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  • 1.
    Deusebio, Enrico
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Numerical Investigation of Rotating and Stratified Turbulence2012Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    Atmospheric and oceanic flows are strongly affected by rotation and stratification. Rotation is exerted through Coriolis forces which mainly act in horizontal planes whereas stratification largely affects the motion along the vertical direction through buoyancy forces, the latters related to the vertical variation of the fluid density. Aiming at a better understanding of atmospheric and oceanic processes, in this thesis the properties of turbulence in rotating and stably stratified flows are studied by means of numerical simulations, with and without the presence of solid walls.                                                                                                                                                                                           A new code is developed in order to carry out high-resolution numerical simulations of geostrophic turbulence forced at large scales. The code was heavily parallelized with MPI (Message Passing Interface) in order to be run on massively parallel computers. The main problem which has been investigated is how the turbulent cascade is affected by the presence of strong but finite rotation and stratification. As opposed to the early theories in the field of geostrophic turbulence, we show that there is a forward energy cascade which is initiated at large scales. The contribution of this process to the general dynamic is secondary at large scales but becomes dominant at smaller scales where leads to a shallowing of the energy spectrum. Despite the idealized set-up of the simulations, two-point statistics show remarkable agreement with measurements in the atmosphere, suggesting that this process may be an important mechanism for energy transfer in the atmosphere.                                                                                                                                                                                                                                                                               The effect of stratification in wall-bounded turbulence is investigated by means of direct numerical simulations of open-channel flows. An existing full-channel code was modified in order to optimize the grid in the vertical direction and avoid the clustering of grid points at the upper boundary, where the solid wall is replaced by a free-shear condition. The stable stratification which results from a cooling applied at the solid wall largely affects the outer structures of the boundary layer, whereas the near-wall structures appear to be mostly unchanged. The effect of gravity waves is also studied, and a new decomposition is introduced in order to separate the gravity wave field from the turbulent field.

  • 2.
    Deusebio, Enrico
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Numerical studies in rotating and stratified turbulence2013Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Although turbulence has been studied for more than five hundred years, a thorough understanding of turbulent flows is still missing. Nowadays computing power can offer an alternative tool, besides measurements and experiments, to give some insights into turbulent dynamics. In this thesis, numerical simulations are employed to study homogeneous and wall-bounded turbulence in rotating and stably stratified conditions, as encountered in geophysical flows where the rotation of the Earth as well as the vertical density variation influence the dynamics.

    In the context of homogeneous turbulence, we investigate how the transfer of energy among scales is affected by the presence of strong but finite rotation and stratification. Unlike geostrophic turbulence, we show that there is a forward energy cascade towards small scales which is initiated at the forcing scales. The contribution of this process to the general dynamic is secondary at large scales but becomes dominant at smaller scales where it leads to a shallowing of the energy spectrum, from k-3 to k-5/3. Two-point statistics show a good agreement with measurements in the atmosphere, suggesting that this process is an important mechanism for energy transfer in the atmosphere.

    Boundary layers subjected to system rotation around the wall-normal axis are usually referred to as Ekman layers and they can be seen as a model of the atmospheric and oceanic boundary layers developing at mid and high latitudes. We study the turbulent dynamics in Ekman layers by means of numerical simulations, focusing on the turbulent structures developing at moderately high Reynolds numbers. For neutrally stratified conditions, we show that there exists a turbulent helicity cascade in the logarithmic region. We focus on the effect of a stable stratification produced by a vertical positive temperature gradient. For moderate stratification, continuously turbulent regimes are produced which are in fair agreement with existing theories and models used in the context of atmospheric boundary layer dynamics. For larger degree of stratification, we show that laminar and turbulent motions coexist and displace along inclined patterns similar to what has been recently observed in other transitional flows.

