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  • 1.
    Alfredsson, P. Henrik
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Örlü, Ramis
    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.
    The viscous sublayer revisited-exploiting self-similarity to determine the wall position and friction velocity2011In: Experiments in Fluids, ISSN 0723-4864, E-ISSN 1432-1114, Vol. 51, no 1, p. 271-280Article in journal (Refereed)
    Abstract [en]

    In experiments using hot wires near the wall, it is well known that wall interference effects between the hot wire and the wall give rise to errors, and mean velocity data from the viscous sublayer can usually not be used to determine the wall position, nor the friction velocity from the linear velocity distribution. Here, we introduce a new method that takes advantage of the similarity of the probability density distributions (PDF) or rather the cumulative distribution functions (CDF) in the near-wall region. By using the velocity data in the CDF in a novel way, it is possible to circumvent the problem associated with heat transfer to the wall and to accurately determine both the wall position and the friction velocity. Prior to its exploitation, the self-similarity of the distribution functions of the streamwise velocity fluctuations within the viscous sublayer is established, and it is shown that they can accurately be described by a lognormal distribution.

  • 2.
    Appelquist, Elinor
    et al.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics. Swedish e-Science Research Centre (SeRC).
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics. Swedish e-Science Research Centre (SeRC).
    Alfredsson, P. Henrik
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics.
    Lingwood, Rebecca J.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics. University of Cambridge, Cambridge .
    Investigation of the Global Instability of the Rotating-disk Boundary Layer2015In: Procedia IUTAM, Elsevier, 2015, p. 321-328Conference paper (Refereed)
    Abstract [en]

    The development of the flow over a rotating disk is investigated by direct numerical simulations using both the linearized and fully nonlinear incompressible Navier-Stokes equations. These simulations allow investigation of the transition to turbulence of the realistic spatially-developing boundary layer. The current research aims to elucidate further the global linear stability properties of the flow, and relate these to local analysis and discussions in literature. An investigation of the nonlinear upstream (inward) influence is conducted by simulating a small azimuthal section of the disk (1/68). The simulations are initially perturbed by an impulse disturbance where, after the initial transient behaviour, both the linear and nonlinear simulations show a temporally growing upstream mode. This upstream global mode originates in the linear case close to the end of the domain, excited by an absolute instability at this downstream position. In the nonlinear case, it instead originates where the linear region ends and nonlinear harmonics enter the flow field, also where an absolute instability can be found. This upstream global mode can be shown to match a theoretical mode from local linear theory involved in the absolute instability at either the end of the domain (linear case) or where nonlinear harmonics enter the field (nonlinear case). The linear simulation grows continuously in time whereas the nonlinear simulation saturates and the transition to turbulence moves slowly upstream towards smaller radial positions asymptotically approaching a global upstream mode with zero temporal growth rate, which is estimated at a nondimensional radius of 582.

  • 3.
    Appelquist, Ellinor
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Physics.
    Imayama, Shintaro
    KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Physics.
    Alfredsson, Henrik
    KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Physics.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    Lingwood, Rebecca
    KTH, School of Engineering Sciences (SCI), Mechanics. School of Engineering and Materials Science, Queen Mary University of London, Mile End Road, London, United Kingdom.
    Linear disturbances in the rotating-disk flow: A comparison between results from simulations, experiments and theory2016In: European journal of mechanics. B, Fluids, ISSN 0997-7546, E-ISSN 1873-7390, Vol. 55, p. 170-181Article in journal (Refereed)
    Abstract [en]

    The incompressible Navier-Stokes equations have an exact similarity solution for the flow over an infinite rotating disk giving a laminar boundary layer of constant thickness, also known as the von Kármán flow. It is well known now that there is an absolute instability of the boundary layer which is linked to transition to turbulence, but convective routes are also observed. It is these convective modes that we focus on here. A comparison of three different approaches to investigate the convective, so called Type-I, stationary crossflow instability is presented here. The three approaches consist of local linear stability analysis, direct numerical simulations (DNS) and experiments. The ’shooting method’ was used to compute the local linear stability whereas linear DNS was performed using a spectral-element method for a full annulus of the disk, a quarter and 1/32 of an annulus, each with one roughness element in the computational domain. These correspond to simulating one, four and 32 roughness elements on the full disk surface and in addition a case with randomly-distributed roughnesses was simulated on the full disk. Two different experimental configurations were used for the comparison: i) a clean-disk condition, i.e. unexcited boundary-layer flow; and ii) a rough-disk condition, where 32 roughness elements were placed on the disk surface to excite the Type-I stationary vortices. Comparisons between theory, DNS and experiments with respect to the structure of the stationary vortices are made. The results show excellent agreement between local linear stability analysis and both DNS and experiments for a fixed azimuthal wavenumber (32 roughnesses). This agreement clearly shows that the three approaches capture the same underlying physics of the setup, and lead to an accurate description of the flow. It also verifies the numerical simulations and shows the robustness of experimental measurements of the flow case. The effects of the azimuthal domain size in the DNS and superposition of multiple azimuthal wavenumbers in the DNS and experiments are discussed.

  • 4.
    Appelquist, Ellinor
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Physics.
    Imayama, Shintaro
    KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Physics.
    Alfredsson, Henrik
    KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Physics.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    Lingwood, Rebecca
    KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Physics. University of Cambridge, UK.
    Linear disturbances in the rotating-disk flow: a comparison between results from simulations, experiments and theory2014Report (Other academic)
  • 5.
    Appelquist, Ellinor
    et al.
    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.
    Imayama, Shintaro
    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. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Alfredsson, Henrik
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Lingwood, Rebecca
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Simulating the linear behaviour of the flow over a rotating disk due to roughness elements2014Report (Other academic)
  • 6.
    Appelquist, Ellinor
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Schlatter, Philip
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Alfredsson, P. Henrik
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Lingwood, Rebecca J.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. University of London, United Kingdom.
    On the global nonlinear instability of the rotating-disk flow over a finite domain2016In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 803, p. 332-355Article in journal (Refereed)
    Abstract [en]

