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An experiment was performed using stereo particle image velocimetry (SPIV) in the Laboratoire de Mécanique des Fluides de Lille boundary layer facility to determine all the derivative moments needed to estimate the average dissipation rate of the turbulence kinetic energy $\epsilon = 2 \nu \langle {\mathsf{s}}_{ij}{\mathsf{s}}_{ij} \rangle$ , where ${\mathsf{s}}_{ij}$ is the fluctuating strain rate and $\langle ~\rangle$ denotes ensemble averages. Also measured were all the moments of the full average deformation rate tensor, as well as all of the first, second and third fluctuating velocity moments except those involving pressure. The Reynolds number was $Re_\theta = 7634$ or $Re_\tau = 2598$ . The present paper gives the measured average dissipation, $\epsilon$ and the derivative moments comprising it. The results are compared with the earlier measurements of Balint, Wallace & Vukolavcevic (J. Fluid Mech., vol. 228, 1991, pp. 53–86) and Honkan & Andreopoulos (J. Fluid Mech., vol. 350, 1997, pp. 29–96) at lower Reynolds numbers and to new results from a plane channel flow DNS at comparable Reynolds number. Of special interest is the prediction by George & Castillo (Appl. Mech. Rev., vol. 50, 1997, pp. 689–729) and Wosnik, Castillo & George (J. Fluid Mech., vol. 421, 2000, pp. 115–145) that $\epsilon ^+ \propto {x_2^+}^{-1}$ for streamwise homogeneous flows and a nearly indistinguishable power law, $\epsilon \propto {x_2^+}^{\gamma -1}$ , for boundary layers. In spite of the modest Reynolds number, the predictions seem to be correct. Then the statistical character of the velocity derivatives is examined in detail, and a particular problem is identified with the breakdown of local homogeneity inside $x_2^+ = 100$ . A more general alternative for partially homogeneous turbulence flows is offered which is consistent with the observations. With the help of DNS, the spatial characteristics of the dissipation very near the wall are also examined in detail.

In a turbulent fluid, the time-reversal symmetry is explicitly broken by viscosity, and spontaneously broken in the inviscid limit. Recently, Drivas [J. Nonlinear Sci. 29, 65 (2019).JNSCEK0938-897410.1007/s00332-018-9476-8] proved the equivalence of two different local indicators of time irreversibility: (i) an Eulerian one, based on regularity properties of the velocity field [Duchon and Robert, Nonlinearity 13, 249 (2000).NONLE50951-771510.1088/0951-7715/13/1/312]; (ii) a Lagrangian one, based on symmetry properties of the trajectories under time reversal [Jucha et al., Phys. Rev. Lett. 113, 054501 (2014).PRLTAO0031-900710.1103/PhysRevLett.113.054501]. We test this equivalence in a turbulent Von Kármán experiment at a resolution of the order of the Kolmogorov scale using a high resolution 4D-PTV technique. We use the equivalence to perform the first joined Eulerian-Lagrangian exploration of the dynamics leading to time irreversibility, and find that it is linked with vortex interaction, suggesting a link between irreversibility and singularity.

International audience; The denoising of Lagrangian trajectories based on regularized B-spline is investigated. The aim is to find systematic criteria for optimization of algorithms used in 4D-PTV in order to optimize the quality of 4D-PTV measurements of turbulent flows as well as high-order of turbulence statistics. We introduce and adapt to this context two innovative tuning strategies which are commonly used in the Tikhonov regularization of inverse problems based on -curve shape and Normalized Cumulative Periodogram (NCP). The corresponding strategies are tested on synthetic Lagrangian trajectories computed from Direct Numerical Simulation with additional white Gaussian noise. Error-based quantities like Signal-to-Noise Ratio as well as statistical Lagrangian quantities are investigated to compare the different strategies. We then apply the algorithm to experimental data from a 4D-PTV Lagrangian measurements in a turbulent Von Kármán flow. We show the ability of those strategies to optimize the quality of the signal compared to conventional methods. Moreover, the strategies are more adaptable to real experimental noise.

International audience; We study the three-dimensional structure of turbulent velocity fields around extreme events of local energy transfer in the dissipative range. Velocity fields are measured by tomographic particle velocimetry at the centre of a von Kármán flow with resolution reaching the Kolmogorov scale. The characterization is performed through both direct observation and an analysis of the velocity gradient tensor invariants at the extremes. The conditional average of local energy transfer on the second and third invariants seems to be the largest in the sheet zone, but the most extreme events of local energy transfer mostly correspond to the vortex stretching topology. The direct observation of the velocity fields allows for identification of three different structures: the screw and roll vortices, and the U-turn. They may correspond to a single structure seen at different times or in different frames of reference. The extreme events of local energy transfer come along with large velocity and vorticity norms, and the structure of the vorticity field around these events agrees with previous observations of numerical works at similar Reynolds numbers.