  • 3.
    Deusebio, Enrico
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    The open-channel version of SIMSON2010Report (Other academic)
  • 4.
    Deusebio, Enrico
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Augier, Pierre
    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.
    Third order structure function in rotating and stratified turbulence: analytical and numerical results compared with data from the stratosphereManuscript (preprint) (Other academic)
  • 5.
    Deusebio, Enrico
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Augier, Pierre
    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.
    Third-order structure functions in rotating and stratified turbulence: a comparison between numerical, analytical and observational results2014In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 755, p. 294-313Article in journal (Refereed)
    Abstract [en]

    First, we review analytical and observational studies on third-order structure functions including velocity and buoyancy increments in rotating and stratified turbulence and discuss how these functions can be used in order to estimate the flux of energy through different scales in a turbulent cascade. In particular, we suggest that the negative third-order velocity-temperature-temperature structure function that was measured by Lindborg & Cho (Phys. Rev. Lett., vol. 85, 2000, p. 5663) using stratospheric aircraft data may be used in order to estimate the downscale flux of available potential energy (APE) through the mesoscales. Then, we calculate third-order structure functions from idealized simulations of forced stratified and rotating turbulence and compare with mesoscale results from the lower stratosphere. In the range of scales with a downscale energy cascade of kinetic energy (KE) and APE we find that the third-order structure functions display a negative linear dependence on separation distance r, in agreement with observation and supporting the interpretation of the stratospheric data as evidence of a downscale energy cascade. The spectral flux of APE can be estimated from the relevant third-order structure function. However, while the sign of the spectral flux of KE is correctly predicted by using the longitudinal third-order structure functions, its magnitude is overestimated by a factor of two. We also evaluate the third-order velocity structure functions that are not parity invariant and therefore display a cyclonic-anticyclonic asymmetry. In agreement with the results from the stratosphere, we find that these functions have an approximate r(2)-dependence, with strong dominance of cyclonic motions.

  • 6.
    Deusebio, Enrico
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. DAMTP, England.
    Boffetta, Guido
    Lindborg, Erik
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Musacchio, Stefano
    Dimensional transition in rotating turbulence2014In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 90, no 2Article in journal (Refereed)
    Abstract [en]

    In this work we investigate, by means of direct numerical hyperviscous simulations, how rotation affects the bidimensionalization of a turbulent flow. We study a thin layer of fluid, forced by a two-dimensional forcing, within the framework of the "split cascade" in which the injected energy flows both to small scales (generating the direct cascade) and to large scale (to form the inverse cascade). It is shown that rotation reinforces the inverse cascade at the expense of the direct one, thus promoting bidimensionalization of the flow. This is achieved by a suppression of the enstrophy production at large scales. Nonetheless, we find that, in the range of rotation rates investigated, increasing the vertical size of the computational domain causes a reduction of the flux of the inverse cascade. Our results suggest that, even in rotating flows, the inverse cascade may eventually disappear when the vertical scale is sufficiently large with respect to the forcing scale. We also study how the split cascade and confinement influence the breaking of symmetry induced by rotation.

  • 7.
    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.

  • 8.
    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.
    Lindborg, Erik
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Helicity in the Ekman boundary layer2014In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 755, p. 654-671Article in journal (Refereed)
    Abstract [en]