    Direct numerical simulations based on the incompressible nonlinear Navier-Stokes equations of the flow over the surface of a rotating disk have been conducted. An impulsive disturbance was introduced and its development as it travelled radially outwards and ultimately transitioned to turbulence has been analysed. Of particular interest was whether the nonlinear stability is related to the linear stability properties. Specifically three disk-edge conditions were considered; (i) a sponge region forcing the flow back to laminar flow, (ii) a disk edge, where the disk was assumed to be infinitely thin and (iii) a physically realistic disk edge of finite thickness. This work expands on the linear simulations presented by Appelquist el al. (J. Fluid. Mech., vol. 765, 2015, pp. 612-631), where, for case (i), this configuration was shown to be globally linearly unstable when the sponge region effectively models the influence of the turbulence on the flow field. In contrast, case (ii) was mentioned there to he linearly globally stable, and here, where nonlinearity is included, it is shown that both cases (ii) and (iii) are nonlinearly globally unstable. The simulations show that the flow can he globally linearly stable if the linear wavepacket has a positive front velocity. However, in the same flow field, a nonlinear global instability can emerge, which is shown to depend on the outer turbulent region generating a linear inward-travelling mode that sustains a transition front within the domain. The results show that the front position does not approach the critical Reynolds number for the local absolute instability, R = 507. Instead, the front approaches R = 583 and both the temporal frequency and spatial growth rate correspond to a global mode originating at this position.

  • 7.
    Appelquist, Ellinor
    et al.
    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.
    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.
    Simulating the laminar von Karman flow in Nek50002014Report (Other academic)
    Abstract [en]

    The laminar incompressible boundary layer over a rotating disk, also called the von Karman flow, is investigated. The goal is to set up a direct numericalsimulation (DNS) environment for further use to investigate the transition from laminar to turbulent flow for this boundary layer. For this the spectral-element code Nek5000 is used. A set of ODE-equations are first derived from the incompressible cylindrical Navier–Stokes equations, which are solved for the exact von Karman solution. Further, Nek5000 is prepared to solve for the same laminar solution. Comparing the two solutions give a quantification of the accuracy of the DNS solver Nek5000. Different scalings of the equations are investigated, together with quantifications of how good the different available boundary conditions are, also investigating different reference frames and grid dependency of the solution. The general conclusion is that the von K ́rm ́na aflow is possible to simulate in Nek5000. The method was robust when it cameto using different scalings, reference frames and resolutions.

  • 8.
    Appelquist, Ellinor
    et al.
    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.
    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.
    Alfredsson, Henrik
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Lingwood, Rebecca
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Global linear instability and the radial boundary of the rotating-disk flowManuscript (preprint) (Other academic)
  • 9.
    Appelquist, Ellinor
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Physics. 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.
    Alfredsson, Henrik
    KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Physics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Lingwood, Rebecca
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. nstitute of Continuing Education, University of Cambridge, Madingley Hall, Madingley Cambridge, United Kingdom .
    Global linear instability of the rotating-disk flow investigated through simulations2015In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 765, p. 612-631Article in journal (Refereed)
    Abstract [en]

    Numerical simulations of the flow developing on the surface of a rotating disk are presented based on the linearized incompressible Navier-Stokes equations. The boundary-layer flow is perturbed by an impulsive disturbance within a linear global framework, and the effect of downstream turbulence is modelled by a damping region further downstream. In addition to the outward-travelling modes, inward-travelling disturbances excited at the radial end of the simulated linear region, r(end), by the modelled turbulence are included within the simulations, potentially allowing absolute instability to develop. During early times the flow shows traditional convective behaviour, with the total energy slowly decaying in time. However, after the disturbances have reached r(end), the energy evolution reaches a turning point and, if the location of r(end) is at a Reynolds number larger than approximately R = 594 (radius non-dimensionalized by root v/Omega*, where v is the kinematic viscosity and Omega* is the rotation rate of the disk), there will be global temporal growth. The global frequency and mode shape are clearly imposed by the conditions at r(end). Our results suggest that the linearized Ginzburg-Landau model by Healey (J. Fluid Mech., vol. 663, 2010, pp. 148-159) captures the (linear) physics of the developing rotating-disk flow, showing that there is linear global instability provided the Reynolds number of r(end) is sufficiently larger than the critical Reynolds number for the onset of absolute instability.

  • 10.
    Appelquist, Ellinor
    et al.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Alfredsson, P. Henrik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Lingwood, R. J.
    Transition to turbulence in the rotating-disk boundary-layer flow with stationary vortices2017In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 836, p. 43-71Article in journal (Refereed)
    Abstract [en]

    This paper proposes a resolution to the conundrum of the roles of convective and absolute instability in transition of the rotating-disk boundary layer. It also draws some comparison with swept-wing flows. Direct numerical simulations based on the incompressible Navier-Stokes equations of the flow over the surface of a rotating disk with modelled roughness elements are presented. The rotating-disk flow has been of particular interest for stability and transition research since the work by Lingwood (J.FluidMech., vol.299, 1995, pp.17-33) where an absolute instability was found. Here stationary disturbances develop from roughness elements on the disk and are followed from the linear stage, growing to saturation and finally transitioning to turbulence. Several simulations are presented with varying disturbance amplitudes. The lowest amplitude corresponds approximately to the experiment by Imayama etal. (J.FluidMech., vol.745, 2014a, pp.132-163). For all cases, the primary instability was found to be convectively unstable, and secondary modes were found to be triggered spontaneously while the flow was developing. The secondary modes further stayed within the domain, and an explanation for this is a proposed globally unstable secondary instability. For the low-amplitude roughness cases, the disturbances propagate beyond the threshold for secondary global instability before becoming turbulent, and for the high-amplitude roughness cases the transition scenario gives a turbulent flow directly at the critical Reynolds number for the secondary global instability. These results correspond to the theory of Pier (J.EngngMaths, vol.57, 2007, pp.237-251) predicting a secondary absolute instability. In our simulations, high temporal frequencies were found to grow with a large amplification rate where the secondary global instability occurred. For smaller radial positions, low-frequency secondary instabilities were observed, tripped by the global instability.