Two scalar fields characterizing respectively pseudo-H\"older exponents and local energy transfers are used to capture the topology and the dynamics of the velocity fields in areas of lesser regularity. The present analysis is conducted using velocity fields from two direct numerical simulations of the Navier-Stokes equations in a triply periodic domain. A typical irregular structure is obtained by averaging over the 213 most irregular events. Such structure is similar to a Burgers vortex, with nonaxisymmetric corrections. A possible explanation for such asymmetry is provided by a detailed time-resolved analysis of birth and death of the irregular structures, which shows that they are connected to vortex interactions, possibly vortex reconnection.

Dynamical behavior of the turbulent channel flow separation induced by a wall-mounted two-dimensional bump is studied, with an emphasis on unsteadiness characteristics of vortical motions evolving in the separated flow. The present investigations are based on an experimental approach and Direct Numerical Simulation ( Dns ). The main interests are devoted to give further insight on mean flow properties, characteristic scales and physical mechanisms of low-frequencies unsteadiness. The study also aims to clarify the Reynolds number effects. Results are presented for turbulent flows at moderate Reynolds-number R e τ ranging from 125 to 730 where R e τ is based on friction velocity and channel half-height. A large database of time-resolved two-dimensional Piv measurements is used to obtain the velocity distributions in a region covering the entire shear layer and the flow surrounding the bump. An examination of both high resolved velocity and wall-shear stress measurements showed that for moderate Reynolds numbers, a separated region exists until a critical value. Under this conditions, a thin region of reverse flow is formed above the bump and a large-scale vortical activity is clearly observed and analyzed. Three distinct self-sustained oscillations are identified in the separated zone. The investigation showed that the flow exhibits the shear-layer instability and vortex-shedding type instability of the bubble. A low-frequency self-sustained oscillation associated with a flapping phenomenon is also identified. The experimental results are further emphasized using post-processed data from Direct Numerical Simulations, such as flow statistics and Dynamic Mode Decomposition. Physical mechanisms associated with observed self-sustained oscillations are then suggested and results are discussed in the light of instabilities observed in a laminar regime for the same flow configuration.

This paper investigates the universality of the Eulerian velocity structure functions using velocity fields obtained from the stereoscopic particle image velocimetry (SPIV) technique in experiments and direct numerical simulations (DNS) of the Navier-Stokes equations. It shows that the numerical and experimental velocity structure functions up to order 9 follow a log-universality (Castaing et al. Phys. D Nonlinear Phenom. 1993), this leads to a collapse on a universal curve, when units including a logarithmic dependence on the Reynolds number are used. This paper then investigates the meaning and consequences of such log-universality, and shows that it is connected with the properties of a &ldquo, multifractal free energy&rdquo, based on an analogy between multifractal and thermodynamics. It shows that in such a framework, the existence of a fluctuating dissipation scale is associated with a phase transition describing the relaminarisation of rough velocity fields with different H&ouml, lder exponents. Such a phase transition has been already observed using the Lagrangian velocity structure functions, but was so far believed to be out of reach for the Eulerian data.

It is still not known whether solutions to the Navier-Stokes equation can develop singularities from regular initial conditions. In particular, a classical and unsolved problem is to prove that the velocity field is Hölder continuous with some exponent h1 (i.e., not necessarily differentiable) at small scales. Different methods have already been proposed to explore the regularity properties of the velocity field and the estimate of its Hölder exponent h. A first method is to detect potential singularities via extrema of an "inertial" dissipation D*=lim_{ℓ→0}D_{ℓ}^{I} that is independent of viscosity [Duchon and Robert, Nonlinearity 13, 249 (2000)0951-771510.1088/0951-7715/13/1/312]. Another possibility is to use the concept of multifractal analysis that provides fractal dimensions of the subspace of exponents h. However, the multifractal analysis is a global statistical method that only provides global information about local Hölder exponents, via their probability of occurrence. In order to explore the local regularity properties of a velocity field, we have developed a local statistical analysis that estimates locally the Hölder continuity. We have compared outcomes of our analysis with results using the inertial energy dissipation D_{ℓ}^{I}. We observe that the dissipation term indeed gets bigger for velocity fields that are less regular according to our estimates. The exact spatial distribution of the local Hölder exponents however shows nontrivial behavior and does not exactly match the distribution of the inertial dissipation.

A study of large-scale motions from a new direct numerical simulation database of the turbulent boundary layer up to Re{\theta} ~ 2500 is presented. The statistics of large-scale streamwise structures have been investigated using two-dimensional and three-dimensional extraction procedures. The large-scale structures are abstracted using a robust skeletonization method usually applied to other research domains to simplify complex 3D objects. Different structure parameters such as the length, shape or angle are investigated. The features of the detected structures are compared to their mean counterparts extracted from two-point correlations. Structures as large as 10 boundary layer thickness are observed. The streamwise length of these structures follows a -2 power law distribution, similar to the experimental findings at higher Reynolds numbers., Comment: 32 pages, 16 figures