    Helicity, which is defined as the scalar product of velocity and vorticity, H = u . omega, is an inviscidly conserved quantity in a barotropic fluid. Mean helicity is zero in flows that are parity invariant. System rotation breaks parity invariance and has therefore the potential of giving rise to non-zero mean helicity. In this paper we study the helicity dynamics in the incompressible Ekman boundary layer. Evolution equations for the mean field helicity and the mean turbulent helicity are derived and it is shown that pressure flux injects helicity at a rate 2 Omega G(2) over the total depth of the Ekman layer, where G is the geostrophic wind far from the wall and Omega = Omega e(y) is the rotation vector and e(y) is the wall-normal unit vector. Thus right-handed/left-handed helicity will be injected if Omega is positive/negative. We also show that in the uppermost part of the boundary layer there is a net helicity injection with opposite sign as compared with the totally integrated injection. Isotropic relations for the helicity dissipation and the helicity spectrum are derived and it is shown that it is sufficient to measure two transverse velocity components and use Taylor's hypothesis in the mean flow direction in order to measure the isotropic helicity spectrum. We compare the theoretical predictions with a direct numerical simulation of an Ekman boundary layer and confirm that there is a preference for right-handed helicity in the lower part of the Ekman layer and left-handed helicity in the uppermost part when Omega > 0. In the logarithmic range, the helicity dissipation conforms to isotropic relations. On the other hand, spectra show significant departures from isotropic conditions, suggesting that the Reynolds number considered in the study is not sufficiently large for isotropy to be valid in a wide range of scales. Our analytical and numerical results strongly suggest that there is a turbulent helicity cascade of right-handed helicity in the logarithmic range of the atmospheric boundary layer when Omega > 0, consistent with recent measurements by Koprov, Koprov, Ponomarev & Chkhetiani (Dokl. Phys., vol. 50, 2005, pp. 419-422). The isotropic relations which are derived may facilitate future measurements of the helicity spectrum in the atmospheric boundary layer as well as in controlled wind tunnel experiments.

  • 9.
    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.

  • 10.
    Deusebio, Enrico
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Vallgren, Andreas
    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.
    The route to dissipation in strongly stratified and rotating flows2013In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 720, p. 66-103Article in journal (Refereed)
    Abstract [en]

    We investigate the route to dissipation in strongly stratified and rotating systems through high-resolution numerical simulations of the Boussinesq equations (BQs) and the primitive equations (PEs) in a triply periodic domain forced at large scales. By applying geostrophic scaling to the BQs and using the same horizontal length scale in defining the Rossby and the Froude numbers, R0 and Fr, we show that the PEs can be obtained from the BQs by taking the limit Fr-2/R0(2)-> 0. When Fr-2/R0(2) is small the difference between the results from the BQ and the PE simulations is shown to be small. For large rotation rates, quasi-geostrophic dynamics are recovered with a forward enstrophy cascade and an inverse energy cascade. As the rotation rate is reduced, a fraction of the energy starts to cascade towards smaller scales, leading to a shallowing of the horizontal spectra from k(h)(-3) to k(h)(-5/3) h at the small-scale end. The vertical spectra show a similar transition as the horizontal spectra and we find that Charney isotropy is approximately valid also at larger wavenumbers than the transition wavenumber. The high resolutions employed allow us to capture both ranges within the same simulation. At the transition scale, kinetic energy in the rotational and in the horizontally divergent modes attain comparable values. The divergent energy is several orders of magnitude larger than the quasi-geostrophic divergent energy given by the Omega-equation. The amount of energy cascading downscale is mainly controlled by the rotation rate, with a weaker dependence on the stratification. A larger degree of stratification favours a downscale energy cascade. For intermediate degrees of rotation and stratification, a constant energy flux and a constant enstrophy flux coexist within the same range of scales. In this range, the enstrophy flux is a result of triad interactions involving three geostrophic modes, while the energy flux is a result of triad interactions involving at least one ageostrophic mode, with a dominant contribution from interactions involving two ageostrophic and one geostrophic mode. Dividing the ageostrophic motions into two classes depending on the sign of the linear wave frequency, we show that the energy transfer is for the largest part supported by interactions within the same class, ruling out the wave-wave-vortex resonant triad interaction as a mean of the downscale energy transfer. The role of inertia-gravity waves is studied through analyses of time-frequency spectra of single Fourier modes. At large scales, distinct peaks at frequencies predicted for linear waves are observed, whereas at small scales no clear wave activity is observed. Triad interactions show a behaviour which is consistent with turbulent dynamics, with a large exchange of energy in triads with one small and two large comparable wavenumbers. The exchange of energy is mainly between the modes with two comparable wavenumbers.