  • 11.
    Appelquist, Ellinor
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Alfredsson, P. Henrik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Lingwood, Rebecca
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Transition to turbulence in the rotating-disk boundary-layer flow with stationary vorticesArticle in journal (Refereed)
  • 12.
    Appelquist, Ellinor
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Alfredsson, P. Henrik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Lingwood, Rebecca
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Turbulence in the rotating-disk boundary layer investigated through direct numerical simulationsArticle in journal (Refereed)
  • 13.
    Appelquist, Ellinor
    et al.
    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.
    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.
    Alfredsson, P. Henrik
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Lingwood, Rebecca
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. Queen Mary University of London, Mile End Road, London, United Kingdom.
    Turbulence in the rotating-disk boundary layer investigated through direct numerical simulations2018In: European journal of mechanics. B, Fluids, ISSN 0997-7546, E-ISSN 1873-7390, Vol. 70, p. 6-18Article in journal (Refereed)
    Abstract [en]

    Direct numerical simulations (DNS) are reported for the turbulent rotating-disk boundary layer for the first time. Two turbulent simulations are presented with overlapping small and large Reynolds numbers, where the largest corresponds to a momentum-loss Reynolds number of almost 2000. Simulation data are compared with experimental data from the same flow case reported by Imayama et al. (2014), and also a comparison is made with a numerical simulation of a two-dimensional turbulent boundary layer (2DTBL) over a flat plate reported by Schlatter and Örlü (2010). The agreement of the turbulent statistics between experiments and simulations is in general very good, as well as the findings of a missing wake region and a lower shape factor compared to the 2DTBL. The simulations also show rms-levels in the inner region similar to the 2DTBL. The simulations validate Imayama et al.’s results showing that the rotating-disk turbulent boundary layer in the near-wall region contains shorter streamwise (azimuthal) wavelengths than the 2DTBL, probably due to the outward inclination of the low-speed streaks. Moreover, all velocity components are available from the simulations, and hence the local flow angle, Reynolds stresses and all terms in the turbulent kinetic energy equation are also discussed. However there are in general no large differences compared to the 2DTBL, hence the three-dimensional effects seem to have only a small influence on the turbulence.

  • 14.
    Bagheri, Shervin
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Fransson, Jens H. M.
    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.
    Research on the interaction between streamwise streaks and Tollmien-Schlichting waves at KTH2007In: ERCOFTAC Bulletin, ISSN 2518-0991, Vol. 74, p. 37-43Article in journal (Refereed)
    Abstract [en]

    This paper summarises the experimental and numericalinvestigations on how two different types of disturbancesmay, in a positive way, interact in a flat plateboundary-layer flow. The project, which mainly hasbeen centered at KTH1, has been performed in collaborationwith colleagues from University of Bologna2and LadHyX CNRS Ecole Polytechnique3, duringthe last years. The main phenomena — the stabilisingeffect of streamwise boundary-layer streakson Tollmien-Schlichting waves (and other exponentialdisturbances) — have been captured both in experiments[1, 2] and with different numerical approachessuch as direct numerical simulations [3], parabolicstability equation calculations [5] and large-eddy simulations[6]. We will here briefly review the methodsand the main results of these studies, and discuss howthey correlate with each other. For related referencesoutside KTH the interested reader is referred to thejournal publications in the reference list.

  • 15.
    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)
  • 16.
    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.

  • 17.
    Bobke, Alexandra
    et al.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Vinuesa, Ricardo
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Örlü, Ramis
    KTH, School of Engineering Sciences (SCI), Mechanics. 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.
    History effects and near equilibrium in adverse-pressure-gradient turbulent boundary layers2017In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 820, p. 667-692Article in journal (Refereed)
    Abstract [en]

    Turbulent boundary layers under adverse pressure gradients are studied using well-resolved large-eddy simulations (LES) with the goal of assessing the influence of the streamwise pressure-gradient development. Near-equilibrium boundary layers were characterized through the Clauser pressure-gradient parameter β. In order to fulfil the near-equilibrium conditions, the free stream velocity was prescribed such that it followed a power-law distribution. The turbulence statistics pertaining to cases with a constant value of β (extending up to approximately 40 boundary-layer thicknesses) were compared with cases with non-constant β distributions at matched values of β and friction Reynolds number Reδ∗. An additional case at matched Reynolds number based on displacement thickness Reδ∗ was also considered. It was noticed that non-constant β cases appear to approach the conditions of equivalent constant β cases after long streamwise distances (approximately 7 boundary-layer thicknesses). The relevance of the constant β cases lies in the fact that they define a 'canonical' state of the boundary layer, uniquely characterized by β and Re. The investigations on the flat plate were extended to the flow around a wing section overlapping in terms of β and Re. Comparisons with the flat-plate cases at matched values of β and Re revealed that the different development history of the turbulent boundary layer on the wing section leads to a less pronounced wake in the mean velocity as well as a weaker second peak in the Reynolds stresses. This is due to the weaker accumulated effect of the β history. Furthermore, a scaling law suggested by Kitsios et al. (Intl J. Heat Fluid Flow, vol. 61, 2016, pp. 129-136), proposing the edge velocity and the displacement thickness as scaling parameters, was tested on two constant-pressure-gradient parameter cases. The mean velocity and Reynolds-stress profiles were found to be dependent on the downstream development. The present work is the first step towards assessing history effects in adverse-pressure-gradient turbulent boundary layers and highlights the fact that the values of the Clauser pressure-gradient parameter and the Reynolds number are not sufficient to characterize the state of the boundary layer.