The modified Townsend-Perry attached eddy model of Vassilicos et al (2015) combines the outer peak/plateau behaviour of rms streamwise turbulence velocity profiles and the Townsend-Perry log-decay of these profiles at higher distances from the wall. This model was validated by these authors for high Reynolds number tur- bulent pipe flow data and is shown here to describe equally well and with about the same parameter values turbulent boundary layer flow data from four different facilities and a wide range of Reynolds numbers. The model has predictive value as, when extrapolated to the extremely high Reynolds numbers of the SLTEST data obtained at the Great Salt Lake Desert atmospheric test facility, it matches these data quite well., Comment: 12 pages, 3 figures

The spatio-temporal pressure–velocity correlation in a turbulent boundary layer is investigated so as to understand the link between pressure fluctuations and turbulent coherent structures. A new experimental set-up is developed to measure the pressure fluctuations at the wall and in the field and, simultaneously, the velocity field by stereoscopic particle image velocimetry. The present measurement area covers the whole boundary layer thickness, and the spatial resolution of the measurement is good enough to assess the representative length scales of the flow. The Reynolds number effect is quantified from the data at $\mathit{Re}_{{\it\theta}}=7300$, 10 000, 18 000. The spatio-temporal three-dimensional structures of the pressure–velocity correlations, $\boldsymbol{R}_{pu}$, $\boldsymbol{R}_{pv}$ and $\boldsymbol{R}_{pw}$, are evaluated. The wall pressure fluctuations are closely coupled with coherent structures which occupy a large region of the boundary layer in the wall-normal and spanwise directions and up to $10{\it\delta}/U_{e}$ in time, where ${\it\delta}$ and $U_{e}$ denote the boundary layer thickness and the free stream velocity. Reynolds number effects are mainly observed on the size and intensity of the pressure–velocity correlations. Conditioning the correlations on the pressure signal sign shows different types of flow phenomena linked to the positive and negative pressure events. For the wall pressure, positive pressure fluctuations appear to be correlated with the leading edge of a large sweeping motion of splatting type followed by a large ejection. The negative pressure fluctuations are linked to a localized ejection upstream, followed by a large sweeping motion downstream. For the pressure fluctuations in the field, in addition to the structures observed with the wall pressure, the pressure–velocity correlations exhibit a significant correlation in a region very extended in time. Such long structures appear to be independent of the one observed at the wall and to grow significantly in time with the Reynolds number when scaling with external variables. When conditioned by the pressure sign, clear ejection and sweeping motions are observed with associated streamwise vortical structures at a scale of the order of $0.2{\it\delta}$. These structures can be linked to the large-scale motion and very-large-scale motion previously observed by different authors and seem to organize in a scheme analogous to the near-wall cycle, but at a much larger scale.

This study reports on experimentally observed rare near-wall reverse flow events in a fully developed turbulent flat plate boundary layer at zero pressure gradient with Reynolds numbers between Re θ ≈ 2500 and Re θ ≈ 8000 ( Re τ ≈ 800 – 2400 ). The reverse flow events are captured using high magnification particle image velocimetry sequences with record lengths varying from 50 000 to 126 000 samples. Time resolved particle image sequences allow singular reverse flow events to be followed over several time steps whereas long records of nearly statistically independent samples provide a variety of single snapshots at a higher spatial resolution. The probability of occurrence lies in the order of 0.012–0.018% which matches predictions from direct numerical simulations (DNS). The typical size of the reverse flow bubble is about 30 wall units in length and 5 wall units in height which agrees well with similar observations made in existing DNS data.

On the basis of (i) particle image velocimetry data of a turbulent boundary layer with large field of view and good spatial resolution and (ii) a mathematical relation between the energy spectrum and specifically modeled flow structures, we show that the scalings of the streamwise energy spectrum E_{11}(k_{x}) in a wave-number range directly affected by the wall are determined by wall-attached eddies but are not given by the Townsend-Perry attached eddy model's prediction of these spectra, at least at the Reynolds numbers Re_{τ} considered here which are between 10^{3} and 10^{4}. Instead, we find E_{11}(k_{x})∼k_{x}^{-1-p} where p varies smoothly with distance to the wall from negative values in the buffer layer to positive values in the inertial layer. The exponent p characterizes the turbulence levels inside wall-attached streaky structures conditional on the length of these structures. A particular consequence is that the skin friction velocity is not sufficient to scale E_{11}(k_{x}) for wave numbers directly affected by the wall.

An experiment conducted in the framework of the EUHIT project and designed to characterize large scale structures in an adverse pressure gradient boundary layer flow is presented. Up to 16 sCMOS cameras were used in order to perform large scale turbulent boundary layer PIV measurements with a large field of view and appropriate spatial resolution. To access the span-wise / wall-normal signature of the structures as well, stereoscopic PIV measurements in span-wise/wall-normal planes were performed at specific stream-wise locations. To complement these large field of view measurements, long-range micro-PIV, time resolved near wall velocity profiles and film-based measurements were performed in order to determine the wall-shear stress and its fluctuations at some specific locations along the model., 50 pages

International audience; Two-point correlations of the wall fluctuating pressure and turbulent pressure and velocities in the flow field are computed in three dimensions using direct numerical simulation (DNS) databases. The mean pressure gradient in the flow has strong influence on these correlations. The DNS () in a converging/diverging channel with streamwise curvature near the lower wall is used to compute the statistics. The correlations in favourable pressure gradient and adverse pressure gradient are compared with the correlation in flat channel flow DNS (). The results show that these pressure–pressure and pressure–velocity correlations are not only sensitive to the local pressure gradient and wall curvature, but also to the pressure gradient history.

