside the pipe is seen to bifurcate at a lower suction ratio than the boundary layer and thus act as an oscillator that forces the external flow over the plate. At low levels of suction, this forcing is not enough to cause transition in the boundary layer, but as the suction level is increased beyond criticality, modes originating from the pipe and extending into the boundary layer are seen to destabilize as well. These modes enable the perturbations forced in the pipe to also amplify in the boundary layer, which leads to a rapid breakdown to turbulence in the wake of the suction hole.

  • 37.
    Brynjell-Rahkola, Mattias
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    Barman, Emelie
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    Peplinski, Adam
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    Hanifi, Ardeshir
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. Swedish Defence Research Agency, FOI.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    On the stability of flat plate boundary layers subject to localized suction2015Report (Other academic)
    Abstract [en]

    The stability of the Blasius boundary layer subject to localized suction is revisited. Using tools of global stability analysis, the leading direct and adjoint eigenpairs are determined, and novel insight into the sensitivity and receptivity of the flow is obtained. The problem is addressed through high-order spectral element simulations, which enables the inclusion of a suction pipe into the domain. Due to this, a detailed investigation of the connection between the pipe flow and the boundary layer flow is possible. For all cases investigated, the former always turns out to transition for a lower Reynolds number and suction rate than the latter, and the transition scenario is found to be due to a global instability originating inside a separation bubble at the pipe inlet. Identification of such regions, provides information that is valuable in further development of algorithms for laminar flow control.

  • 38.
    Brynjell-Rahkola, Mattias
    et al.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Hanifi, Ardeshir
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    On the stability of a Blasius boundary layer subject to localised suction2019In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 871, p. 717-741Article in journal (Refereed)
    Abstract [en]

    In this study the origins of premature transition due to oversuction in boundary layers are studied. An infinite row of circular suction pipes that are mounted at right angles to a flat plate subject to a Blasius boundary layer is considered. The interaction between the flow originating from neighbouring holes is weak and for the parameters investigated, the pipe is always found to be unsteady regardless of the state of the flow in the boundary layer. A stability analysis reveals that the appearance of boundary layer transition can be associated with a linear instability in the form of two unstable eigenmodes inside the pipe that have weak tails, which extend into the boundary layer. Through an energy budget and a structural sensitivity analysis, the origin of this flow instability is traced to the structures developing inside the pipe near the pipe junction. Although the amplitudes of the modes in the boundary layer are orders of magnitude smaller than the corresponding amplitudes inside the pipe, a Koopman analysis of the data gathered from a nonlinear direct numerical simulation confirms that it is precisely these disturbances that are responsible for transition to turbulence in the boundary layer due to oversuction.

  • 39.
    Brynjell-Rahkola, Mattias
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    A note on the numerical realization of helical vortices: application to vortex instability2017Report (Other academic)
    Abstract [en]

    The need to numerically represent a free vortex system arises frequently in fundamental and applied research. Many possible techniques for realizing this vortex system exist but most tend to prioritize accuracy either inside or outside of the vortex core, which therefore makes them unsuitable to for a stability analysis considering the entire flow field. In this article, a simple method is presented that is shown to yield an accurate representation of the flow inside and outside of the vortex core. The method is readily implemented in any incompressible Navier–Stokes solver using primitive variables and Cartesian coordinates. It can potentially be used to model a wide range of vortices but is here applied to reproduce a recent experiment by Quaranta et al. (2017) considering two helices. A three-dimensional stability analysis is performed and yields an eigenvalue spectrum that features both long- and short-wave instabilities.