  • 18.
    Bobke, Alexandra
    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.
    Vinuesa, Ricardo
    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.
    Örlü, Ramis
    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. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    History effects and near-equilibrium in adverse-pressure-gradient turbulent boundary layersManuscript (preprint) (Other academic)
    Abstract [en]

    This study deals with turbulent boundary layers under adverse-pressure gradients. Well-resolved large-eddy simulations (LES) were performed to assess the influence of the streamwise pressure development. The pressure gradient is imposed by prescribing the free-stream velocity in the free-stream above the layer. In order to fulfill the near-equilibrium conditions, the free-stream velocity has to follow a power-law distribution. The turbulence statistics pertaining tocases with a constant Clauser pressure-gradient parameter β were compared with cases with a non-constant pressure distribution at matched β and friction Reynolds number  Reτ. It was noticed that the non-constant cases appear toconverge slowly to a certain state of the boundary layer, which is uniquelycharacterised by β and Reτ . The investigations on the flat plate were extended to the flow around a wing section. Comparisons with the flat-plate cases revealed some interesting features: In turbulent boundary layers with strong pressure gradients in the development history the energy-carrying structures in the outerregion are strongly enhanced, which can be detected by the pronounced wake inthe mean velocity as well as the large second peak in the Reynolds stresses. This was also confirmed by one-dimensional energy spectra, where more energetic large structures were identified in the outer region for stronger pressure gradients overall. A scaling law suggested by Kitsios et al. (2015) was tested on a constant pressure gradient case. The mean velocity and Reynolds stress profiles were found to be dependent on the downstream development when they were scaled with the edge velocity and displacement thickness.

  • 19.
    Bobke, Alexandra
    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.
    Vinuesa, Ricardo
    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.
    Örlü, Ramis
    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. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Large-eddy simulations of adverse pressure gradient turbulent boundary layersManuscript (preprint) (Other academic)
    Abstract [en]

    Adverse pressure-gradient (APG) turbulent boundary layers (TBL) are studied by performing well-resolved large-eddy simulations. The pressure gradient is imposed by defining the free-stream velocity distribution with the description of a power law. Different inflow conditions, box sizes and upper boundary conditions are tested in order to determine the final set-up. The statistics ofturbulent boundary layers with three different power-law coefficients and thus magnitudes of adverse pressure gradients are then compared to zero pressure-gradient (ZPG) data. The effect of the APG on TBLs is manifested in the mean flow through a much more prominent wake region and in the Reynolds stresses through the existence of an outer peak. The pre-multiplied energy budgets shows the APG influence on the distribution of the turbulent kinetic energy transfer mechanism across the boundary layer.

  • 20.
    Bobke, Alexandra
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Vinuesa, Ricardo
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Örlü, Ramis
    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, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Large-eddy simulations of adverse pressure gradient turbulent boundary layers2016In: 2nd Multiflow Summer School on Turbulence, Institute of Physics (IOP), 2016, article id 012012Conference paper (Refereed)
    Abstract [en]

    Adverse pressure-gradient (APG) turbulent boundary layers (TBL) are studied by performing well-resolved large-eddy simulations. The pressure gradient is imposed by defining the free-stream velocity distribution with the description of a power law. Different inflow conditions, box sizes and upper boundary conditions are tested in order to determine the final set-up. The statistics of turbulent boundary layers with two different power-law coefficients and thus magnitudes of adverse pressure gradients are then compared to zero pressure-gradient (ZPG) data. The effect of the APG on TBLs is manifested in the mean flow through a much more prominent wake region and in the Reynolds stresses through the existence of an outer peak. The pre-multiplied energy budgets show, that more energy is transported from the near-wall region to farther away from the wall.

  • 21.
    Bobke, Alexandra
    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.
    Örlü, Ramis
    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. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Simulations of turbulent asymptotic suction boundary layers2015In: Journal of turbulence, ISSN 1468-5248, E-ISSN 1468-5248, Vol. 17, p. 157-180Article in journal (Refereed)
    Abstract [en]

    A series of large-eddy simulations of a turbulent asymptotic suction boundary layer (TASBL) was performed in a periodic domain, on which uniform suction was applied over a flat plate. Three Reynolds numbers (defined as ratio of free-stream and suction velocity) of Re = 333, 400 and 500 and a variety of domain sizes were considered in temporal simulations in order to investigate the turbulence statistics, the importance of the computational domain size, the arising flow structures as well as temporal development length required to achieve the asymptotic state. The effect of these two important parameters was assessed in terms of their influence on integral quantities, mean velocity, Reynolds stresses, higher order statistics, amplitude modulation and spectral maps. While the near-wall region up to the buffer region appears to scale irrespective of Re and domain size, the parameters of the logarithmic law (i.e. von Kármán and additive coefficient) decrease with increasing Re, while the wake strength decreases with increasing spanwise domain size and vanishes entirely once the spanwise domain size exceeds approximately two boundary-layer thicknesses irrespective of Re. The wake strength also reduces with increasing simulation time. The asymptotic state of the TASBL is characterised by surprisingly large friction Reynolds numbers and inherits features of wall turbulence at numerically high Re. Compared to a turbulent boundary layer (TBL) or a channel flow without suction, the components of the Reynolds-stress tensor are overall reduced, but exhibit a logarithmic increase with decreasing suction rates, i.e. increasing Re. At the same time, the anisotropy is increased compared to canonical wall-bounded flows without suction. The reduced amplitudes in turbulence quantities are discussed in light of the amplitude modulation due to the weakened larger outer structures. The inner peak in the spectral maps is shifted to higher wavelength and the strength of the outer peak is much less than for TBLs. An additional spatial simulation was performed, in order to relate the simulation results to wind tunnel experiments, which – in accordance with the results from the temporal simulation – indicate that a truly TASBL is practically impossible to realise in a wind tunnel. Our unique data set agrees qualitatively with existing literature results for both numerical and experimental studies, and at the same time sheds light on the fact why the asymptotic state could not be established in a wind tunnel experiment, viz. because experimental studies resemble our simulation results from too small simulation boxes or insufficient development times.

  • 22.
    Bobke, Alexandra
    et al.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Örlü, Ramis
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Turbulent asymptotic suction boundary layers: Effect of domain size and development time2016In: Springer Proceedings in Physics, Springer, 2016, p. 173-177Conference paper (Refereed)
    Abstract [en]

    A series of large-eddy simulations of a turbulent asymptotic suction boundary layer (TASBL) was performed in a periodic domain, on which uniform suction was applied over a flat plate. The Reynolds number (defined as the ratio between free-stream and suction velocity) was Re=333" role="presentation" style="border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; margin: 0px; padding: 0px; vertical-align: baseline; outline: 0px; display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">Re=333Re=333and a variety of domain sizes were considered in temporal simulations in order to investigate the effect of the computational domain size and temporal development length. The asymptotic state is related to high friction Reynolds numbers and was found to require large computational domains and development lengths.