A direct numerical simulation of a turbulent channel flow with a lower curved wall is performed at Reynolds number Reτ ≈ 600. Low-speed streak structures are extracted from the turbulent flow field using methods known as skeletonization in image processing. Individual streaks in the wall-normal plane averaged in time and superimposed to the mean streamwise velocity profile are used as basic states for a linear stability analysis. Instability modes are computed at positions along the lower and upper wall and the instability onset is shown to coincide with the strong production peaks of turbulent kinetic energy near the maximum of pressure gradient on both the curved and the flat walls. The instability modes are spanwise-symmetric (varicose) for the adverse pressure gradient streak base flows with wall-normal inflection points, when the total average of the detected streaks is considered. The size and shape of the counter-rotating streamwise vortices associated with the instability modes are shown to be reminiscent of the coherent vortices emerging from the streak skeletons in the direct numerical simulation. Conditional averages of streaks have also been computed and the distance of the streak's centre from the wall is shown to be an essential parameter. For the upper-wall weak pressure gradient flow, spanwise-antisymmetric (sinuous) instability modes become unstable when sets of highest streaks are considered, whereas varicose modes dominate for the streaks closest to the wall.

Three-dimensional pressure–velocity correlations in a turbulent boundary layer have been investigated to understand the relationship between the pressure fluctuations and the coherent structures. Simultaneous measurements of the fluctuating pressure and velocity fields have been performed by the point pressure measurement technique and stereo PIV. The space–time three-dimensional structures of the pressure–velocity correlations, \(R_{pu}\), \(R_{pv}\) and \(R_{pw}\), are evaluated. The wall pressure fluctuations are closely coupled with large-scale coherent structures, i.e., large-scale sweep and ejection. For the pressure fluctuations in the field, the pressure–velocity correlations \(R_{pu}\) and \(R_{pw}\) exhibit a meaningful correlation in a region very extended in time in addition to the structures observed with the wall pressure. The Reynolds number effect is quantified from the data at \(Re_\theta \) \(=\) 7 300, 10 000, and 18 000, it is mostly evidenced on the size and intensity of the correlations. Such 3D structures of the pressure–velocity correlations can be consistent with the evidence of large-scale and very-large-scale motions reported in the literature.

LES results are presented for the flow over different bump profiles installed on the bottom wall of a channel. Three bump geometries are considered in order to investigate the effects of adverse pressure gradients and changes in curvature on the mean flow and Reynolds stresses. The first bump geometry corresponds to a profile for which DNS results are available at a Reynolds number \(Re_{\tau } =\) 617 based on the channel inlet friction velocity. The other two geometries are generated by modifying the rear portion of the initial profile to produce a longer APG region and promote smoother curvature changes as compared to the original profile. LES computations are performed at the same Reynolds numbers than previous DNS, which is also used to validate LES results in the original bump. Finally, RANS results are also presented for the three bump profiles. RANS computations are performed using a two-equation eddy-viscosity Shear Stress Transport (SST) model and one Reynolds stresses transport model.

The spectral model of Perry, Henbest & Chong (1986) predicts that the integral length-scale varies very slowly with distance to the wall in the intermediate layer. The only way for the integral length scale's variation to be more realistic while keeping with the Townsend-Perry attached eddy spectrum is to add a new wavenumber range to the model at wavenumbers smaller than that spectrum. This necessary addition can also account for the high Reynolds number outer peak of the turbulent kinetic energy in the intermediate layer. An analytic expression is obtained for this outer peak in agreement with extremely high Reynolds number data by Hultmark, Vallikivi, Bailey & Smits (2012, 2013). The finding of Dallas, Vassilicos & Hewitt (2009) that it is the eddy turnover time and not the mean flow gradient which scales with distance to the wall and skin friction velocity in the intermediate layer implies, when combined with Townsend's (1976) production-dissipation balance, that the mean flow gradient has an outer peak at the same location as the turbulent kinetic energy. This is seen in the data of Hultmark, Vallikivi, Bailey & Smits (2012, 2013). The same approach also predicts that the mean flow gradient has a logarithmic decay at distances to the wall larger than the position of the outer peak, a qualitative prediction which the aforementioned data also support., 14 pages, 9 figures