  • 40.
    Brynjell-Rahkola, Mattias
    et al.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Mechanics.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Mechanics.
    Numerical realization of helical vortices: application to vortex instability2019In: Theoretical and Computational Fluid Dynamics, ISSN 0935-4964, E-ISSN 1432-2250Article in journal (Refereed)
    Abstract [en]

    The need to numerically represent a free vortex system arises frequently in fundamental and applied research. Many possible techniques for realizing this vortex system exist but most tend to prioritize accuracy either inside or outside of the vortex core, which therefore makes them unsuitable for a stability analysis considering the entire flow field. In this article, a simple method is presented that is shown to yield an accurate representation of the flow inside and outside of the vortex core. The method is readily implemented in any incompressible Navier–Stokes solver using primitive variables and Cartesian coordinates. It can potentially be used to model a wide range of vortices but is here applied to the case of two helices, which is of renewed interest due to its relevance for wind turbines and helicopters. Three-dimensional stability analysis is performed in both a rotating and a translating frame of reference, which yield eigenvalue spectra that feature both mutual inductance and elliptic instabilities. Comparison of these spectra with available theoretical predictions is used to validate the proposed baseflow model, and new insights into the elliptic instability of curved Batchelor vortices are presented. Furthermore, it is shown that the instabilities in the rotating and the translating reference frames have the same structure and growth rate, but different frequency. A relation between these frequencies is provided.

  • 41.
    Brynjell-Rahkola, Mattias
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Mechanics of Industrial Processes. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Hanifi, Ardeshir
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Modal analysis of roughness-induced crossflow vortices in a Falkner-Skan-Cooke boundary layer2013In: International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2013, TSFP-8 , 2013Conference paper (Refereed)
    Abstract [en]

    A three-dimensional global stability analysis using high-order direct numerical simulations is performed to investigate the effect of surface roughness with Reynolds number (based on roughness height) Rek above and below the critical value for transition, on the eigenmodes of a Falkner-Skan-Cooke boundary layer. The surface roughness is introduced with the immersed boundary method and the eigenvalues and eigenfunctions are solved using an iterative time-stepper method. The study reveals a global instability for the case with higher Reynolds number that causes the flow in the non-linear simulations to break down to turbulence shortly downstream of the roughness. Examination of the unstable linear global modes show that these are the same modes that are observed in experiments immediately before breakdown due to secondary instability, which emphasizes the importance of these modes in transition.

  • 42.
    Brynjell-Rahkola, Mattias
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Hanifi, Ardeshir
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Henningson, Dan Stefan
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    Global Stability Analysis of a Roughness Wake in a Falkner-Skan-Cooke Boundary Layer2015In: Procedia IUTAM, Elsevier, 2015, p. 192-200Conference paper (Refereed)
    Abstract [en]

    A global stability analysis of a Falkner-Skan-Cooke boundary layer with distributed three-dimensional surface roughness is per- formed using high-order direct numerical simulations. Computations have been performed for different sizes of the roughness elements, and a time-stepping method has been used to find the instability modes. The study shows that a critical roughness height beyond which a global instability is excited does exist. Furthermore, the origins of this instability is examined by means of an energy analysis, which reveals the production and dissipation terms responsible for the instability, as well as the region in space where the instability originates.

  • 43.
    Brynjell-Rahkola, Mattias
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    Shahriari, Nima
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    Hanifi, Ardeshir
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. Swedish Defence Research Agency, FOI.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    Onset of global instability behind distributed surface roughness in a Falkner–Skan–Cooke boundary layer2015Report (Other academic)
    Abstract [en]

    A three-dimensional linear global stability analysis of a Falkner–Skan–Cooke boundary layer with distributed three-dimensional surface roughness is performed. The Falkner–Skan–Cooke boundary layer models the flow over swept airplane wings, and investigation of the critical roughness size for which a global instability emerges is thus of great importance within aeronautical applications. The study considers high-order direct numerical simulations and shows that such a critical roughness height exists for the Falkner–Skan–Cooke boundary layer. The roughness Reynolds number and roughness element aspect ratio for which this happens is comparable to the transition data reported in the literature for two-dimensional boundary layers. This demonstrates the importance of the local flow conditions in the vicinity of the roughness for triggering a global instability, although the resulting breakdown scenario is completely different from that of two-dimensional boundary layers. This breakdown scenario is studied in detail, and a global energy analysis is used to reveal the structures and mechanisms responsible for production and dissipation of perturbation energy.