  • 23.
    Brandt, Luca
    et al.
    KTH, Superseded Departments, Mechanics.
    Schlatter, Philipp
    KTH, Superseded Departments, Mechanics.
    Henningson, Dan S.
    KTH, Superseded Departments, 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.

  • 24.
    Brethouwer, Geert
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Duguet, Yohann
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Numerical study of turbulent-laminar patterns in MHD, rotating and stratified shear flows2011In: Direct and Large-Eddy Simulation VIII, 2011, p. 125-130Conference paper (Refereed)
    Abstract [en]

    Coexisting laminar and turbulent regions have been observed in several types of wall bounded flows. In Taylor Couette flow, for example, alternating helical shaped laminar and turbulent regions have been observed within a limited Reynolds number range (Prigent et al., 2002) and oblique laminar and turbulent bands have been seen in experiments (Prigent et al., 2002) and simulations (Barkley and Tuckerman, 2005), (Duguet et al., 2010) of plane Couette flow for Reynolds numbers Re=U w h/ν between about 320 and 380. Here ±U w is the velocity of the two walls, h is the half width of the wall gap and ν is the viscosity. In this Reynolds number range the turbulent-laminar patterns seem to sustain while at lower Re the flow becomes fully laminar and at higher Re no clear laminar patterns can be distinguished and the flow eventually becomes fully turbulent. Similar oblique laminar-turbulent bands appeared as well in direct numerical simulations (DNS) of plane channel flow for friction Reynolds numbers Re τ =u τ h/ν=60 and 80 (Fukudome et al., 2009), (Tsukahara, 2010), where u τ is the friction velocity and h is again the gap half width.

  • 25.
    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.

  • 26.
    Brethouwer, Geert
    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.
    Johansson, Arne
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Effects of rapid spanwise rotation on turbulent channel flow with a passive scalar2011In: Proc. 7th International Symposium on Turbulence and Shear Flow Phenomena, 2011Conference paper (Refereed)
    Abstract [en]

    Direct numerical simulations of fully developed turbulentchannel flow including a passive scalar rotating about thespanwise axis have been performed. The mean bulk Reynoldsnumber, Reb = Ubh/n ≥ 20000, where Ub is the bulk meanvelocity and h the channel half width, is higher than in previoussimulations and the rotation rate covers a wide range.At moderate rotation rates, turbulence on the stable channelside is significantly less damped than in DNS at lower Reb. Athigh rotation rates we observe re-occurring, quasi-periodic instabilitieson the stable channel side. Between these events theturbulence is weak, but during the instability events the wallshear stress and turbulence intensity are much stronger. Theinstabilities are caused by structures resembling Tollmien-Schlichting (TS) waves that at some instant rapidly grow, thenbecome unstable and finally break down into intense turbulence.After some time the TS waves form again and the processrepeats itself in a periodic-like manner.Mean scalar profiles are also strongly affected by rotationand large scalar fluctuations are found on the border of the stableand unstable channel side. The turbulent Prandtl/Schmidtnumber of the scalar is much less than unity if there is rotation.Predicting scalar transport in rotating channel flow willtherefore pose a challenge to turbulence models.

  • 27.
    Brethouwer, Geert
    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.
    Johansson, Arne
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Turbulence instabilities and passive scalars in rotating channel flow2011In: 13th European Turbulence Conference (ETC13): Instability, Transition, Grid Turbulence And Jets / [ed] K. Bajer, Institute of Physics Publishing (IOPP), 2011, p. 032025-Conference paper (Refereed)
    Abstract [en]

    Fully developed channel flow with a passive scalar rotating about the spanwise axis is studied by direct numerical simulations. The Reynolds number based on the bulk mean velocity Re-b is up to 30000, substantially higher than in previous studies, and the rotation rates cover a broad range. Turbulence on the stable channel side is less strongly damped at moderate rotation rates than in channel flow at lower Re-b. At high rotation rates and sufficiently high Re-b, intermittent strong instabilities occur on the stable side caused by rapidly growing modes resembling two-dimensional Tollmien-Schlichting waves which at some instant become unstable and break down into intense turbulence. The turbulence decays and after some time the waves form again and the process is repeated in a cyclic manner. Rotation also strongly affects the mean passive scalar profiles and turbulent scalar fluxes. Large scalar fluctuations are observed on the border between the stable and unstable channel sides. While in non-rotating channel flow the turbulent Prandtl number of the passive scalar is about one like in other shear flows, it is much smaller in the rotating cases.

  • 28.
    Brethouwer, Gert
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Duguet, Y.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Turbulent-laminar coexistence in wall flows with Coriolis, buoyancy or Lorentz forces2012In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 704, p. 137-172Article in journal (Refereed)
    Abstract [en]

    Direct numerical simulations of subcritical rotating, stratified and magnetohydrodynamic wall-bounded flows are performed in large computational domains, focusing on parameters where laminar and turbulent flow can stably coexist. In most cases, a regime of large-scale oblique laminar-turbulent patterns is identified at the onset of transition, as in the case of pure shear flows. The current study indicates that this oblique regime can be shifted up to large values of the Reynolds number R e by increasing the damping by the Coriolis, buoyancy or Lorentz force. We show evidence for this phenomenon in three distinct flow cases: plane Couette flow with spanwise cyclonic rotation, plane magnetohydrodynamic channel flow with a spanwise or wall-normal magnetic field, and open channel flow under stable stratification. Near-wall turbulence structures inside the turbulent patterns are invariably found to scale in terms of viscous wall units as in the fully turbulent case, while the patterns themselves remain large-scale with a trend towards shorter wavelength for increasing Re. Two distinct regimes are identified: at low Reynolds numbers the patterns extend from one wall to the other, while at large Reynolds number they are confined to the near-wall regions and the patterns on both channel sides are uncorrelated, the core of the flow being highly turbulent without any dominant large-scale structure.