The study of turbulent flows calls for measurements with high resolution both in space and in time. We propose a new approach to reconstruct High-Temporal-High-Spatial resolution velocity fields by combining two sources of information that are well-resolved either in space or in time, the Low-Temporal-High-Spatial (LTHS) and the High-Temporal-Low-Spatial (HTLS) resolution measurements. In the framework of co-conception between sensing and data post-processing, this work extensively investigates a Bayesian reconstruction approach using a simulated database. A Bayesian fusion model is developed to solve the inverse problem of data reconstruction. The model uses a Maximum A Posteriori estimate, which yields the most probable field knowing the measurements. The DNS of a wall-bounded turbulent flow at moderate Reynolds number is used to validate and assess the performances of the present approach. Low resolution measurements are subsampled in time and space from the fully resolved data. Reconstructed velocities are compared to the reference DNS to estimate the reconstruction errors. The model is compared to other conventional methods such as Linear Stochastic Estimation and cubic spline interpolation. Results show the superior accuracy of the proposed method in all configurations. Further investigations of model performances on various range of scales demonstrate its robustness. Numerical experiments also permit to estimate the expected maximum information level corresponding to limitations of experimental instruments., Comment: 15 pages, 6 figures

The dynamical behavior of the flow separation induced by a wall-mounted two-dimensional bump is studied. The present investigation is based on an experimental approach that aims to provide further insight into the separate flow dynamic in such configuration. The main interest is devoted to the separation Reynolds number dependency. A general feature of separated flows dynamics is also addressed by statistical and structural information derived from the present experimental approach. Results are presented for turbulent water inflow for a moderate Reynolds-number range from 165 to 605 based on friction velocity and channel half-height (so-called Karman number). The ratio of the bump height h and the channel full height H is 0.335. The unsteady separation process and the associate instability mechanism are very sensitive to small perturbations. So, in order to preserve the flow physics, all of the experimental techniques employed in the present study are non-intrusive. An examination of the high resolved velocity fields showed that for a moderate Karman number, a separate area exists. Under this condition, a thin region of reverse flow was formed above the bump and a large-scale vortical activity, characterized by low-frequencies, are clearly observed. The reported results do not only yield the expected turbulent separation bubble dependencies. They also show that the well known coexisting instabilities process, which find their origin in laminar flow regime, persist for higher Karman numbers.Copyright © 2014 by ASME

The work presents comparative results between wall friction and pressure coefficient predictions from Large Eddy Simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) computations in channel flows with an adverse pressure gradient created by a 2-D bump. LES results are obtained using the semi-spectral code, MFLOPS3D, developed at Laboratoire de Mecanique de Lille, while RANS solutions are computed using a commercial code based on 2nd-order finite volume discretization with typical two-equation turbulence models and one seven-equation Reynolds stress transport model. Reynolds numbers range from Reτ = 617 to 2000, based on the friction velocity at the channel inlet. It is found that LES produces very consistent results when compared to DNS or other highly resolved LES. Two-equation and seven-equation RANS models are found to correctly predict friction coefficients in zero and favorable pressure gradient regions, but they fail in regions of adverse pressure gradients. The Reynolds stress transport model shows a better performance when compared to two-equation eddy-viscosity models, particularly in the higher Reynolds number cases. However, none of the RANS models is able to capture the full physics of turbulence related with adverse pressure gradients. The limitations of RANS models are observed both in separated and attached flow conditions at the rear portion of the bump. Such limitations seem to be related to the fact that these models do not correctly describe the evolution of the turbulent kinetic energy close to the walls in adverse pressure gradient regions.

A new dynamical subgrid model of 2D turbulence has been recently derived from the rapid distortion theory. This model is based on an hypothesis of nonlocality of the interaction of the scales of turbulence. The validity of this hypothesis was demonstrated by numerical simulation in 2D turbulence. It is supported here for real 3D turbulence at high Reynolds number by a spectral analysis of hot wire measurements in a turbulent boundary layer.

We develop a new numerical method which treats resolved and sub-grid scales as two different fluid components evolving according to their own dynamical equations. These two fluids are nonlinearly interacting and can be transformed one into another when their scale becomes comparable to the grid size. Equations describing the two-fluid dynamics were rigorously derived from Euler equations [B. Dubrulle, S. Nazarenko, Physica D 110 (1997) 123‐138] and they do not involve any adjustable parameters. The main assumption of such a derivation is that the large-scale vortices are so strong that they advect the sub-grid scales as a passive scalar, and the interactions of small scales with small and intermediate scales can be neglected. As a test for our numerical method, we performed numerical simulations of 2D turbulence with a spectral gap, and we found a good agreement with analytical results obtained for this case by Nazarenko and Laval [Non-local 2D turbulence and passive scalars in Batchelor’s regime, J. Fluid Mech., in press]. We used the two-fluid method to study three typical problems in 2D dynamics of incompressible fluids: decaying turbulence, vortex merger and forced turbulence. The two-fluid simulations performed on at 128 2 and 256 2 resolution were compared with pseudo-spectral simulations using hyperviscosity performed at the same and at much higher resolution. This comparison shows that performance of the two-fluid method is much better than one of the pseudo-spectral method at the same resolution and comparable computational cost. The most significant improvement is observed in modeling of the small-scale component, so that effective inertial interval increases by about two decades compared to the high-resolution pseudo-spectral method. Using the two-fluid method, we demonstrated that the k 3 tail always exists for the energy spectrum, although its amplitude is slowly decreasing in decaying turbulence. © 2000 Elsevier Science B.V. All rights reserved.