  • 44.
    Brynjell-Rahkola, Mattias
    et al.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Mechanics.
    Shahriari, Nima
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Mechanics.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Mechanics.
    Hanifi, Ardeshir
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Mechanics.
    Stability and sensitivity of a cross-flow-dominated Falkner-Skan-Cooke boundary layer with discrete surface roughness2017In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 826, p. 830-850Article in journal (Refereed)
    Abstract [en]

    With the motivation of determining the critical roughness size, a global stability and sensitivity analysis of a three-dimensional Falkner-Skan-Cooke (FSC) boundary layer with a cylindrical surface roughness is performed. The roughness size is chosen such that breakdown to turbulence is initiated by a global version of traditional secondary instabilities of the cross-flow (CF) vortices instead of an immediate flow tripping at the roughness. The resulting global eigenvalue spectra of the systems are found to be very sensitive to numerical parameters and domain size. This sensitivity to numerical parameters is quantified using the epsilon-pseudospectrum, and the dependency on the domain is analysed through an impulse response, structural sensitivity analysis and an energy budget. It is shown that while the frequencies remain relatively unchanged, the growth rates increase with domain size, which originates from the inclusion of stronger CF vortices in the baseflow. This is reflected in a change in the rate of advective energy transport by the baseflow. It is concluded that the onset of global instability in a FSC boundary layer as the roughness height is increased does not correspond to an immediate flow tripping behind the roughness, but occurs for lower roughness heights if sufficiently long domains are considered. However, the great sensitivity results in an inability to accurately pinpoint the exact parameter values for the bifurcation, and the large spatial growth of the disturbances in the long domains eventually becomes larger than can be resolved using finite-precision arithmetic.

  • 45.
    Brynjell-Rahkola, Mattias
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Shahriari, Nima
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Hanifi, Ardeshir
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. Swedish Defence Research Agency, Sweden.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Stability and sensitivity of a crossflow-dominated Falkner–Skan–Cooke boundary layer with discrete surface roughness2016In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645Article in journal (Refereed)
    Abstract [en]

    With the motivation of determining the critical roughness size, a global stability and sensitivity analysis of a three-dimensional Falkner–Skan–Cooke (FSC) boundary layer with a cylindrical surface roughness is performed. The roughness size is chosen such that breakdown to turbulence is initiated by a global version of traditional secondary instabilities of the crossflow (CF) vortices, instead of an immediate flow tripping at the roughness. The resulting global eigenvalue spectra of the systems are found to be very sensitive to numerical parameters and domain size. This sensitivity to numerical parameters is quantified using the "-pseudospectrum, and the dependency on the domain is analysed through an impulse response and an energy budget. It is shown that the growth rates increase with domain size, which originates from the inclusion of stronger CF vortices in the baseflow. This is reflected in a change in the rate of advective energy transport by the baseflow. It is concluded that the onset of global instability in a FSC boundary layer as the roughness height is increased does not correspond to an immediate flow tripping behind the roughness, but occurs for lower roughness heights if su ciently long domains are considered. However, the great sensitivity results in an inability to accurately pinpoint the exact parameter values for the bifurcation, and the large spatial growth of the disturbances in the long domains eventually becomes larger than what can be resolved using finite precision arithmetics. 

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  • 46.
    Brynjell-Rahkola, Mattias
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Tuckerman, L. S.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Computing Optimal Forcing Using Laplace Preconditioning2017In: Communications in Computational Physics, ISSN 1815-2406, E-ISSN 1991-7120, Vol. 22, no 5, p. 1508-1532Article in journal (Refereed)
    Abstract [en]