  • 29.
    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.

  • 30.
    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.

  • 31.
    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.

  • 32.
    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.

  • 33.
    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. 

  • 34.
    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.

  • 35.
    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.

  • 36.
    Canton, Jacopo
    et al.
    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.
    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.
    Örlü, Ramis
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Physics. KTH, School of Industrial Engineering and Management (ITM), Centres, Competence Center for Gas Exchange (CCGEx). KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Linear stability of the flow in a toroidal pipe2015In: 9th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2015, TSFP-9 , 2015Conference paper (Refereed)
    Abstract [en]

    While hydrodynamic stability and transition to turbulence in straight pipes - being one of the most fundamental problems in fluid mechanics - has been studied extensively, the stability of curved pipes has received less attention. In the present work, the first (linear) instability of the canonical flow inside a toroidal pipe is investigated as a first step in the study of the related laminar-turbulent transition process. The impact of the curvature of the pipe, in the range 8 e [0.002,1], on the stability properties of the flow is studied in the framework of linear stability analysis. Results show that the flow is indeed modally unstable for all curvatures investigated and that the wave number corresponding to the critical mode depends on the curvature, as do several other features of this problem. The critical modes are mainly located in the region of the Dean vortices, and are characterised by oscillations which are symmetric or antisymmetric as a function of the curvature. The neutral curve associated with the first bifurcation is the result of a complex interaction between isolated modes and branches composed by several modes characterised by a common structure. This behaviour is in obvious contrast to that of straight pipes, which are linearly stable for all Reynolds numbers.

  • 37.
    Canton, Jacopo
    et al.
    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.
    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.
    Örlü, Ramis
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Modal instability of the flow in a toroidal pipe2016In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 792, p. 894-909Article in journal (Refereed)
    Abstract [en]

    The modal instability encountered by the incompressible flow inside a toroidal pipe is studied, for the first time, by means of linear stability analysis and direct numerical simulation (DNS). In addition to the unquestionable aesthetic appeal, the torus represents the smallest departure from the canonical straight pipe flow, at least for low curvatures. The flow is governed by only two parameters: the Reynolds number (Formula presented.) and the curvature of the torus (Formula presented.), i.e. the ratio between pipe radius and torus radius. The absence of additional features, such as torsion in the case of a helical pipe, allows us to isolate the effect that the curvature has on the onset of the instability. Results show that the flow is linearly unstable for all curvatures investigated between 0.002 and unity, and undergoes a Hopf bifurcation at (Formula presented.) of about 4000. The bifurcation is followed by the onset of a periodic regime, characterised by travelling waves with wavelength (Formula presented.) pipe diameters. The neutral curve associated with the instability is traced in parameter space by means of a novel continuation algorithm. Tracking the bifurcation provides a complete description of the modal onset of instability as a function of the two governing parameters, and allows a precise calculation of the critical values of (Formula presented.) and (Formula presented.). Several different modes are found, with differing properties and eigenfunction shapes. Some eigenmodes are observed to belong to groups with a set of common characteristics, deemed ‘families’, while others appear as ‘isolated’. Comparison with nonlinear DNS shows excellent agreement, confirming every aspect of the linear analysis, its accuracy, and proving its significance for the nonlinear flow. Experimental data from the literature are also shown to be in considerable agreement with the present results.

  • 38.
    Canton, Jacopo
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Örlü, Ramis
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Chin, C.
    Hutchins, N.
    Monty, J.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    On Large-Scale Friction Control in Turbulent Wall Flow in Low Reynolds Number Channels2016In: Flow Turbulence and Combustion, ISSN 1386-6184, E-ISSN 1573-1987, Vol. 97, no 3, p. 811-827Article in journal (Refereed)
    Abstract [en]

    The present study reconsiders the control scheme proposed by Schoppa & Hussain (Phys. Fluids 10, 1049–1051 1998), using a new set of numerical simulations. The computations are performed in a turbulent channel at friction Reynolds numbers of 104 (the value employed in the original study) and 180. In particular, the aim is to better characterise the physics of the control as well as to investigate the optimal parameters. The former purpose lead to a re-design of the control strategy: moving from a numerical imposition of the mean flow to the application of a volume force. A comparison between the two is presented. Results show that the original method only gave rise to transient drag reduction. The forcing method, on the other hand, leads to sustained drag reduction, and thus shows the superiority of the forcing approach for all wavelengths investigated. A clear maximum efficiency in drag reduction is reached for the case with a viscous-scaled spanwise wavelength of the vortices of 1200, which yields a drag reduction of 18 %, as compared to the smaller wavelength of 400 suggested as the most efficient vortex in Schoppa & Hussain. Various turbulence statistics are considered, in an effort to elucidate the causes of the drag-reducing effect. For instance, a region of negative production was found, which is quite unusual for developed turbulent channel flow.

  • 39.
    Canton, Jacopo
    et al.
    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.
    Örlü, Ramis
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Chin, Cheng
    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.
    Reynolds number dependence of large-scale friction control in turbulent channel flow2016In: PHYSICAL REVIEW FLUIDS, ISSN 2469-990X, Vol. 1, no 8, article id 081501Article in journal (Refereed)
    Abstract [en]

    The present work investigates the effectiveness of the control strategy introduced by Schoppa and Hussain [Phys. Fluids 10, 1049 (1998)] as a function of Reynolds number (Re). The skin-friction drag reduction method proposed by these authors, consisting of streamwise-invariant, counter-rotating vortices, was analyzed by Canton et al. [Flow, Turbul. Combust. 97, 811 (2016)] in turbulent channel flows for friction Reynolds numbers (Re t) corresponding to the value of the original study (i.e., 104) and 180. For these Re, a slightly modified version of the method proved to be successful and was capable of providing a drag reduction of up to 18%. The present study analyzes the Reynolds number dependence of this drag-reducing strategy by performing two sets of direct numerical simulations (DNS) for Re-tau = 360 and 550. A detailed analysis of the method as a function of the control parameters (amplitude and wavelength) and Re confirms, on the one hand, the effectiveness of the large-scale vortices at low Re and, on the other hand, the decreasing and finally vanishing effectiveness of this method for higher Re. In particular, no drag reduction can be achieved for Re t = 550 for any combination of the parameters controlling the vortices. For low Reynolds numbers, the large-scale vortices are able to affect the near-wall cycle and alter the wall-shear-stress distribution to cause an overall drag reduction effect, in accordance with most control strategies. For higher Re, instead, the present method fails to penetrate the near-wall region and cannot induce the spanwise velocity variation observed in other more established control strategies, which focus on the near-wall cycle. Despite the negative outcome, the present results demonstrate the shortcomings of the control strategy and show that future focus should be on methods that directly target the near-wall region or other suitable alternatives.