We use numerical simulations to prove that the dynamics of the small-scale vorticity in twodimensional incompressible fluids is nearly passive and that the feedback of the small scales onto the large-scale dynamics is important only for the part of the large-scale range which is adjacent or close to the small-scale range. The dynamics of high Reynolds number turbulent flows usually couples a broad range of scales, from the energy injection scale to the dissipative scale. This range is too wide to be fully resolved by direct numerical simulations of the Navier-Stokes equations. This motivated a number of attempts to describe separately the behavior of the “energy containing” scales (corresponding to either the large scales or the scales of the mean motions) via modeling of the action of the “dissipative” small or random scales of motions. In most cases, the modeling is empirical and based on hand waving or dimensional arguments about the small-scale dynamics. There are a few attempts to derive a model from asymptotic expansions based on the NavierStokes equations. Traditionally, these models are based on two different expansion parameters, based on the ratio of the typical length and time t of the small scale motions, and the typical length L and time scale T of the energy containing large-scale motions. This results in two parameters: e L and h tT . For example, the

We study the probability distribution functions and scaling properties of truncated Levy processes with sharp cut-offs. We find that they display features analog to those observed in some 2D numerical simulations of turbulence.

The work presents comparative results between wall friction coe cient predictions from Large Eddy Simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) computations in channel ows with an adverse pressure gradient created by a two-dimensional bump. LES results are obtained using the semi-spectral code, MFLOPS3D, developed at Laboratoire de M ecanique de Lille (LML), while RANS solutions are computed using a commercial code based on 2nd-order nite volume discretization with typical two-equation turbulence models and one seven-equation Reynolds stresses transport model. Computations are performed in two bump pro les installed in a channel. Reynolds numbers range from Re = 617 to 950 based on the friction velocity at the channel inlet. It is found that LES produces very consistent results when compared to DNS or other highly resolved LES. On the other hand, RANS models are found to predict an incorrect evolution of the friction coe cient in regions of adverse pressure gradient, even if separation or re-attachment locations are correctly predicted. This limitation of RANS models is observed both in separated and attached ow situations and it seems to be related to the fact that these models do not correctly describe the evolution of the turbulent kinetic energy close to the walls in adverse pressure gradient regions.

We hypothesize that far enough downstream the mean velocity profile in any non − separating adverse pressure gradient turbulent bounday layer will become inflectional. While this evolution is underway a universal scaling for the outer flow is impossible. Once the profile is fully-developed, however, there is significant support for the Castillo/George [2, 4] theory.

International audience; A direct numerical simulation (DNS) of a turbulent channel flow with a lower curved wall is performed at Reynolds number $Re_\tau \simeq 617$ at inlet. This adverse-pressure gradient turbulent flow is characterized by strong peaks of turbulent kinetic energy at both walls, as a consequence of the breakdown of more organized flow structures. To elucidate the underlying instability scenario, low-speed streak structures are extracted from the turbulent flow field and base flows formed with conditional streak averages, superimposing the mean streamwise velocity profile, are used for linear stability analyzes. The size and shape of the counter-rotating streamwise vortices associated with the instability modes are shown to be reminiscent of the coherent vortices emerging from the streak skeletons in the direct numerical simulation. The distance of the streak's centre from the wall is used as a criterion for the conditional averages and the corresponding streak base flows are characterised by more or less pronounced contours of inflection points in the averaging windows normal to the wall. It is shown, that the strength of instability of the streak base flows can be inferred from a simplified one-dimensional stability analysis, using local inflectional profiles at different spanwise locations.

A direct numerical simulation of a turbulent channel flow with a lower curved wall is performed at Reynolds number Reτ ≈ 600. Low-speed streak structures are extracted from the turbulent flow field and base flows formed with conditional streaks averages, superimposing the mean streamwise velocity profile, are used for linear stability analyses. The instability in the presence of a strong pressure gradient at the lower wall is shown to be of varicose type, whereas at the upper wall (with weak pressure gradient) varicose and sinuous unstable modes can coexist. The onset of the dominant instability mechanism of varicose type is shown to coincide with the strong production peaks of turbulent kinetic energy near the maximum of pressure gradient on both the curved and the flat walls. The size and shape of the counter-rotating streamwise vortices associated with the instability modes are shown to be reminiscent of the coherent vortices emerging from the streak skeletons in the direct numerical simulation.