  • 11.
    Schlatter, Philipp
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Deusebio, Enrico
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Brandt, Luca
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    de Lange, Rick
    Interaction of noise disturbances and streamwise streaks2010In: SEVENTH IUTAM SYMPOSIUM ON LAMINAR-TURBULENT TRANSITION / [ed] Schlatter, P.; Henningson, D. S., 2010, Vol. 18, p. 355-360Conference paper (Refereed)
    Abstract [en]

    The evolution of disturbances in boundary layers modified through span-wise periodic, steady streamwise streaks is studied via numerical simulations The disturbances are introduced via random two- and three-dimensional noise of various amplitudes close to the inlet (Re-iota approximate to 60000) The aim of the present work is to determine the impact of the interaction of streaks and noise on the arising Bow structures and, eventually, on the location and details of the breakdown to turbulence. It is shown that large-scale 2D noise can be controlled via streaks, whereas the more general 3D noise configuration is prone to premature transition due to increased instability of the introduced streaks It is interesting to note that the latter transition scenario closely resembles the flow structures found in bypass transition. Transition in true bypass transtion forced by ambient free-stream turbulence is also promoted by the addition of streamwise streaks in the laminar part of the boundary layer.

  • 12.
    Schlatter, Philipp
    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.
    Deusebio, Enrico
    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.
    de Lange, Rick
    Brandt, Luca
    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.
    Numerical study of the stabilisation of boundary-layer disturbances by finite amplitude streaks2010In: International Journal of Flow Control, ISSN 1756-8250, Vol. 2, no 4, p. 259-288Article in journal (Refereed)
    Abstract [en]

    Well-resolved large-eddy simulations of passive control of the laminar-turbulent transition process in flat-plate boundary-layer flows are presented. A specific passive control mechanism is studied, namely the modulation of the laminar boundary-layer profile by a periodic array of steady boundary-layer streaks. This has been shown experimentally to stabilise the exponential growth of Tollmien-Schlichting (TS) waves and delay transition to turbulence. Here we examine the effect of the steady modulations on the amplification of different types of disturbances such as TS-waves, stochastic noise and free-stream turbulence. In our numerical simulations, the streaks are forced at the inflow as optimal solutions to the linear parabolic stability equations (PSE), whereas the additional disturbances are excited via volume forcing active within the computational domain. The simulation results show, in agreement with experimental and theoretical studies, significant damping of unstable two-dimensional TS-waves of various frequencies when introduced into a modulated base flow: The damping characteristics are mainly dependent on the streak amplitude. A new phenomenon is also identified which is characterised by the strong amplification via nonlinear interactions of the second spanwise harmonic of the streak when the streak amplitude is comparable to the TS amplitude. Furthermore, we demonstrate that control by streaks can be effective also in case of stochastic two-dimensional noise. However, as soon as a significant three-dimensionality is dominant, as in e.g. oblique or bypass transition, control by streaks leads often to premature transition. Visualisations of the flow fields are used to highlight the different vortical structures and their interactions that are relevant to the various transition scenarios and the corresponding control by streamwise streaks.

  • 13.
    Vallgren, Andreas
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Deusebio, Enrico
    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.
    Possible Explanation of the Atmospheric Kinetic and Potential Energy Spectra2011In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 107, no 26, p. 268501-Article in journal (Refereed)
    Abstract [en]

    We hypothesize that the observed wave number spectra of kinetic and potential energy in the atmosphere can be explained by assuming that there are two related cascade processes emanating from the same large-scale energy source, a downscale cascade of potential enstrophy, giving rise to the k(-3) spectrum at synoptic scales and a downscale energy cascade giving rise to the k(-5/3) spectrum at mesoscales. The amount of energy which is going into the downscale energy cascade is determined by the rate of system rotation, with negligible energy going downscale in the limit of very fast rotation. We present a set of simulations of a system with strong rotation and stratification, supporting these hypotheses and showing good agreement with observations.

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