  • 40.
    Canton, Jacopo
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    Örlü, Ramis
    KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Physics.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    Characterisation of the steady, laminar incompressible flow in toroidal pipes covering the entire curvature rangeManuscript (preprint) (Other academic)
  • 41.
    Canton, Jacopo
    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.
    Örlü, Ramis
    KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Physics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    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.
    Characterisation of the steady, laminar incompressible flow in toroidal pipes covering the entire curvature range2017In: International Journal of Heat and Fluid Flow, ISSN 0142-727X, E-ISSN 1879-2278, Vol. 66, p. 95-107Article in journal (Refereed)
    Abstract [en]

    This work is concerned with a detailed investigation of the steady (laminar), incompressible flow inside bent pipes. In particular, a toroidal pipe is considered in an effort to isolate the effect of the curvature, δ, on the flow features, and to compare the present results to available correlations in the literature. More than 110 000 numerical solutions are computed, without any approximation, spanning the entire curvature range, 0 ≤ δ ≤ 1, and for bulk Reynolds numbers Re up to 7 000, where the flow is known to be unsteady. Results show that the Dean number De provides a meaningful non-dimensional group only below very strict limits on the curvature and the Dean number itself. For δ>10−6 and De > 10, in fact, not a single flow feature is found to scale well with the Dean number. These considerations are also valid for quantities, such as the Fanning friction factor, that were previously considered Dean-number dependent only. The flow is therefore studied as a function of two equally important, independent parameters: the curvature of the pipe and the Reynolds number. The analysis shows that by increasing the curvature the flow is fundamentally changed. Moderate to high curvatures are not only quantitatively, but also qualitatively different from low δ cases. A complete description of some of the most relevant flow quantities is provided. Most notably the friction factor f for laminar flow in curved pipes by Ito [J. Basic Eng. 81:123–134 (1959)] is reproduced, the influence of the curvature on f is quantified and the scaling is discussed. A complete database including all the computed solutions is available at www.flow.kth.se.

  • 42.
    Canton, Jacopo
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    Örlü, Ramis
    KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Physics.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
    On the Reynolds number dependence of large-scale friction control in turbulent channel flowManuscript (preprint) (Other academic)
  • 43.
    Chevalier, Mattias
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Lundbladh, Anders
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    SIMSON: A Pseudo-Spectral Solver for Incompressible Boundary Layer Flows2007Report (Other academic)
  • 44. Chin, C
    et al.
    Monty, J
    Hutchins, N
    Ooi, A
    Örlü, Ramis
    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.
    Simulation of a large-eddy-break-up device (LEBU) in a moderate Reynolds number turbulent boundary layer2015In: Proc 9th Turbulence and Shear Flow Phenomena Conference, 2015Conference paper (Refereed)
  • 45. Chin, C.
    et al.
    Örlü, Ramis
    KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Physics.
    Monty, J.
    Hutchins, N.
    Ooi, A.
    Schlatter, Phillip
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Simulation of a Large-Eddy-Break-up Device (LEBU) in a Moderate Reynolds Number Turbulent Boundary Layer2016In: Flow Turbulence and Combustion, ISSN 1386-6184, E-ISSN 1573-1987, p. 1-16Article in journal (Refereed)
    Abstract [en]

    A well-resolved large eddy simulation (LES) of a large-eddy break-up (LEBU) device in a spatially evolving turbulent boundary layer is performed with, Reynolds number, based on free-stream velocity and momentum-loss thickness, of Reθ ≈ 4300. The implementation of the LEBU is via an immersed boundary method. The LEBU is positioned at a wall-normal distance of 0.8 δ (δ denoting the local boundary layer thickness at the location of the LEBU) from the wall. The LEBU acts to delay the growth of the turbulent boundary layer and produces global skin friction reduction beyond 180δ downstream of the LEBU, with a peak local skin friction reduction of approximately 12 %. However, no net drag reduction is found when accounting for the device drag of the LEBU in accordance with the towing tank experiments by Sahlin et al. (Phys. Fluids 31, 2814, 1988). Further investigation is performed on the interactions of high and low momentum bulges with the LEBU and the corresponding output is analysed, showing a ‘break-up’ of these large momentum bulges downstream of the LEBU. In addition, results from the spanwise energy spectra show consistent reduction in energy at spanwise length scales for (Formula presented.) independent of streamwise and wall-normal location when compared to the corresponding turbulent boundary layer without LEBU.

  • 46. Chin, Cheng
    et al.
    Örlü, Ramis
    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.
    Monty, Jason
    Hutchins, Nicholas
    Influence of a Large-Eddy-Breakup-Device on the Turbulent Interface of Boundary Layers2017In: Flow Turbulence and Combustion, ISSN 1386-6184, E-ISSN 1573-1987, Vol. 99, no 3-4, p. 823-835Article in journal (Refereed)
    Abstract [en]

    The effects of implementing a large-eddy break-up device (LEBU) in a turbulent boundary layer on the interaction with the boundary layer is investigated with particular emphasis on the turbulent/non-turbulent interface (TNTI). The simulation data is taken from a recent well-resolved large eddy simulation (Chin et al. Flow Turb. Combust. 98, 445-460 2017), where the LEBU was implemented at a wall-normal distance of 0.8 delta (local boundary layer thickness) from the wall. A comparison of the TNTI statistics is performed between a zero-pressure-gradient boundary layer with and without the LEBU. The LEBU is found to delay the growth of the turbulent boundary layer and also attenuates the fluctuations of the TNTI. The LEBU appears to alter the structure size at the interface, resulting in a narrower and shorter dominant structure (in an average sense). Further analysis beneath the TNTI using two-point correlations shows that the LEBU affects the turbulent structures in excess of 100 delta downstream of the LEBU.