Two Direct Numerical Simulations (DNS) of a converging–diverging channel flows were performed at Re τ = 395 and Re τ =617. The present DNS of adverse pressure gradient flow were designed within the WALLTURB project to meet two main objectives. The first one was to gather three-dimensional fully resolved data in order to investigate statistics and coherent structures of turbulence under strong pressure gradient with and without curvature. The second one was to have a reference for the evaluation of RANS and LES models. The flow slightly separates at the lower curved wall and is at the onset of separation at the opposite flat wall. Intense vortices are generated at the location of the minimum friction velocity even without averaged recirculation. The full budget of the Reynolds stresses were computed along the channel at both walls. The occurrence of a well documented secondary peak of velocity fluctuations due to adverse pressure gradient is shown to be the consequence of a very strong production peak.

Only limited regions of turbulent/unsteady flows can generally be simulated. The physical character of the solution thus depends on the reliability of the boundary conditions. Various methods (synthetic eddies, recycling/rescaling procedures) have already been proposed for inflow conditions of turbulent boundary layers, yielding various degrees of efficiency. But the prescription of realistic conditions at boundaries parallel to the wall is still an open question.

Adverse pressure gradient turbulent flows are of prime importance for aeronautics as they are characteristic of the suction side flow along an airfoil at any positive angle of attack. These flows have been known for a long time to pose modelling problems. The turbulence behaviour departs significantly from the standard near wall turbulence (as observed in flat plate boundary layers and channels). In diffusers, as well as in boundary layers, the flow separates from the wall as soon as the adverse pressure gradient is strong enough. In the present contribution, a few selected data from the literature are reviewed and compared together and with a recent DNS of converging–diverging channel flow performed in the frame of the WALLTURB project. This simulation provides data on APG near wall flow, both with and without curvature. The analysis of these data indicates that an instability is developing inside the turbulent near wall flow in both cases. The comparison of turbulent statistics with the data from the literature indicates that this phenomenon is fairly general in APG near wall flows.

The LES-Langevin model was studied on turbulent channel flows. The approach is based on the dynamics of the subgrid velocity scales previously studied in the frame of Rapid Distortion Theory. The subgrid stress tensor is modeled through a combination of a turbulent force and an eddy-viscosity. The turbulent force equation is derived from the subgrid scales velocity dynamics within the hypotheses of the Rapid Distortion Theory. The complex nonlinear terms containing the subgrid scale pressure were modeled by a stochastic forcing. The well-known eddy-viscosity closure was chosen to improve the resolved scales dissipation due to subgrid Reynolds stress. The advantage of the model is that the dynamics of turbulent force is prescribed by a dynamical equation derived from the Navier–Stokes equations. This allows a possibility to include all the important physical effects of the subgrid scales like the backward subgrid scale energy transfer. The direct modeling of the gradient of the subgrid scale tensor allows a reduction of the computational time compared to direct numerical simulation, which is the global objective of LES. The work demonstrates a need for further investigation on the equation of the turbulent force in order to better estimate the subgrid scale action.

A Direct Numerical Simulation of turbulent flow subjected to an adverse pressure gradient (APG) was performed. As already noticed by many authors in such configurations, a second outer peak of turbulent kinetic energy is observed in the region of APG. In the present configuration, this peak is due to the production of intense vortices which are shown to be related to the instability of low speed streaks.

International audience; We use proper orthogonal decomposition (POD) to estimate the flow in the near-wall region based on information from the outer buffer layer. Our goal is to assess how the flow structures in the inner wall region are connected to those further away from the wall, and to investigate the nature of the coupling between the inner and the outer region in the POD framework. Reconstructions are carried out for numerical simulations of a plane channel flow at two different Reynolds numbers. We show that elongated structures with a spanwise wavelength smaller than a critical value tend to be concentrated in the inner layer. The critical wavelength is shown to scale with the inner layer height, and interactions between the inner and the outer layer appear to take place predominantly over a self-similar, height-dependent, range of wavenumbers, in agreement with Townsend's attached eddy hypothesis. The reconstructed field appears to capture an adequate energy content and to remain correlated with the real field even close to the wall, which reflects the persistence of energetic structures over the extent of the buffer layer.

International audience; The flow in a converging-diverging channel at Reτ = 180 is studied by Direct Numerical and Large Eddy Simulations. Continuous and pulsed jets are applied normally to the wall through a spanwise slot to delay the separation. The influence of the position is first analysed and it is shown that the control efficiency is closely linked to the location of the actuation within the channel. A parametric study on both the intensity and pulsating frequency for the "optimal" position shows that the separation can be drastically reduced and even vanishes with a proper choice of parameters. It is additionally reported that pulsed jets yield better results than continuous jets at an equivalent mass-flux. Moreover, low frequencies are shown to be more efficient than high frequencies. Aphysical analysis finally demonstrates that the efficiency of the low frequency pulsed jets is mainly due to the creation of spanwise structures, that does not occur in other cases.

We present a reconstruction method to estimate the instantaneous flow close to the wall of a turbulent channel. The motivation for the procedure is to come up with suitable wall models for large-eddy simulations. The idea is to apply the Proper Orthogonal Decomposition to the velocity field u over a zone extending over the lower wall region to be modelled \( \Omega _1 :0 \le y + \le y_1 \) and the LES numerical domain, \( \Omega _2 : y_1 \le y + \le y_2 \). The reconstruction method is a straightforward extension of the procedure described in Podvin et al. [Podvin et al., Journal of Fluids Engineering 2006]. The POD modes an(t) are estimated by solving a linear system where the right-hand side contains information about the flow in the upper region, and the operator is the inner product of the empirical eigenfunctions restricted to the lower region.