    For problems governed by a non-normal operator, the leading eigenvalue of the operator is of limited interest and a more relevant measure of the stability is obtained by considering the harmonic forcing causing the largest system response. Various methods for determining this so-called optimal forcing exist, but they all suffer from great computational expense and are hence not practical for large-scale problems. In the present paper a new method is presented, which is applicable to problems of arbitrary size. The method does not rely on timestepping, but on the solution of linear systems, in which the inverse Laplacian acts as a preconditioner. By formulating the search for the optimal forcing as an eigenvalue problem based on the resolvent operator, repeated system solves amount to power iterations, in which the dominant eigenvalue is seen to correspond to the energy amplification in a system for a given frequency, and the eigenfunction to the corresponding forcing function. Implementation of the method requires only minor modifications of an existing timestepping code, and is applicable to any partial differential equation containing the Laplacian, such as the Navier-Stokes equations. We discuss the method, first, in the context of the linear Ginzburg-Landau equation and then, the two-dimensional lid-driven cavity flow governed by the Navier-Stokes equations. Most importantly, we demonstrate that for the lid-driven cavity, the optimal forcing can be computed using a factor of up to 500 times fewer operator evaluations than the standard method based on exponential timestepping.

  • 47.
    Brynjell-Rahkola, Mattias
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    Tuckerman, Laurette
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    A method for computing optimal forcing of convectively unstable flows using Laplace preconditioningManuscript (preprint) (Other academic)
    Abstract [en]

    For problems governed by a non-normal operator, the leading eigenvalue of the operator is of limited interest and a more relevant measure of the stability is obtained by considering the harmonic forcing causing the largest system response. Various methods for determining this so-called optimal forcing exist, but they all suffer from great computational expense and are hence not practical for large-scale problems. In the present paper a new method is presented, which is applicable to problems of arbitrary size. The method does not rely on timestepping, but on the solution of linear systems, in which the inverse Laplacian acts as a preconditioner. By formulating the problem of finding the optimal forcing as an eigenvalue problem based on the resolvent operator, repeated system solves amount to power iterations, in which the dominant eigenvalue is seen to correspond to the energy amplification in a system for a given frequency, and the eigenfunction to the optimal forcing function. Implementation of the method requires only minor modifications of an existing time-stepping code, and is applicable to any partial differential equation containing the Laplacian, such as the Navier-Stokes equations. We discuss it in the context of the linear Ginzburg-Landau equation.

  • 48. Byström, Martin G.
    et al.
    Hanifi, Ardeshir
    Henningson, Dan S.
    Optimal disturbances in the Falkner-Skan-Cooke boundary laters2007Report (Other academic)
  • 49.
    Byström, Martin G.
    et al.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics.
    Pralits, Jan O.
    Hanifi, Ardeshir
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Heninngson, Dan S.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Luchini, Paolo
    University of Salerno.
    Optimal Disturbances in Three-dimensional Boundary-Layer Flows2007Conference paper (Refereed)
    Abstract [en]

    In the present paper,  two di!erent approaches tocompute the optimal disturbances in the quasi three-dimensional flows are presented. One of the approachesis based on the Multiple Scales method and the otherone utilises the Parabolised Stability Equations.

  • 50.
    Byström, Martin
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Levin, Ori
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Henningson, Dan
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Optimal disturbances in suction boundary layers.2007In: European journal of mechanics. B, Fluids, ISSN 0997-7546, E-ISSN 1873-7390, Vol. 26, no 3, p. 330-343Article in journal (Refereed)
    Abstract [en]

    A well-known optimization procedure is used to find the optimal disturbances in two different suction boundary layers within the spatial framework. The maximum algebraic growth in the asymptotic suction boundary layer is presented and compared to previous temporal results. Furthermore, the spatial approach allows a study of a developing boundary layer in which a region at the leading edge is left free from suction. This new flow, which emulates the base flow of a recent wind-tunnel experiment, is herein denoted a semi-suction boundary layer. It is found that the optimal disturbances for these two suction boundary layers consist of streamwise vortices that develop into streamwise streaks, as previously found for a number of shear flows. It is shown that the maximum energy growth in the semi-suction boundary layer is obtained over the upstream region where no suction is applied. The result indicates that the spanwise scale of the streaks is set in this region, which is in agreement with previous experimental findings.

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