  • 47. Cimarelli, A.
    et al.
    De Angelis, E.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Brethouwer, Geert
    KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Talamelli, A.
    Casciola, C. M.
    Sources and fluxes of scale energy in the overlap layer of wall turbulence2015In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 771, p. 407-423Article in journal (Refereed)
    Abstract [en]

    Direct numerical simulations of turbulent channel flows at friction Reynolds numbers (Re) of 550, 1000 and 1500 are used to analyse the turbulent production, transfer and dissipation mechanisms in the compound space of scales and wall distances by means of the Kolmogorov equation generalized to inhomogeneous anisotropic flows. Two distinct peaks of scale-energy source are identified. The first, stronger one, belongs to the near-wall cycle. Its location in the space of scales and physical space is found to scale in viscous units, while its intensity grows slowly with Re, indicating a near-wall modulation. The second source peak is found further away from the wall in the putative overlap layer, and it is separated from the near-wall source by a layer of significant scale-energy sink. The dynamics of the second outer source appears to be strongly dependent on the Reynolds number. The detailed scale-by-scale analysis of this source highlights well-defined features that are used to make the properties of the outer turbulent source independent of Reynolds number and wall distance by rescaling the problem. Overall, the present results suggest a strong connection of the observed outer scale-energy source with the presence of an outer region of turbulence production whose mechanisms are well separated from the near-wall region and whose statistical features agree with the hypothesis of an overlap layer dominated by attached eddies. Inner-outer interactions between the near-wall and outer source region in terms of scale-energy fluxes are also analysed. It is conjectured that the near-wall modulation of the statistics at increasing Reynolds number can be related to a confinement of the near-wall turbulence production due to the presence of increasingly large production scales in the outer scale-energy source region.

  • 48. Daly, C. A.
    et al.
    Schneider, Tobias M.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Peake, N.
    Secondary instability and tertiary states in rotating plane Couette flow2014In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 761, p. 27-61Article in journal (Refereed)
    Abstract [en]

    Recent experimental studies have shown rich transition behaviour in rotating plane Couette flow (RPCF). In this paper we study the transition in supercritical RPCF theoretically by determination of equilibrium and periodic orbit tertiary states via Floquet analysis on secondary Taylor vortex solutions. Two new tertiary states are discovered which we name oscillatory wavy vortex flow (oWVF) and skewed vortex flow (SVF). We present the bifurcation routes and stability properties of these new tertiary states and, in addition, we describe a bifurcation procedure whereby a set of defected wavy twist vortices is approached. Further to this, transition scenarios at flow parameters relevant to experimental works are investigated by computation of the set of stable attractors which exist on a large domain. The physically observed flow states are shown to share features with states in our set of attractors.

  • 49.
    Deusebio, Enrico
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. Centre for Mathematical Sciences, Cambridge, England.
    Brethouwer, Geert
    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.
    Lindborg, Erik
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    A numerical study of the unstratified and stratified Ekman layer2014In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 755, p. 672-704Article in journal (Refereed)
    Abstract [en]

    We study the turbulent Ekman layer at moderately high Reynolds number, 1600 < Re = delta(E)G/v < 3000, using direct numerical simulations (DNS). Here, delta(E) = root 2v/f is the laminar Ekman layer thickness, G the geostrophic wind, v the kinematic viscosity and f is the Coriolis parameter. We present results for both neutrally, moderately and strongly stably stratified conditions. For unstratified cases, large-scale roll-like structures extending from the outer region down to the wall are observed. These structures have a clear dominant frequency and could be related to periodic oscillations or instabilities developing near the low-level jet. We discuss the effect of stratification and Re on one-point and two-point statistics. In the strongly stratified Ekman layer we observe stable co-existing large-scale laminar and turbulent patches appearing in the form of inclined bands, similar to other wall-bounded flows. For weaker stratification, continuously sustained turbulence strongly affected by buoyancy is produced. We discuss the scaling of turbulent length scales, height of the Ekman layer, friction velocity, veering angle at the wall and heat flux. The boundary-layer thickness, the friction velocity and the veering angle depend on Lf/u(tau), where u(tau) is the friction velocity and L the Obukhov length scale, whereas the heat fluxes appear to scale with L+ = Lu-tau/v.

  • 50.
    Deusebio, Enrico
    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.
    Brethouwer, Gert
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Lindborg, Erik
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Direct numerical simulations of stratified open channel flows2011In: 13th European Turbulence Conference (ETC13): Wall-Bounded Flows And Control Of Turbulence, 2011, p. 022009-Conference paper (Refereed)
    Abstract [en]

    We carry out numerical simulations of wall-bounded stably stratified flows. We mainly focus on how stratification affects the near-wall turbulence at moderate Reynolds numbers, i.e. Re-tau = 360. A set of fully-resolved open channel flow simulations is performed, where a stable stratification has been introduced through a negative heat flux at the lower wall. In agreement with previous studies, it is found that turbulence cannot be sustained for h/L values higher than 1.2, where L is the so-called Monin-Obukhov length and h is the height of the open channel. For smaller values, buoyancy does not re-laminarize the flow, but nevertheless affects the wall turbulence. Near-wall streaks are weakly affected by stratification, whereas the outer modes are increasingly damped as we move away from the wall. A decomposition of the wall-normal velocity is proposed in order to separate the gravity wave and turbulent flow fields. This method has been tested both for open channel and full channel flows. Gravity waves are likely to develop and to dominate close to the upper boundary (centerline for full channel). However, their intensity is weaker in the open channel, possibly due to the upper boundary condition. Moreover, the presence of internal gravity waves can also be deduced from a correlation analysis, which reveals (together with spanwise spectra) a narrowing of the outer structures as the stratification is increased.

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