An experiment has been performed in a large wind tunnel with the objectives to record 2D3C velocity fields of a fully developed turbulent boundary layer along a flat plate by means of stereoscopic PIV (SPIV) and to study the characteristics of this turbulence. The present study starts from determining the suitable method to process the database that was recorded with the stereoscopic PIV system. It suggests that the Soloff method with 3 calibration planes and integer shift is the best choice. Then, by using this method the analysis of the mean streamwise velocity, velocity fluctuations, Reynolds shear stress, spectrum, probability density function (PDF) as well as skewness and flatness, was performed and compared with values from hot-wire anemometry (HWA) and direct numerical simulation (DNS). The comparison indicates that SPIV is a well-qualified method to investigate near-wall turbulence.

International audience; Streaks play a major role in the process of turbulent generation. Numerous studies have been performed to characterize them, most of which used only single point measurements and only a few characteristics were studied. To investigate the streaks in more detail, a stereoscopic particle image velocimetry (SPIV) experiment was conducted to record 2D3C velocity fields in ten planes parallel to the wall from y + = 14.5 to y + = 48 at Reynolds number Re θ = 7,800 in a fully developed turbulent boundary layer along a flat plate. This study develops a method based on pattern recognition to detect streaks from velocity fields obtained by SPIV and characteristizes them in depth. The results are in good agreement with the previous studies and expand significantly the information about the characteristics of the streaks

A direct numerical simulation (DNS) of a channel flow with one curved surface was performed at moderate Reynolds number (Re_tau = 395 at the inlet). The adverse pressure gradient was obtained by a wall curvature through a mathematical mapping from physical coordinates to Cartesian ones. The code, using spectral spanwise and normal discretization, combines the advantage of a good accuracy with a fast integration procedure compared to standard numerical procedures for complex geometries. The turbulent flow slightly separates on the profile at the lower curved wall and is at the onset of separation at the opposite flat wall. The thin separation bubble is characterized with a reversal flow fraction. Intense vortices are generated near the separation line on the lower wall but also at the upper wall. Turbulent normal stresses and kinetic energy budget are investigated along the channel., Comment: 23 pages, submitted to Journal of Turbulence

We report successive bifurcations in direct numerical simulations (DNSs) of a Taylor–Green flow, in both a hydro- and a magneto-hydrodynamic case. Hydrodynamic bifurcations occur in between different metastable states with different dynamo action, and are triggered by the numerical noise. The various states encountered range from stationary to chaotic or turbulent through possible oscillatory states. The corresponding sequence of bifurcations is reminiscent of the sequence obtained in the von Karman (VK) flow, at aspect ratio Γ=2 (Nore et al 2003 J. Fluid Mech. 477 51). We then use kinematic simulations to compute the dynamo thresholds of the different metastable states. A more detailed study of the turbulent state reveals the existence of two windows of dynamo action. Stochastic numerical simulations are then used to mimic the influence of turbulence on the dynamo threshold of the turbulent state. We show that the dynamo threshold is increased (respectively decreased) by the presence of large scale (resp. small scale) turbulent velocity fluctuations. Finally, DNSs of the magneto-hydrodynamic equations are used to explore the linear and nonlinear stage of the dynamo instability. In the linear stage, we show that the magnetic field favours the bifurcation from the basic state directly towards the turbulent or chaotic stable state. The magnetic field can also temporarily stabilize a metastable state, resulting in cycles of dynamo action, with different Lyapunov exponents. The critical magnetic Reynolds number for dynamo action is found to increase strongly with the Reynolds number. Finally, we provide a preliminary study of the saturation regime above the dynamo threshold. At large magnetic Prandtl number, we have observed two main types of saturations, in agreement with an analytical prediction of Leprovost and Dubrulle (2005 Eur. Phys. J. B 44 395): (i) intermittent dynamo, with vanishing most probable value of the magnetic energy; (ii) dynamo with non vanishing mean value of the magnetic energy. We describe a sequence of bifurcation of the dynamo at low Reynolds number and at increasing magnetic Prandtl number, where the dynamo switches from stationary mode to chaotic modes in a complex manner, involving intermittency in a way reminiscent to what is observed in dynamical systems with low number of degrees of freedom.

We use direct and stochastic numerical simulations of the magnetohydrodynamic equations to explore the influence of turbulence on the dynamo threshold. In the spirit of the Kraichnan-Kazantsev model, we model the turbulence by a noise, with given amplitude, injection scale and correlation time. The addition of a stochastic noise to the mean velocity significantly alters the dynamo threshold. When the noise is at small (resp. large) scale, the dynamo threshold is decreased (resp. increased). For a large scale noise, a finite correlation time reinforces this effect.